Showing 1–50 of 311 results for author: Xie, X C

Revealing Hidden Unconventional Pairing through Nonreciprocal Transport

Authors: Wen-Bo Dai, Ming Gong, Xianxin Wu, Chui-Zhen Chen, X. C. Xie

Abstract: Identifying the pairing symmetry of Cooper pairs is a fundamental step toward understanding the microscopic mechanisms of unconventional superconductors. However, experimental identification remains a formidable challenge, particularly when unconventional pairing is obscured by a dominant $s$-wave component that masks its spectroscopic signatures. Here, we develop a symmetry-resolved framework to… ▽ More Identifying the pairing symmetry of Cooper pairs is a fundamental step toward understanding the microscopic mechanisms of unconventional superconductors. However, experimental identification remains a formidable challenge, particularly when unconventional pairing is obscured by a dominant $s$-wave component that masks its spectroscopic signatures. Here, we develop a symmetry-resolved framework to identify superconducting pairing symmetry through nonreciprocal conductance upon exchanging source and detector terminals in multiterminal devices. We show that nonreciprocal transport arises from symmetry-breaking components of the superconducting order parameter and exhibits a characteristic angular dependence that encodes the momentum-space structure of the pairing gap. In particular, time-reversal-breaking singlet pairing induces nonreciprocal charge transport, while spin-triplet pairing generates nonreciprocal spin responses, providing distinct transport fingerprints of the underlying order. We demonstrate this mechanism using representative models of iron-based and noncentrosymmetric superconductors and outline experimental protocols for multiterminal measurements. Our results advance the theoretical understanding of nonreciprocal transport in superconductors, and establish it as a symmetry-selective probe for identifying hidden unconventional pairing in a wide range of superconducting materials. △ Less

Submitted 10 August, 2026; originally announced August 2026.

Comments: 19 pages, 11 figures, including Supplementary Material

Logarithmic Aging Diffusion from a Multiplicative Event Clock: Rare Event Statistics, Ultraslow Transport, and Ensemble-Time Inequivalence

Authors: Chunyan Li, Zheng Li, Yueyan Li, Haiwen Liu, X. C. Xie

Abstract: Logarithmic time dependences occur in many aging materials, but neither a $\ln t$ relaxation law nor a $1/t$ event rate uniquely identifies the underlying stochastic mechanism. We examine a specific log-aging process defined by iterating the age-conditioned forward-recurrence law after every event. This rule makes the event times multiplicative: the logarithmic ratios $U_n=\ln(T_{n+1}/T_n)$ are in… ▽ More Logarithmic time dependences occur in many aging materials, but neither a $\ln t$ relaxation law nor a $1/t$ event rate uniquely identifies the underlying stochastic mechanism. We examine a specific log-aging process defined by iterating the age-conditioned forward-recurrence law after every event. This rule makes the event times multiplicative: the logarithmic ratios $U_n=\ln(T_{n+1}/T_n)$ are independent and identically distributed with an explicit non-exponential density. Consequently, both the mean and the variance of the event count grow linearly with $\ln(t/t_0)$, while the density of the $n$th event time has a log-normal central sector and a fixed-$n$ algebraic far tail. These clock statistics generate logarithmic drift and spreading, an Einstein relation under local detailed balance, and ultraslow transit and target-survival laws. They also separate trajectory reproducibility from ensemble--time equivalence: the relative scatter of the time-averaged mean-square displacement decays as $1/\ln(T/t_0)$, although its mean does not converge to the ensemble lag MSD. We distinguish the exact event-level construction from its diffusion-limit generalized Fokker--Planck and random-clock subordination representations, and from a generalized-Langevin closure that can match selected responses and covariances but need not reproduce event counts or rare-duration statistics. The proposed clock is therefore tested not by a single logarithmic curve, but by the joint, no-refitting consistency of multiplier, count, transport, first-passage, and finite-window observables. △ Less

Submitted 28 July, 2026; originally announced July 2026.

Comments: 86 pages, 12 figures

Superconducting triode effect in a quantum-dot Josephson junction with a biased top gate

Authors: Yu-Hang Li, Xiaan Du, Hua Jiang, X. C. Xie

Abstract: Non-reciprocal supercurrents enable non-dissipative rectification, holding great promise for superconducting electronics. Conventionally, this non-reciprocity, termed the superconducting diode effect, requires the simultaneous breaking of time-reversal and parity symmetries. Here, we propose a superconducting triode effect in an asymmetric quantum-dot Josephson junction coupled to an additional me… ▽ More Non-reciprocal supercurrents enable non-dissipative rectification, holding great promise for superconducting electronics. Conventionally, this non-reciprocity, termed the superconducting diode effect, requires the simultaneous breaking of time-reversal and parity symmetries. Here, we propose a superconducting triode effect in an asymmetric quantum-dot Josephson junction coupled to an additional metallic top gate, which breaks the parity symmetry while explicitly preserving time-reversal symmetry. We demonstrate that the supercurrent across this junction exhibits a strong non-reciprocal effect that can be continuously manipulated via the top gate to achieve an ideal unidirectional supercurrent, thus manifesting a superconducting triode effect. Furthermore, under radio-frequency radiation, this junction exhibits highly asymmetric Shapiro steps, realizing fully quantized supercurrent rectification. Our work not only provides an alternative physical mechanism for the superconducting diode effect observed in Josephson junctions with explicit time-reversal symmetry, but also introduces a new tuning knob to manipulate supercurrent non-reciprocity. △ Less

Submitted 4 June, 2026; originally announced June 2026.

Anisotropic Surface Spin Waves as Signature of A-type Altermagnets

Authors: Zhoujian Sun, Yiyuan Chen, Tao Yu, Hai-Zhou Lu, X. C. Xie

Abstract: Altermagnets have attracted intense interest because they have the advantages of both ferromagnets and antiferromagnets. However, their experimental identification remains challenging, in particular for the A-type altermagnets that account for a large group of material candidates. Here, we discover a kind of anisotropic surface spin waves in A-type altermagnets, which is absent in ferromagnets and… ▽ More Altermagnets have attracted intense interest because they have the advantages of both ferromagnets and antiferromagnets. However, their experimental identification remains challenging, in particular for the A-type altermagnets that account for a large group of material candidates. Here, we discover a kind of anisotropic surface spin waves in A-type altermagnets, which is absent in ferromagnets and conventional antiferromagnets. The anisotropic surface spin waves arise directly from the nature of altermagnets, i.e., the spin-opposite sublattices cannot be related by translation or inversion, which breaks the combined spatial-inversion and time-reversal symmetry, leading to the anisotropic surface spin waves with two properties, the chirality-dependent top-bottom positions and chiral split constant frequency contours. We further show that these two properties can be measured experimentally from the stray field and by resonance absorption spectrum, respectively. Our results provide a signature for detecting altermagnets and will inspire spin-based logic and information-storage devices. △ Less

Submitted 14 May, 2026; originally announced May 2026.

3D Quantum Hall Effect with Two Distinct Plateaus

Authors: Jun-Hong Li, Yi-Yuan Chen, Peng-Lu Zhao, Hai-Zhou Lu, X. C. Xie

Abstract: The recent discovery of the 3D quantum Hall effect in $\mathrm{HfTe_5}$ has also revealed puzzling signatures of possible 3D fractionalization. Beyond the first plateau associated with the lowest Landau band, Hall conductivity exhibits a second plateau with a value of about $3/5$ of the first, accompanied by a suppressed longitudinal resistivity. Here, we attribute this second plateau to an insula… ▽ More The recent discovery of the 3D quantum Hall effect in $\mathrm{HfTe_5}$ has also revealed puzzling signatures of possible 3D fractionalization. Beyond the first plateau associated with the lowest Landau band, Hall conductivity exhibits a second plateau with a value of about $3/5$ of the first, accompanied by a suppressed longitudinal resistivity. Here, we attribute this second plateau to an insulating ground state arising from spin-density-wave order. We show that a magnetic-field-driven Lifshitz transition causes the spin-down holelike zeroth Landau band to cross the Fermi energy and that the resulting nesting between the lowest spin-up and spin-down Landau bands induces a spin-density wave. We calculate the Hall and longitudinal resistivity and reproduce the experimental behaviors. Our renormalization-group analysis further supports this insulating ground state. Our work reveals that the tunability of Landau bands along the magnetic-field direction endows the 3D quantum Hall effect with a broader phenomenology than its 2D counterpart and merits further exploration. △ Less

Submitted 3 May, 2026; originally announced May 2026.

Comments: 7 pages, 4 figures

Electron Dynamics Reconstruction and Nontrivial Transport by Acoustic Waves

Authors: Zi-Qian Zhou, Zhi-Fan Zhang, Cong Xiao, Hua Jiang, X. C. Xie

Abstract: Surface acoustic waves (SAWs) become a popular driving source in modern condensed matter physics, but most existing theories simplify them as electric fields and ignore the non-uniform Brillouin zone folding effect. We develop a semiclassical framework and reconstruct the electron dynamics by treating SAW as a quasi-periodic potential modulating electronic momentum distribution. This framework nat… ▽ More Surface acoustic waves (SAWs) become a popular driving source in modern condensed matter physics, but most existing theories simplify them as electric fields and ignore the non-uniform Brillouin zone folding effect. We develop a semiclassical framework and reconstruct the electron dynamics by treating SAW as a quasi-periodic potential modulating electronic momentum distribution. This framework naturally explains the experimentally observed DC drag current and predicts acousto-electric Hall effect. The theory further reveals various SAW-driven transport phenomena, emerging anomalous Hall, thermal Hall, and Nernst effects within time-reversal symmetric systems. Illustrated in bilayer graphene and $\mathrm{MX_2}$ (M = Mo, W; X = S, Se, Te), the angular-dependent acousto-electric Hall effect provides an experimental probe for Berry curvature distribution. △ Less

Submitted 25 March, 2026; originally announced March 2026.

Comments: 8 pages, 2 figures

Nonperturbative Magnetic Orbital Hall Effect in Altermagnets

Authors: Xukun Feng, Jin Cao, Lay Kee Ang, Shengyuan A. Yang, Cong Xiao, X. C. Xie

Abstract: Recent studies on altermagnets have focused considerable attention on nonrelativistic effects that persist in the absence of spin-orbit coupling (SOC). As a result, the relative importance of various phenomena in altermagnets has commonly been judged by their dependence on SOC. Here, we challenge this common wisdom by uncovering the magnetic orbital Hall effect, which is nonperturbative in SOC str… ▽ More Recent studies on altermagnets have focused considerable attention on nonrelativistic effects that persist in the absence of spin-orbit coupling (SOC). As a result, the relative importance of various phenomena in altermagnets has commonly been judged by their dependence on SOC. Here, we challenge this common wisdom by uncovering the magnetic orbital Hall effect, which is nonperturbative in SOC strength. We establish the symmetry properties of this effect, demonstrating that it is strictly forbidden in conventional collinear antiferromagnets yet universally allowed in all ten spin-Laue classes of collinear altermagnets. Counterintuitively, although SOC-induced, it reaches giant magnitudes in altermagnets-comparable to or even exceeding the nonrelativistic spin Hall effect. Moreover, altermagnetic symmetry enables unconventional collinear-polarized orbital currents, allowing field-free manipulation of perpendicular magnetization. Our first-principles calculations predict strong room-temperature responses in the experimentally established altermagnets CrSb and FeSb2. These findings reveal the previously overlooked potential of altermagnetic orbitronics and broaden the horizons for altermagnets in high-performance magnetic memory applications. △ Less

Submitted 21 May, 2026; v1 submitted 22 February, 2026; originally announced February 2026.

Theory of Integer Quantum Hall Effect in Irrational Magnetic Field

Authors: Zhao-Wen Miao, Chen Zhao, Jin-Hua Gao, X. C. Xie

Abstract: The conventional theory of the integer quantum Hall effect (IQHE) fails for irrational magnetic fields owing to the breakdown of magnetic translational symmetry. Here, based on the recently proposed incommensurate energy band (IEB) theory, we present a universal IQHE theory that does not rely on magnetic translation symmetry and is applicable to both rational and irrational magnetic fluxes. Using… ▽ More The conventional theory of the integer quantum Hall effect (IQHE) fails for irrational magnetic fields owing to the breakdown of magnetic translational symmetry. Here, based on the recently proposed incommensurate energy band (IEB) theory, we present a universal IQHE theory that does not rely on magnetic translation symmetry and is applicable to both rational and irrational magnetic fluxes. Using the square lattice as a paradigmatic example, we first show that the IEB framework provides a superior description of its energy spectrum in a magnetic field, as it explicitly reveals the momentum-space distribution of eigenstates. Key to our IQHE theory is that each gap in the IEB spectrum is intrinsically labeled by an integer pair (m,g), defined by the corresponding Bragg planes. When the Fermi energy lies within such a gap, the occupied electron states $N_{\text{occ}}$ is determined by the k-space volume enclosed by these Bragg planes, leading to the fundamental relation $N_{\text{occ}}/N_0 = m(φ/φ_0) + g$. Through Středa formula, this leads directly to the quantized Hall conductance $σ_{xy} = m e^2/h$ under arbitrary magnetic fields. Our work resolves the long-standing problem of IQHE under irrational flux, and establishes a new paradigm for IQHE. △ Less

Submitted 7 February, 2026; originally announced February 2026.

Comments: 6 pages, 3 figures

Quantum Christoffel Nonlinear Magnetization

Authors: Xiao-Bin Qiang, Xiaoxiong Liu, Hai-Zhou Lu, X. C. Xie

Abstract: The Christoffel symbol is an essential quantity in Einstein's general theory of relativity. We discover that an electric field can induce a nonlinear magnetization in quantum materials, described by a Christoffel symbol defined in the Hilbert space of quantum states (quantum Christoffel symbol). Quite different from the previous scenarios, this orbital magnetization does not need spin-orbit coupli… ▽ More The Christoffel symbol is an essential quantity in Einstein's general theory of relativity. We discover that an electric field can induce a nonlinear magnetization in quantum materials, described by a Christoffel symbol defined in the Hilbert space of quantum states (quantum Christoffel symbol). Quite different from the previous scenarios, this orbital magnetization does not need spin-orbit coupling and inversion symmetry breaking. Through symmetry analysis and first-principles calculations, we identify a number of point groups and 2D material candidates (e.g., BiF$_3$, ZnI$_2$, and Ru$_4$Se$_5$) that host this quantum Christoffel nonlinear magnetization. More importantly, this nonlinear magnetization allows the quantum Christoffel symbol to be probed by optical techniques such as magneto-optical Kerr spectroscopy or transport measurements such as tunneling magneto-resistance. This quantum Christoffel nonlinear magnetization gives a paradigm of how geometry dictates physics. △ Less

Submitted 3 February, 2026; originally announced February 2026.

Comments: 9 pages, 3 figures

Journal ref: Phys. Rev. Lett. 136, 056302 (2026)

Long-distance spin transport in frustrated hyperkagome magnet Gd3Ga5O12

Authors: Di Chen, Bingcheng Luo, Lei Xu, Zian Xia, Linhao Jia, Shaomian Qi, Congkuan Tian, Kangyao Chen, Hang Cui, Guangyi Chen, Shili Yan, Miaoling Huang, Jian Cui, Ya Feng, Zhentao Wang, Jiang Xiao, Jianhua Zhang, Ryuichi Shindou, X. C. Xie, Jian-Hao Chen

Abstract: Transport of spin angular momentum over large distance has been a long sought-after goal in the field of spintronics. While the majority of the research effort has been devoted to the spin transport properties of magnetically ordered materials, spin transport in magnetically frustrated materials has received little attention. Here, we report an anomalous state in frustrated hyperkagome magnetic in… ▽ More Transport of spin angular momentum over large distance has been a long sought-after goal in the field of spintronics. While the majority of the research effort has been devoted to the spin transport properties of magnetically ordered materials, spin transport in magnetically frustrated materials has received little attention. Here, we report an anomalous state in frustrated hyperkagome magnetic insulator Gd3Ga5O12, where spin angular momenta can be transported over a long distance of 480 μm, far exceeding the transport distance of any diffusive spin current in magnetically ordered materials, to the best of our knowledge. Monte Carlo simulations reveal significant spin fluctuations, spin-spin correlations and an absence of conventional magnons in such anomalous state; while the response of the anomalous state to perturbation is found to be akin to an overdamped forced oscillator. We find close relation of such state to the correlated ``director'' state in the material. Our result provides an effective electrical technique to characterize spin-spin correlations and frustrations; it also unveils the potential of frustrated magnets as powerful channel materials for spin transport. △ Less

Submitted 30 January, 2026; originally announced January 2026.

Comments: 24 pages, 5 figures

Theory of Correlated Hofstadter Spectrum in Magic-Angle Graphene

Authors: Chen Zhao, Zhaowen Miao, Zhen Ma, Ying-Hai Wu, Ming Lu, Jin-Hua Gao, X. C. Xie

Abstract: The magnetic-field-induced correlated Chern insulator (CCI) states in magic-angle twisted bilayer graphene (MATBG) have been intensively studied in experiments, but a simple and clear understanding of their origin is still lacking. Here, we propose a unified theoretical framework for the CCI states in MATBG that successfully explains most experimental observations. The key insight of our theory is… ▽ More The magnetic-field-induced correlated Chern insulator (CCI) states in magic-angle twisted bilayer graphene (MATBG) have been intensively studied in experiments, but a simple and clear understanding of their origin is still lacking. Here, we propose a unified theoretical framework for the CCI states in MATBG that successfully explains most experimental observations. The key insight of our theory is that, due to the very narrow bandwidth of MATBG, correlation-enhanced valley and spin Zeeman terms are critical for shaping the intricate Hofstadter spectrum, resulting in an interwoven, flavor-resolved (spin and valley) Hofstadter spectrum that can well describe the observed CCI states. Crucially, due to the Zeeman effect, the crossings between these flavor-polarized Hofstadter spectra are magnetic-field-dependent, causing certain CCI states to emerge only above a critical field. This is the main mechanism underlying the critical field phenomenon of the CCI states observed in experiments. Our theory provides a clear and unified physical picture for the correlated Hofstadter spectrum in MATBG. △ Less

Submitted 19 January, 2026; originally announced January 2026.

Quantum Geometric Origin of Orbital Magnetization

Authors: Xiao-Bin Qiang, Tianyu Liu, Hai-Zhou Lu, X. C. Xie

Abstract: The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the understanding of various electronic phenomena, its potential for illuminating magnetic phenomena has remained less explored. In this Perspective, we highlight… ▽ More The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the understanding of various electronic phenomena, its potential for illuminating magnetic phenomena has remained less explored. In this Perspective, we highlight how quantum geometry paves a new way for understanding magnetization within a single-particle framework. We first elucidate the geometric origin of equilibrium magnetization in the modern theory of magnetization, then discuss the role of quantum geometry in kinetic magnetization, and finally outline promising future directions at the frontier of quantum geometric magnetization. △ Less

Submitted 7 January, 2026; originally announced January 2026.

Comments: 6 pages, 2 figures

Journal ref: Appl. Phys. Lett. 128, 010501 (2026)

Fractional High-Chern Insulator in Twisted Rhombohedral Graphene

Authors: Zexu Li, Wenxuan Wang, Fajie Wang, Zaizhe Zhang, Qiu Yang, Kenji Watanabe, Takashi Taniguchi, X. C. Xie, Jie Wang, Kaihui Liu, Zhida Song, Xiaobo Lu

Abstract: The realization of fractional Chern insulators opens up the possibility of exploring fractionally charged excitations and anyonic statistics in the absence of a magnetic field. A central question is whether lattice-based systems can give rise to radically new states, distinct from those observed in traditional fractional quantum Hall systems. In this work, we investigate a new type of moiré flat b… ▽ More The realization of fractional Chern insulators opens up the possibility of exploring fractionally charged excitations and anyonic statistics in the absence of a magnetic field. A central question is whether lattice-based systems can give rise to radically new states, distinct from those observed in traditional fractional quantum Hall systems. In this work, we investigate a new type of moiré flat band system composed of Bernal bilayer graphene and rhombohedral tetralayer graphene. We discover an unprecedented richness of quantum anomalous Hall insulators with Chern numbers from C = 1 to C = 7 at v = 1 and around v = 3. Remarkably, we observe an exotic fractional Chern insulator with C = 7/3 around v = 2/3 which is beyond all known fractional Chern insulators described by either the Jain sequence or current high Chern theory. Our work expands the understanding of fractionally charged excitations beyond the Landau level basis and offers a new moire platform for exploring anyons. △ Less

Submitted 2 June, 2026; v1 submitted 25 December, 2025; originally announced December 2025.

Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study

Authors: Shengdu Chai, Chen Lin, Xinyang Dong, Yuqiang Li, Wanli Ouyang, Lei Wang, X. C. Xie

Abstract: The crystal structure of high-pressure solid hydrogen remains a fundamental open problem. Although the research frontier has mostly shifted toward ultra-high pressure phases above 400 GPa, we show that even the broken symmetry phase observed around 130~GPa requires revisiting due to its intricate coupling of electronic and nuclear degrees of freedom. Here, we develop a first principle quantum Mont… ▽ More The crystal structure of high-pressure solid hydrogen remains a fundamental open problem. Although the research frontier has mostly shifted toward ultra-high pressure phases above 400 GPa, we show that even the broken symmetry phase observed around 130~GPa requires revisiting due to its intricate coupling of electronic and nuclear degrees of freedom. Here, we develop a first principle quantum Monte Carlo framework based on a deep neural network wave function that treats both electrons and nuclei quantum mechanically within the constant pressure ensemble. Our calculations reveal an unreported ground-state structure candidate for the broken symmetry phase with $Cmcm$ space group symmetry, and we test its stability up to 96 atoms. The predicted structure quantitatively matches the experimental equation of state and X-ray diffraction patterns. Furthermore, our group-theoretical analysis shows that the $Cmcm$ structure is compatible with existing Raman and infrared spectroscopic data. Crucially, static density functional theory calculation reveals the $Cmcm$ structure as a dynamically unstable saddle point on the Born-Oppenheimer potential energy surface, demonstrating that a full quantum many-body treatment of the problem is necessary. These results shed new light on the phase diagram of high-pressure hydrogen and call for further experimental verifications. △ Less

Submitted 28 December, 2025; v1 submitted 19 December, 2025; originally announced December 2025.

Shot noise signatures identifying non-Abelian properties of Jackiw-Rebbi zero modes

Authors: Haoran Ge, Zhen Chen, Yijia Wu, X. C. Xie

Abstract: Jackiw-Rebbi zero modes were first proposed in 1976 as topologically protected zero-energy states localized at domain walls in one-dimensional Dirac systems. They have attracted widespread attention in the field of topological quantum computing, as they serve as non-superconducting analogs of Majorana zero modes and support non-Abelian statistics in topological insulator systems. %In the braiding… ▽ More Jackiw-Rebbi zero modes were first proposed in 1976 as topologically protected zero-energy states localized at domain walls in one-dimensional Dirac systems. They have attracted widespread attention in the field of topological quantum computing, as they serve as non-superconducting analogs of Majorana zero modes and support non-Abelian statistics in topological insulator systems. %In the braiding process of the Jackiw-Rebbi zero modes, their braiding properties are closely related to the strength of disorder. However, compared to their Majorana cousins, the braiding properties of Jackiw-Rebbi zero modes are vulnerable to the on-site energy deviation between the modes involved in the experiment. In this work, we propose to estimate the braiding properties of Jackiw-Rebbi zero-modes through measurements of transport signatures, which are readily measurable in current experiments. We find that the fidelity of braiding operation reaches unity when the current noise is fully suppressed, while this braiding fidelity monotonously decreases with the increasing of the current noise. Based on these transport signatures, we further discuss the correspondence between Majorana and Jackiw-Rebbi zero modes, highlighting their similarity in supporting non-Abelian statistics. △ Less

Submitted 30 December, 2025; v1 submitted 18 December, 2025; originally announced December 2025.

Comments: 11 pages, 8 pages

Journal ref: Phys. Rev. B 114, 055407 (2026)

Giant field-tunable nonlinear Hall effect by Lorentz skew scattering in a graphene moire superlattice

Authors: Pan He, Min Zhang, Yue-Xin Huang, Jingru Li, Ruibo Wang, Shiwen Zhao, Chaoyu Pan, Yuxiao Gao, Takashi Taniguchi, Kenji Watanabe, Junxiong Hu, Yinyan Zhu, Cong Xiao, X. C. Xie, Shengyuan A. Yang, Jian Shen

Abstract: The nonlinear Hall effect (NHE) can enable rectification and energy harvesting, and its control by external fields, including gate, strain and magnetic field, has been pursued intensively. However, existing tuning pathways rely predominantly on fully quantum mechanical effects and are typically inefficient, resulting in weak NHE signals that limit further progress. In this work, we report the disc… ▽ More The nonlinear Hall effect (NHE) can enable rectification and energy harvesting, and its control by external fields, including gate, strain and magnetic field, has been pursued intensively. However, existing tuning pathways rely predominantly on fully quantum mechanical effects and are typically inefficient, resulting in weak NHE signals that limit further progress. In this work, we report the discovery of a distinct type of NHE in a graphene-hBN moire superlattice, which arises from a classical-quantum cooperative effect called Lorentz skew scattering (LSK), induced by a perpendicular magnetic field. This field-driven NHE exhibits a linear dependence on magnetic field and a pronounced unidirectional angular dependence. Remarkably, its magnitude reaches up to 32% of the linear Hall signal. We show that this giant, field-tunable NHE originating from LSK follows a unique quartic scaling law and produces a record-high nonlinear Hall conductivity (36000 μmV-1Ω-1) near van Hove singularities of moire minibands, which is over an order of magnitude larger than all previously reported NHEs. Our findings establish an efficient, magnetic-field-driven route to giant Hall rectification in high-mobility materials, offering a broadly applicable paradigm for modulating the NHE beyond electrostatic gating. △ Less

Submitted 5 November, 2025; originally announced November 2025.

Identifying geometric third-order nonlinear transport in disordered materials

Authors: Zhen-Hao Gong, Zhi-Hao Wei, Hai-Zhou Lu, X. C. Xie

Abstract: In nonlinear transport, the quantum-geometric effects can generate higher-harmonic voltages in response to a driving current, which has defined a fast-moving field of intense interest. However, in realistic materials where disorder scattering also contributes to nonlinear transport, identifying the geometric mechanisms remains a challenge. In particular, a theoretical framework for data analysis i… ▽ More In nonlinear transport, the quantum-geometric effects can generate higher-harmonic voltages in response to a driving current, which has defined a fast-moving field of intense interest. However, in realistic materials where disorder scattering also contributes to nonlinear transport, identifying the geometric mechanisms remains a challenge. In particular, a theoretical framework for data analysis is still lacking for nonlinear transport at any order. Here, we develop a mechanism-resolved and symmetry-guided framework for identifying mechanisms of third-order nonlinear transport in disordered materials. We find a total of 20 mechanisms of third-order nonlinear transport, by treating quantum-geometric and disorder-mediated mechanisms on an equal footing. More importantly, we propose a protocol of data analysis that combines symmetry diagnosis of magnetic point groups and scaling law of relation between the third-order nonlinear Hall conductivity and linear longitudinal conductivity. We identify characteristic fingerprints in the scaling-law weights, which allow the mechanisms to be quantitatively distinguished in experiments. We have applied the protocol to identify the geometric mechanisms in materials with and without time-reversal symmetry, including 2D materials, topological materials, and altermagnets. The theory can be generalized to arbitrary orders of nonlinear transport, further promoting nonlinear transport as a probe of geometric effects and phase transitions in quantum materials. △ Less

Submitted 15 July, 2026; v1 submitted 28 October, 2025; originally announced October 2025.

Comments: 10 pages, 3 figures, 2 table

Journal ref: Phys. Rev. X 16, 031012 (2026)

Sliding-tuned Quantum Geometry in Moiré Systems: Nonlinear Hall Effect and Quantum Metric Control

Authors: Shi-Ping Ding, Miao Liang, Tian-Le Wu, Meng-Hao Wu, Jing-Tao Lü, Jin-Hua Gao, X. C. Xie

Abstract: Sliding is a ubiquitous phenomenon in moiré systems, but its direct influence on moiré bands, especially in multi-twist moiré systems, has been largely overlooked to date. Here, we theoretically show that sliding provides a unique pathway to engineer the quantum geometry (Berry curvature and quantum metric) of moiré bands, exhibiting distinct advantages over conventional strategies. Specifically,… ▽ More Sliding is a ubiquitous phenomenon in moiré systems, but its direct influence on moiré bands, especially in multi-twist moiré systems, has been largely overlooked to date. Here, we theoretically show that sliding provides a unique pathway to engineer the quantum geometry (Berry curvature and quantum metric) of moiré bands, exhibiting distinct advantages over conventional strategies. Specifically, we first suggest alternating twisted trilayer $\mathrm{MoTe_2}$ (AT3L-$\mathrm{MoTe_2}$) and chirally twisted triple bilayer graphene (CT3BLG) as two ideal paradigmatic systems for probing sliding-engineered quantum geometric phenomena. Then, two sliding-induced exotic quantum geometry phenomena are predicted: (1) an intrinsic nonlinear Hall effect via sliding-produced non-zero Berry curvature dipole, with CT3BLG as an ideal platform; (2) significant quantum metric modulation in AT3L-$\mathrm{MoTe_2}$, enabling tests of quantum geometric criteria for fractional Chern insulating state (FCIS). Our work establishes sliding as a new degree of freedom for manipulating quantum geometry of moiré bands, which emerges as a signature phenomenon of multi-twist moiré systems. △ Less

Submitted 10 September, 2025; originally announced September 2025.

Comments: 6 pages, 4 figures

Theory of Localized States in Quasiperiodic Lattices

Authors: Jin-Rong Chen, Xin-Yu Guo, Shi-Ping Ding, Tian-Le Wu, Miao Liang, Jin-Hua Gao, X. C. Xie

Abstract: The physics of localized states in quasiperiodic lattices has been extensively studied for decades, but still lacks an comprehensive theoretical framework. Recently, we developed a incommensurate energy band (IEB) theory, which extends the concept of energy bands to quasiperiodic systems lacking translational symmetry, thereby achieving a breakthrough in elucidating extended states. Here, we demon… ▽ More The physics of localized states in quasiperiodic lattices has been extensively studied for decades, but still lacks an comprehensive theoretical framework. Recently, we developed a incommensurate energy band (IEB) theory, which extends the concept of energy bands to quasiperiodic systems lacking translational symmetry, thereby achieving a breakthrough in elucidating extended states. Here, we demonstrate that, due to the inherent duality between momentum and real space, the IEB theory also offers a comprehensive framework for elucidating localized states. Specifically, via a so-called spiral (module) mapping, the energy spectrum of localized states can be represented as a function defined on a compact circular manifold-akin to the Brillouin zone-whose form resembles conventional energy bands. These localized state energy bands (LSEBs) fully characterize all the properties of the localized states. Moreover, we show that quasiperiodic systems with mobility edges exhibit a unique hybrid band structure: the IEB for extended states (momentum space) and LSEB for localized states (real space), separated by mobility edges. Our theory thus establishes a comprehensive framework for analyzing the localized states in quasiperiodic lattices. △ Less

Submitted 7 September, 2025; originally announced September 2025.

Comments: 6 pages, 3 figures

First-Order PT Phase Transition in Non-Hermitian Superconductors

Authors: Xuezhu Liu, Ming Lu, Haiwen Liu, X. C. Xie

Abstract: The interplay between superconductivity and environmental dissipation, effectively captured by non-Hermitian Hamiltonian, is a new frontier for exotic quantum phases. We explore a PT-symmetric non-Hermitian superconductor with balanced gain and loss. To ensure experimental relevance, we develop a right-eigenstate-based non-Hermitian mean-field theory. We uncover a novel first-order phase transitio… ▽ More The interplay between superconductivity and environmental dissipation, effectively captured by non-Hermitian Hamiltonian, is a new frontier for exotic quantum phases. We explore a PT-symmetric non-Hermitian superconductor with balanced gain and loss. To ensure experimental relevance, we develop a right-eigenstate-based non-Hermitian mean-field theory. We uncover a novel first-order phase transition that coincides exactly with the PT symmetry breaking point, driven by the interplay between superconducting pairing interactions and non-Hermitian dissipation. In the PT-symmetric phase, moderate NH dissipation enhances superconductivity, while in the PT-broken phase, intensified dissipation significantly suppresses it. These phenomena, characterized by abrupt jumps in observables, can be probed through localized spectral measurements and macroscopic superfluid density analysis. Additionally, the stability analysis offers robust theoretical insights to support experimental investigations of this unique transition. △ Less

Submitted 3 September, 2025; originally announced September 2025.

Domain Wall Engineering in Graphene-Based Josephson Junctions

Authors: Xia'an Du, Junjie Qi, Hua Jiang, X. C. Xie

Abstract: Recent progress has enabled the controlled fabrication of domain walls (DWs) in graphene, which host topological kink states. Meanwhile, reliable techniques for constructing graphene-based Josephson junctions have been established. While the experimental prerequisites for combining DWs with Josephson junctions are now available, this direction remains largely unexplored. In this work, we theoretic… ▽ More Recent progress has enabled the controlled fabrication of domain walls (DWs) in graphene, which host topological kink states. Meanwhile, reliable techniques for constructing graphene-based Josephson junctions have been established. While the experimental prerequisites for combining DWs with Josephson junctions are now available, this direction remains largely unexplored. In this work, we theoretically investigate transport properties in graphene-based Josephson junctions mediated by topological kink states and propose three DW engineering strategies. (i) DW number engineering uncovers a continuous evolution of critical current interference pattern from Aharonov-Bohm oscillation to Fraunhofer diffraction with increasing DW number, reproducing experimental observations [Barrier et al., Nature 628, 741 (2024)] and suggesting enhanced sensitivity for magnetometry applications. (ii) DW symmetry engineering demonstrates that an asymmetric configuration of DWs under magnetic field yields an ideal Josephson diode characterized by pronounced nonreciprocal transport. (iii) DW geometry engineering reveals that intersecting DWs enable controllable supercurrent splitting with ratios among leads tunable through the intersection angle, magnetic field, and superconducting phase difference. Our findings elucidate the rich physics of DW-based Josephson junctions and establish a versatile platform for next-generation quantum devices. △ Less

Submitted 2 September, 2025; originally announced September 2025.

Comments: 12 pages, 7 figures

Non-Hermitian superconducting diode effect

Authors: Junjie Qi, Ming Lu, Jie Liu, Chui-Zhen Chen, X. C. Xie

Abstract: The study of non-reciprocal phenomena has long captivated interest in both Hermitian and non-Hermitian systems. The superconducting diode effect (SDE) is a non-reciprocal phenomenon characterized by unequal critical charge supercurrents flowing in opposite directions in Hermitian superconducting systems. In this study, we introduce an SDE driven by non-Hermiticity in a superconducting quantum inte… ▽ More The study of non-reciprocal phenomena has long captivated interest in both Hermitian and non-Hermitian systems. The superconducting diode effect (SDE) is a non-reciprocal phenomenon characterized by unequal critical charge supercurrents flowing in opposite directions in Hermitian superconducting systems. In this study, we introduce an SDE driven by non-Hermiticity in a superconducting quantum interference device (SQUID) under an external magnetic flux, which we refer to as the non-Hermitian SDE. Non-Hermiticity is introduced by coupling one of the two Josephson junctions to a gapless electron reservoir, introducing phase decoherence. Remarkably, we find that an emergent non-Hermitian Fermi-Dirac distribution can give rise to SDE in the non-Hermitian SQUID. We analyze the behavior of the SDE under both direct current (dc) and alternating current (ac) biases, highlighting the appearance of direction-dependent critical currents and asymmetric Shapiro steps as hallmarks of the SDE. Our findings not only reveal an experimentally accessible mechanism for non-Hermitian SDE but also open new avenues for investigating non-reciprocal phenomena in non-Hermitian systems. △ Less

Submitted 7 August, 2025; originally announced August 2025.

Journal ref: Phys. Rev. B 112, L06050 (2025)

A Clarification on Quantum-Metric-Induced Nonlinear Transport

Authors: Xiao-Bin Qiang, Tianyu Liu, Zi-Xuan Gao, Hai-Zhou Lu, X. C. Xie

Abstract: Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has been recognized as indispensable in comprehensively characterizing the intrinsic properties of condensed matter systems. The intrinsic second-order nonlinear condu… ▽ More Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has been recognized as indispensable in comprehensively characterizing the intrinsic properties of condensed matter systems. The intrinsic second-order nonlinear conductivity induced by the quantum metric has attracted significant recent interest. However, its expression varies across the literature. Here, we reconcile this discrepancy by systematically examining the nonlinear conductivity using the standard perturbation theory, the wave packet dynamics, and the Luttinger-Kohn approach. Moreover, inspired by the Dirac model, we propose a toy model that suppresses the Berry-curvature-induced nonlinear transport, making it suitable for studying the quantum-metric-induced nonlinear conductivity. This work provides a clearer and more unified understanding of the quantum-metric contributions to nonlinear transport. It also establishes a solid foundation for future theoretical developments and experimental explorations in this highly active and rapidly evolving field. △ Less

Submitted 24 November, 2025; v1 submitted 4 August, 2025; originally announced August 2025.

Comments: Published version with supplemental materials

Journal ref: Adv. Sci. 2025, e14818

Programmable Quantum Anomalous Hall Insulator in Twisted Crystalline Flatbands

Authors: Wenxuan Wang, Yijie Wang, Zaizhe Zhang, Zihao Huo, Gengdong Zhou, Kenji Watanabe, Takashi Taniguchi, X. C. Xie, Kaihui Liu, Zhida Song, Xiaobo Lu

Abstract: The isospin flavors in condensed matters can be continuously broken, forming various symmetry-broken quantum states. In moiré crystals, the competition between different isospin configurations can be effectively tuned by the twist angles and staciking orders. Here we report twisted double rhombohedral-trilayer-gaphene as a new twisted crystalline flatbands system showing rich moiré dependent topol… ▽ More The isospin flavors in condensed matters can be continuously broken, forming various symmetry-broken quantum states. In moiré crystals, the competition between different isospin configurations can be effectively tuned by the twist angles and staciking orders. Here we report twisted double rhombohedral-trilayer-gaphene as a new twisted crystalline flatbands system showing rich moiré dependent topological phenomena. In devices with small twist angles, programmable Chern insulators with Chern number C = 3 at integer moiré filling v = 1 have been observed. We have further revealed an exotic hidden order which can quench the Chern insulator as well as multiple first-order transitions between different symmetry-broken phases. Interestly, in the device with a slightly larger twist angle, multiple Chern insulators with C = 1 at fractional moiré fillings including v = 1/4, 1/3 and 1/2 have been observed, whereas the Chern insulator at v = 1 is abscent. Our study demonstrated the twisted flatbands form rhombohedral-multilayer-graphene as a new platform to study tunable high Chern insulators as well as new devices for quantum storage and computation. △ Less

Submitted 6 January, 2026; v1 submitted 14 July, 2025; originally announced July 2025.

Quantized Topological States and Parity Anomaly in Intrinsic Quantum Anomalous Hall Insulator MnBi2Te4

Authors: Zhongxun Guo, Jingjing Gao, Zhiwei Huang, Di Yue, Zhaochen Liu, Mingyan Luo, Shuang Wu, Xinyu Chen, Guangyi Huang, Yujun Deng, Mengzhu Shi, Yin Xia, Zihan Xu, Chuanying Xi, Guangli Kuang, Changlin Zheng, Shiwei Wu, Hua Jiang, X. C. Xie, Wenzhong Bao, Yuping Sun, Xian Hui Chen, Jing Wang, Wei Ruan, Yuanbo Zhang

Abstract: When thinned down to just a few atomic layers, the layered magnetic topological insulator MnBi2Te4 offers an exceptional platform for exploring a wide range of topological phenomena. In this work, we overcome longstanding challenges in synthesizing high-purity MnBi2Te4 crystals and report the observation of a myriad of quantized topological states in high-quality five-septuple-layer (5-SL) samples… ▽ More When thinned down to just a few atomic layers, the layered magnetic topological insulator MnBi2Te4 offers an exceptional platform for exploring a wide range of topological phenomena. In this work, we overcome longstanding challenges in synthesizing high-purity MnBi2Te4 crystals and report the observation of a myriad of quantized topological states in high-quality five-septuple-layer (5-SL) samples under magnetic fields up to 45 Tesla. We show that the nontrivial topology of 5-SL MnBi2Te4, in the presence of Landau quantization, is governed by a generalized topological index rooted in the parity anomaly of Dirac fermions in (2+1) dimensions. The anomaly manifests as an anomalous Landau level, giving rise to gate-tunable helical edge transport. Our results establish high-quality MnBi2Te4 as a robust platform for exploring emergent topological states and for advancing novel quantum device applications. △ Less

Submitted 4 July, 2025; originally announced July 2025.

Comments: 13 pages,4 figures

Nonlinear Néel Spin-Orbit Torque in Centrosymmetric Antiferromagnets

Authors: Jin Cao, Weikang Wu, Huiying Liu, Shen Lai, Cong Xiao, X. C. Xie, Shengyuan A. Yang

Abstract: Electric control of Néel vector is a central task of antiferromagnetic (AFM) spintronics. The major scheme so far relies on the linear Néel torque, which however is restricted to AFMs with broken inversion symmetry. Here, we propose a nonlinear Néel spin-orbit torque, uniquely enabling electric control in the vast class of centrosymmetric AFMs, where the existing scheme fails. Importantly, its int… ▽ More Electric control of Néel vector is a central task of antiferromagnetic (AFM) spintronics. The major scheme so far relies on the linear Néel torque, which however is restricted to AFMs with broken inversion symmetry. Here, we propose a nonlinear Néel spin-orbit torque, uniquely enabling electric control in the vast class of centrosymmetric AFMs, where the existing scheme fails. Importantly, its intrinsic component, rooted in sublattice-resolved band quantum geometry, offers two additional advantages: It operates also in $\mathcal{PT}$-symmetric AFM insulators, where linear torque is forbidden; and it has anti-damping character, making it more efficient in driving magnetic dynamics. Combined with first-principles calculations, we predict large effect in MnRh and MnBi$_{2}$Te$_{4}$, which can be readily detected in experiment. Our work unveils a new fundamental effect, offers a new strategy of electric control in AFM systems beyond the existing paradigm, and opens the door to the field of nonlinear AFM spintronics. △ Less

Submitted 11 June, 2025; originally announced June 2025.

Comments: 6 pages, 4 figures and 1 table

Three-Majorana Cotunneling Interferometer for Non-Abelian Braiding and Topological Quantum Gate Implementation

Authors: Zhen Chen, Yijia Wu, X. C. Xie

Abstract: We propose a novel scheme for performing Majorana zero mode (MZM) braiding utilizing cotunneling processes in a three-MZM system incorporating reference arms. This approach relies on the interference between cotunneling paths through the MZMs and reference arms, establishing an effective, tunable coupling between the MZMs. The strength and sign of this coupling can be manipulated via the reference… ▽ More We propose a novel scheme for performing Majorana zero mode (MZM) braiding utilizing cotunneling processes in a three-MZM system incorporating reference arms. This approach relies on the interference between cotunneling paths through the MZMs and reference arms, establishing an effective, tunable coupling between the MZMs. The strength and sign of this coupling can be manipulated via the reference arms and applied magnetic flux. Notably, the introduction of a half quantum flux reverses the coupling sign, enabling an echo-like protocol to eliminate dynamic phases during braiding. Our setup, requiring only three MZMs, represents a minimal platform for demonstrating non-Abelian braiding statistics. We demonstrate that this system facilitates the implementation of Clifford gates via braiding and, significantly, permits the realization of non-Clifford gates, such as the $T$ gate, by geometric phase, thereby offering a potential pathway towards universal topological quantum computation. △ Less

Submitted 10 September, 2025; v1 submitted 4 June, 2025; originally announced June 2025.

Comments: 18 pages, 9 figures

Unconventional Orbital Magnetism in Graphene-based Fractional Chern Insulators

Authors: Jian Xie, Zaizhe Zhang, Xi Chen, Yves H. Kwan, Zihao Huo, Jonah Herzog-Arbeitman, Liangliang Guo, Kenji Watanabe, Takashi Taniguchi, Kaihui Liu, X. C. Xie, B. Andrei Bernevig, Zhi-Da Song, Xiaobo Lu

Abstract: Orbital magnetism in graphene originates from correlation-driven spontaneous valley symmetry breaking1-7. It can lead to various anomalous transport phenomena such as integer and fractional quantum anomalous Hall effects8-11. In general, the in-plane magnetic field B|| primarily couples to the spin degrees of freedom in graphene and has long been presumed to have a negligible effect on orbital mag… ▽ More Orbital magnetism in graphene originates from correlation-driven spontaneous valley symmetry breaking1-7. It can lead to various anomalous transport phenomena such as integer and fractional quantum anomalous Hall effects8-11. In general, the in-plane magnetic field B|| primarily couples to the spin degrees of freedom in graphene and has long been presumed to have a negligible effect on orbital magnetism due to the ultra-weak spin-orbit coupling12-18. In this work, we report multiple unconventional orbital magnetic phenomena that are highly sensitive to the B|| field in graphene/hBN superlattices hosting both integer and fractional Chern insulators (FCIs). We observed chirality-switching behaviors of the Chern insulator at moiré filling factor ν = 1 under a finite B_par, demonstrating that both the C = +-1 states are permissible ground states at zero perpendicular magnetic field B_per. For the FCI at ν = 2/3, we observed topological phase transitions between two states characterized by Hall resistivity \r{ho}xy = +-3h/2e2 under both B_per and B_par fields. In-plane B|| field can effectively suppress the FCI state at zero B_per field and enhance the FCI state with the opposite chirality, as resolved in Landau fan diagrams. Moreover, we observed rich phase transitions at 1 < ν < 2, accompanied by intervalley coherence and anomalous Hall effects (AHE) that can be triggered by sweeping either B_per or B_par. Our work has unveiled new properties of orbital magnetism, providing a new knob for engineering various AHE in graphene. △ Less

Submitted 2 June, 2025; originally announced June 2025.

Transdimensional anomalous Hall effect in rhombohedral thin graphite

Authors: Qingxin Li, Hua Fan, Min Li, Yinghai Xu, Junwei Song, Kenji Watanabe, Takashi Taniguchi, Hua Jiang, X. C. Xie, James Hone, Cory Dean, Yue Zhao, Jianpeng Liu, Lei Wang

Abstract: Anomalous Hall effect (AHE), occurring in materials with broken time-reversal symmetry, epitomizes the intricate interplay between magnetic order and orbital motions of electrons[1-4]. In two dimensional (2D) systems, AHE is always coupled with out-of-plane orbital magnetization associated in-plane chiral orbital motions. In three dimensional (3D) systems, carriers can tunnel or scatter along the… ▽ More Anomalous Hall effect (AHE), occurring in materials with broken time-reversal symmetry, epitomizes the intricate interplay between magnetic order and orbital motions of electrons[1-4]. In two dimensional (2D) systems, AHE is always coupled with out-of-plane orbital magnetization associated in-plane chiral orbital motions. In three dimensional (3D) systems, carriers can tunnel or scatter along the third dimension within the vertical mean free path lz. When sample thickness far exceeds lz, scattering disrupts coherent out-of-plane motion, making 3D AHE effectively a thickness-averaged 2D counterpart[4] -- still governed by out-of-plane orbital magnetization arising from in-plane orbital motions. Here, we explore an uncharted regime where the sample thickness is much larger than the atomic layer thickness yet smaller than or comparable to lz. In such "transdimensional" regime, carriers can sustain coherent orbital motions both within and out of the 2D plane, leading to a fundamentally new type of AHE that couples both out-of-plane and in-plane orbital magnetizations. We report the first observation of such phenomenon -- transdimensional AHE (TDAHE) -- in electrostatically gated rhombohedral ennealayer graphene. This state emerges from a peculiar metallic phase that spontaneously breaks time-reversal, mirror and rotational symmetries driven by electron-electron interactions. Such TDAHE manifests as concurrent out-of-plane and in-plane Hall resistance hysteresis, controlled by external magnetic fields along either direction. Our findings unveils a new class of AHE, opening an unexplored paradigm for correlated and topological physics in transdimensional systems. △ Less

Submitted 6 May, 2025; originally announced May 2025.

Comments: 35pages, 15figures

Rare-Event-Induced Ergodicity Breaking in Logarithmic Aging Systems

Authors: Chunyan Li, Qingyang Feng, Tianjie Zhou, Haiwen Liu, X. C. Xie

Abstract: Ergodicity breaking and aging effects are fundamental challenges in out-of-equilibrium systems. Various mechanisms have been proposed to understand the non-ergodic and aging phenomena, possibly related to observations in systems ranging from structural glass and Anderson glasses to biological systems and mechanical systems. While anomalous diffusion described by Levy statistics efficiently capture… ▽ More Ergodicity breaking and aging effects are fundamental challenges in out-of-equilibrium systems. Various mechanisms have been proposed to understand the non-ergodic and aging phenomena, possibly related to observations in systems ranging from structural glass and Anderson glasses to biological systems and mechanical systems. While anomalous diffusion described by Levy statistics efficiently captures ergodicity breaking, the origin of aging and ergodicity breaking in systems with ultraslow dynamics remain unclear. Here, we report a novel mechanism of ergodicity breaking in systems exhibiting log-aging diffusion. This mechanism, characterized by increasingly infrequent rare events with aging, yields statistics deviating significantly from Levy distribution, breaking ergodicity as shown by unequal time- and ensemble-averaged mean squared displacements and two distinct asymptotic probability distribution functions. Notably, although these rare events contribute negligibly to statistical averages, they dramatically change the system's characteristic time. This work lays the groundwork for microscopic understanding of out-of-equilibrium systems and provides new perspectives on glasses and Griffiths-McCoy singularities. △ Less

Submitted 17 April, 2025; originally announced April 2025.

Comments: 26 pages, 9 figures, 1 table

Coherent detection of the oscillating acoustoelectric effect in graphene

Authors: Yicheng Mou, Jiayu Wang, Haonan Chen, Yingchao Xia, Hailong Li, Qing Yan, Xue Jiang, Yijia Wu, Wu Shi, Hua Jiang, X. C. Xie, Cheng Zhang

Abstract: In recent years, surface acoustic waves (SAWs) have emerged as a novel technique for generating quasiparticle transport and band modulation in condensed matter systems. SAWs interact with adjacent materials through piezoelectric and strain fields, dragging carriers in the direction of wave propagation. Most studies on the acoustoelectric effect have focused on the collective directional motion of… ▽ More In recent years, surface acoustic waves (SAWs) have emerged as a novel technique for generating quasiparticle transport and band modulation in condensed matter systems. SAWs interact with adjacent materials through piezoelectric and strain fields, dragging carriers in the direction of wave propagation. Most studies on the acoustoelectric effect have focused on the collective directional motion of carriers, which generates a steady electric potential difference, while the oscillating component from dynamic spatial charge modulation has remained challenging to probe. In this work, we report the coherent detection of oscillating acoustoelectric effect in graphene. This is achieved through the coherent rectification of spatial-temporal charge oscillation with electromagnetic waves emitted by interdigital transducers. We systematically investigate the frequency and gate dependence of rectified signals and quantitatively probe the carrier redistribution dynamics driven by SAWs. The observation of oscillating acoustoelectric effect provides direct access to the dynamic spatial charge modulation induced by SAWs through transport experiments. △ Less

Submitted 13 February, 2025; originally announced February 2025.

Comments: 12 pages, 4 figures, to appear in PRL

Journal ref: Phys. Rev. Lett. 134, 096301 (2025)

Quantifying Non-Abelian Stability in Majorana Qubits through Rabi Beating Signatures

Authors: Yu Zhang, Jiayi Chen, Jie Liu, X. C. Xie

Abstract: Evaluating the stability of Majorana qubits (MQs) is a central challenge for topological quantum computation. Here we propose a simple and experimentally accessible protocol to quantify MQ stability by coupling a quantum dot (QD) to an MQ, which induces Rabi oscillations in the QD charge occupation that can be directly detected using recently developed single-shot readout techniques. In realistic… ▽ More Evaluating the stability of Majorana qubits (MQs) is a central challenge for topological quantum computation. Here we propose a simple and experimentally accessible protocol to quantify MQ stability by coupling a quantum dot (QD) to an MQ, which induces Rabi oscillations in the QD charge occupation that can be directly detected using recently developed single-shot readout techniques. In realistic systems, deviations from ideal MQ behavior lead to a characteristic beating pattern in the Rabi dynamics. We show that the beating frequency scales linearly with these deviations while remaining independent of the base Rabi frequency, thereby providing a direct and quantitative measure of MQ stability. Importantly, the beating signature is robust against weak dissipation, and we further demonstrate that the effective model remains quantitatively accurate when benchmarked against a realistic minimal Kitaev chain. Our results establish a practical and scalable route for quantitatively characterizing Majorana qubit stability in current experimental platforms. △ Less

Submitted 3 June, 2026; v1 submitted 13 February, 2025; originally announced February 2025.

Comments: 5 pages, 4 figures

Quantum kinetic theory of the semiclassical side jump, skew scattering and longitudinal velocity

Authors: Da Ma, Zhi-Fan Zhang, Hua Jiang, X. C. Xie

Abstract: The semiclassical Boltzmann equation is widely used to study transport effects. However, being semiclassical and borrowing heavily from classical mechanics, the formalism calls for verification from the perspective of quantum mechanics. Although previous works discussed the relation between the quantum density matrix and the semiclassical formalism, direct comparison, especially of disorder effect… ▽ More The semiclassical Boltzmann equation is widely used to study transport effects. However, being semiclassical and borrowing heavily from classical mechanics, the formalism calls for verification from the perspective of quantum mechanics. Although previous works discussed the relation between the quantum density matrix and the semiclassical formalism, direct comparison, especially of disorder effects, including side jumps and skew scattering in the two approaches, has not been fully conducted. In this work, we systematically and directly compare the semiclassical Boltzmann equation and its counterpart arising from the density matrix. We find that there is an additional correction to the side-jump velocity, the longitudinal velocity, which is longitudinal in the leading order, and its resultant current does not require time-reversal symmetry breaking. Moreover, we find the semiclassical side-jump collision integral is an approximation of the quantum result at moderate temperatures, and it also contains a correction induced by the longitudinal velocity. We also show that the scattering rate obtained from the density matrix agrees with the semiclassical results. Our work illuminates the quantum roots of the semiclassical Boltzmann equation. △ Less

Submitted 4 August, 2025; v1 submitted 8 February, 2025; originally announced February 2025.

Journal ref: Phys. Rev. B 112, 045136 (2025)

Chern Vector Protected Three-dimensional Quantized Hall Effect

Authors: Zhi-Qiang Zhang, Shu-Guang Cheng, Hongfang Liu, Hailong Li, Hua Jiang, X. C. Xie

Abstract: Recently, Chern vector with arbitrary formula $\textbf{C}\!=\!(\mathcal{C}_{yz},\mathcal{C}_{xz},\mathcal{C}_{xy})$ in three-dimensional systems has been experimentally realized [\B{Nature 609, 925 (2022)}]. Motivated by these progresses, we propose the Chern vector $\textbf{C}\!=\!(0,m,n)$-protected quantized Hall effect in three-dimensional systems. By examining samples with Chern vector… ▽ More Recently, Chern vector with arbitrary formula $\textbf{C}\!=\!(\mathcal{C}_{yz},\mathcal{C}_{xz},\mathcal{C}_{xy})$ in three-dimensional systems has been experimentally realized [\B{Nature 609, 925 (2022)}]. Motivated by these progresses, we propose the Chern vector $\textbf{C}\!=\!(0,m,n)$-protected quantized Hall effect in three-dimensional systems. By examining samples with Chern vector $\textbf{C}\!=\!(0,m,n)$ and dimensions $L_y$ and $L_z$ along the $y$- and $z$-directions, we demonstrate a topologically protected two-terminal response. This response can be reformulated as the sum of the transmission coefficients along the $x$- and $y$-directions, given by $(mL_y\!+\!nL_z)$. When applied to Hall bar setups, this topological mechanism gives rise to quantized Hall conductances, such as \(G_{xy}\) and \(G_{xz}\), which are expressed by $\pm(mL_y\!+\!nL_z)$. These Hall conductances exhibit a clear dependency on sample dimensions, illuminating the intrinsic three-dimensional nature. Finally, we propse potential candidates for experimental realization. Our findings not only deepen the understanding of the topological nature of Chern vectors but also enlighten the exploration of their transport properties. △ Less

Submitted 24 January, 2025; originally announced January 2025.

Three-dimensional quantum anomalous Hall effect in Weyl semimetals

Authors: Zhi-Qiang Zhang, Yu-Hang Li, Ming Lu, Hongfang Liu, Hailong Li, Hua Jiang, X. C. Xie

Abstract: The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e^2$ in the absence of magnetic field, where $h$ is the Planck constant and $e$ is the electron charge. In this work, we extend this novel phase to three dimensions and thus propose a three-dimensional QAHE exhibiting richer and more versatile transport behavio… ▽ More The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e^2$ in the absence of magnetic field, where $h$ is the Planck constant and $e$ is the electron charge. In this work, we extend this novel phase to three dimensions and thus propose a three-dimensional QAHE exhibiting richer and more versatile transport behaviors. We first confirm this three-dimensional QAHE through the quantized Chern number, then establish its bulk-boundary correspondence, and finally reaffirm it via the distinctive transport properties. Remarkably, we find that the three-dimensional QAHE hosts two chiral surface states along one spatial direction while a pair of chiral hinge states along another direction, and the location of the hinge states depends sensitively on the Fermi energy. These two types of boundary states are further connected through a perpendicular chiral surface states, whose chirality is also Fermi energy dependent. Consequently, depending on the transport direction, its Hall resistance can quantize to $0$, $h/e^2$, or $\pm h/e^2$ when the Fermi energy is tuned across the charge neutral point. This three-dimensional QAHE not only fill the gap in the Hall effect family but also holds significant potentials in device applications such as in-memory computing. △ Less

Submitted 10 January, 2026; v1 submitted 2 January, 2025; originally announced January 2025.

Comments: 4 pages, 2 figures

Journal ref: Science Bulletin 70 (22), 3729 (2025)

Electrical switching of altermagnetism

Authors: Yiyuan Chen, Xiaoxiong Liu, Hai-Zhou Lu, X. C. Xie

Abstract: Switching magnetism using only electricity is of great significance for industrial applications but remains challenging. We find that, altermagnetism, as a newly discovered unconventional magnetism, may open an avenue along this effort. Specifically, to have deterministic switching, i.e., reversing current direction must reverse magnetic structure, parity symmetry has to be broken. We discover tha… ▽ More Switching magnetism using only electricity is of great significance for industrial applications but remains challenging. We find that, altermagnetism, as a newly discovered unconventional magnetism, may open an avenue along this effort. Specifically, to have deterministic switching, i.e., reversing current direction must reverse magnetic structure, parity symmetry has to be broken. We discover that, due to their symmetry which depends on chemical environments, altermagnet devices may naturally carry the parity symmetry breaking required for deterministic electrical switching of magnetism. More importantly, we identify MnTe bilayers (Te-Mn-Te-Mn-Te) as candidate devices, with the help of symmetry analysis, first-principles calculations, and magnetic dynamics simulations. This scheme will inspire further explorations on unconventional magnetism. △ Less

Submitted 4 June, 2025; v1 submitted 30 December, 2024; originally announced December 2024.

Comments: 8 pages, 5 figures

Journal ref: Phys. Rev. Lett. 135, 016701 (2025)

Coulomb Drag in Altermagnets

Authors: Hao-Jie Lin, Song-Bo Zhang, Hai-Zhou Lu, X. C. Xie

Abstract: An altermagnet is a newly discovered antiferromagnet, characterized by unique anisotropic spin-split energy bands. It has attracted tremendous interest, because of its promising potential in information storage and processing. However, measuring the distinctive spin-split energy bands arising from altermagnetism remains a challenge. Here, we propose to employ the Coulomb drag to probe altermagneti… ▽ More An altermagnet is a newly discovered antiferromagnet, characterized by unique anisotropic spin-split energy bands. It has attracted tremendous interest, because of its promising potential in information storage and processing. However, measuring the distinctive spin-split energy bands arising from altermagnetism remains a challenge. Here, we propose to employ the Coulomb drag to probe altermagnetism. In the Coulomb drag, an electric current in an active layer of electron gases can induce currents in a close but well-isolated passive layer, due to interlayer Coulomb interactions. We find that the Coulomb drag effects in altermagnets are highly sensitive to the orientation of the spin-split Fermi surfaces. As a result, transverse currents can be dragged in the passive layer, leading to Hall drag effects even in absence of spin-orbit coupling, a feature quite different from all previous systems. More importantly, all the drag effects of altermagnets have unique angle dependence, which can be measured in a multi-terminal setup to serve as signatures for altermagnetism. This proposal will inspire increasing explorations on emergent magnetism. △ Less

Submitted 2 April, 2025; v1 submitted 18 December, 2024; originally announced December 2024.

Comments: 5+2 pages, 4 figures, 1 table

Journal ref: PRL 134, 136301 (2025)

Rules for dissipationless topotronics

Authors: Qing Yan, Hailong Li, Hua Jiang, Qing-Feng Sun, X. C. Xie

Abstract: Topological systems hosting gapless boundary states have attracted huge attention as promising components for next-generation information processing, attributed to their capacity for dissipationless electronics. Nevertheless, recent theoretical and experimental inquiries have revealed the emergence of energy dissipation in precisely quantized electrical transport. Here, we present a criterion for… ▽ More Topological systems hosting gapless boundary states have attracted huge attention as promising components for next-generation information processing, attributed to their capacity for dissipationless electronics. Nevertheless, recent theoretical and experimental inquiries have revealed the emergence of energy dissipation in precisely quantized electrical transport. Here, we present a criterion for the realization of truly no-dissipation design, characterized as $N_{in}=N_{tunl}+N_{bs}$, where $N_{in}$, $N_{tunl}$, and $N_{bs}$ represent the number of modes participating in injecting, tunneling, and backscattering processes, respectively. The key lies in matching the number of injecting, tunneling and backscattering modes, ensuring the equilibrium among all engaged modes inside the device. Among all the topological materials, we advocate for the indispensability of Chern insulators exhibiting higher Chern numbers to achieve functional devices and uphold the no-dissipation rule simultaneously. Furthermore, we design the topological current divider and collector, evading dissipation upon fulfilling the established criterion. Our work paves the path for developing the prospective topotronics. △ Less

Submitted 12 December, 2024; originally announced December 2024.

Journal ref: Sci. Adv.10,eado4756 (2024)

Fractional spin Josephson effect in topological spin superconductors

Authors: Liang Du, Hua Jiang, Yijia Wu, X. C. Xie

Abstract: Topological spin superconductors are $p$-wave spin-triplet exciton insulators whose topological edge modes have been shown to obey non-Abelian braiding statistics. Based on a toy model as the spin counterpart of the Kitaev's chain, we study the spin Josephson effect adopting the $S$-matrix as well as the Green's function method. The on-site energies of these topological edge modes lead to a transi… ▽ More Topological spin superconductors are $p$-wave spin-triplet exciton insulators whose topological edge modes have been shown to obey non-Abelian braiding statistics. Based on a toy model as the spin counterpart of the Kitaev's chain, we study the spin Josephson effect adopting the $S$-matrix as well as the Green's function method. The on-site energies of these topological edge modes lead to a transition between the fractional and integer spin Josephson effects. Moreover, non-vanishing on-site energies will also induce a charge pump through the spin Josephson junction. These two effects, distinct features of topological spin superconductors and absent in Majorana systems, can be utilized for spin transport detection of topological spin superconductors. △ Less

Submitted 11 December, 2024; originally announced December 2024.

Comments: 10 pages, 6 figures

Journal ref: Physical Review B 111, 094524 (2025)

Quantum oscillation in Hopf-link semimetals

Authors: Lei Shi, Xiaoxiong Liu, C. M. Wang, Tianyu Liu, Hai-Zhou Lu, X. C. Xie

Abstract: Since the discovery of the relation between the Chern number and quantum Hall effect, searching for observables of topological invariants has been an intriguing topic. Topological Hopf-link semimetals have attracted tremendous interest, in which the conduction and valence energy bands touch at linked nodal lines. However, it is challenging to identify this sophisticated topology. We propose to use… ▽ More Since the discovery of the relation between the Chern number and quantum Hall effect, searching for observables of topological invariants has been an intriguing topic. Topological Hopf-link semimetals have attracted tremendous interest, in which the conduction and valence energy bands touch at linked nodal lines. However, it is challenging to identify this sophisticated topology. We propose to use the quantum oscillation in strong magnetic fields to probe the Hopf links. For a generic model of Hopf-link semimetal that captures the linked-trivial phase transition, we figure out the phase shifts of oscillation for all Fermi pockets in all magnetic-field directions, by presenting self-consistent results from the Fermi surface tomography, Landau fan diagram, and electrical resistivity. As the magnetic field is rotated, the phase shifts exhibit a unique pattern, which could help to identify Hopf links in real materials, such as those in Li$_2$NaN. △ Less

Submitted 26 June, 2025; v1 submitted 9 December, 2024; originally announced December 2024.

Comments: 6 pages, 3 figures, 2 tables

Journal ref: Phys. Rev. B 111, L201103 (2025)

Edge supercurrent in Josephson junctions based on topological materials

Authors: Junjie Qi, Chui-Zhen Chen, Juntao Song, Jie Liu, Ke He, Qing-Feng Sun, X. C. Xie

Abstract: The interplay between novel topological states and superconductivity has garnered substantial interest due to its potential for topological quantum computing. The Josephson effect serves as a useful probe for edge superconductivity in these hybrid topological materials. In Josephson junctions based on topological materials, supercurrents exhibit unique quantum interference patterns, including the… ▽ More The interplay between novel topological states and superconductivity has garnered substantial interest due to its potential for topological quantum computing. The Josephson effect serves as a useful probe for edge superconductivity in these hybrid topological materials. In Josephson junctions based on topological materials, supercurrents exhibit unique quantum interference patterns, including the conventional Fraunhofer oscillations, the $Φ_0$-periodic oscillation, and the $2Φ_0$-periodic oscillation in response to the external magnetic field ($Φ_0 = h/2e$ is the flux quantum, $h$ the Planck constant, and $e$ the electron charge). These interference patterns stem from varied Andreev reflection mechanisms and the associated current density profiles. This review seeks to comprehensively examine the theoretical and experimental advancements in understanding the quantum interference patterns of edge supercurrents in Josephson junctions based on quantum spin Hall, quantum Hall, and quantum anomalous Hall systems. △ Less

Submitted 11 November, 2024; originally announced November 2024.

Comments: 14 pages, 7 figures

Journal ref: Sci. China- Phys. Mech. Astron. 68,227401 (2025)

Dispersions and magnetism of strain-induced pseudo Landau levels in Bernal-stacked bilayer graphene

Authors: Tianyu Liu, Jun-Hong Li, Xingchuan Zhu, Huaiming Guo, Hai-Zhou Lu, X. C. Xie

Abstract: Elastic strain can displace the massless Dirac fermions in monolayer graphene in a space-dependent fashion, similar to the effect of an external magnetic field, thus giving rise to Landau quantization. We here show that the strain-induced Landau quantization can also take place in Bernal-stacked bilayer graphene, where the low-energy excitations are massive rather than Dirac-like. The zigzag ribbo… ▽ More Elastic strain can displace the massless Dirac fermions in monolayer graphene in a space-dependent fashion, similar to the effect of an external magnetic field, thus giving rise to Landau quantization. We here show that the strain-induced Landau quantization can also take place in Bernal-stacked bilayer graphene, where the low-energy excitations are massive rather than Dirac-like. The zigzag ribbon of Bernal-stacked bilayer graphene realizes a two-legged Su-Schrieffer-Heeger model with a domain wall, which coincides with the guiding center of the strain-induced pseudo Landau levels. We reduce the lattice model of the ribbon in the vicinity of the guiding center into an exactly solvable coupled Dirac model and analytically derive the dispersions of the strain-induced pseudo Landau levels. Remarkably, the zeroth and first pseudo Landau levels are dispersionless and sublattice-polarized. We elucidate that the interaction on these two pseudo Landau levels results in a global antiferromagnetic order. Our study extends the strain-induced Landau quantization to the massive excitations and indicates strain as a tuning knob of magnetism. △ Less

Submitted 29 October, 2024; originally announced October 2024.

Comments: 11 pages main text + 4.5 pages appendices, 9 figures

Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires

Authors: Yu Zhang, Yijia Wu, Jie Liu, X. C. Xie

Abstract: Non-Abelian braiding is a key property of Majorana zero modes (MZMs) that can be utilized for topological quantum computation. However, the presence of trivial Andreev bound states (ABSs) in topological superconductors can hinder the non-Abelian braiding of MZMs. We systematically investigate the braiding properties of ABSs induced by various inhomogeneous potentials in nanowires and quantify the… ▽ More Non-Abelian braiding is a key property of Majorana zero modes (MZMs) that can be utilized for topological quantum computation. However, the presence of trivial Andreev bound states (ABSs) in topological superconductors can hinder the non-Abelian braiding of MZMs. We systematically investigate the braiding properties of ABSs induced by various inhomogeneous potentials in nanowires and quantify the main obstacles to non-Abelian braiding. We find that if a trivial ABSs is present at zero energy with a tiny energy fluctuation, their non-Abelian braiding property can be sustained for a longer braiding time cost, since the undesired dynamic phase is suppressed. Under certain conditions, the non-Abelian braiding of ABSs can even surpass that of MZMs in realistic systems, suggesting that ABSs might also be suitable for topological quantum computation. △ Less

Submitted 22 October, 2024; originally announced October 2024.

Comments: 13 pages, 9 figures

Energy Bands of Incommensurate Systems

Authors: Xin-Yu Guo, Jin-Rong Chen, Chen Zhao, Miao Liang, Ying-Hai Wu, Jin-Hua Gao, X. C. Xie

Abstract: Energy band theory is a fundamental cornerstone of condensed matter physics. According to conventional wisdom, discrete translational symmetry is mandatory for defining energy bands. Here, we illustrate that, in fact, the concept of energy band can be generalized to incommensurate systems lacking such symmetry, thus transcending the traditional paradigm of energy band. The validity of our theory i… ▽ More Energy band theory is a fundamental cornerstone of condensed matter physics. According to conventional wisdom, discrete translational symmetry is mandatory for defining energy bands. Here, we illustrate that, in fact, the concept of energy band can be generalized to incommensurate systems lacking such symmetry, thus transcending the traditional paradigm of energy band. The validity of our theory is verified by extensive numerical calculations in the celebrated Aubry-André-Harper model and a two-dimensional incommensurate model of graphene. Building upon the proposed concept of incommensurate energy bands, we further develop a theory of angle-resolved photoemission spectroscopy (ARPES) for incommensurate systems, providing a clear physical picture for the incommensurate ARPES spectra. Our work establishes a comprehensive energy band theory for incommensurate systems. △ Less

Submitted 13 October, 2024; originally announced October 2024.

Comments: 8 pages, 3 figures

Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes

Authors: Tianyu Huang, Rui Zhang, Xiaopeng Li, Xiong-Jun Liu, X. C. Xie, Yijia Wu

Abstract: Majorana zero modes (MZMs) are the most intensively studied non-Abelian anyons. The Dirac fermion zero modes in topological insulators, which are symmetry-protected doubling of MZMs under fermion number conservation, offer an alternative approach to explore non-Abelian anyons. However, a unified model that elucidates the braiding statistics of these types of topological zero modes remains absent.… ▽ More Majorana zero modes (MZMs) are the most intensively studied non-Abelian anyons. The Dirac fermion zero modes in topological insulators, which are symmetry-protected doubling of MZMs under fermion number conservation, offer an alternative approach to explore non-Abelian anyons. However, a unified model that elucidates the braiding statistics of these types of topological zero modes remains absent. We show that the minimal Kitaev chain model beyond fine-tuning regime provides a unified characterization of the non-Abelian statistics of both MZMs and Dirac fermion zero modes in different parameter regimes. In particular, we introduce a minimal tri-junction setting based on the minimal Kitaev chain model and show it facilitates the unified scheme of braiding Dirac fermion zero modes, as well as the MZMs in the assistance of a Dirac mode. This unified minimal model provides deeper insights into non-Abelian statistics, demonstrating that the non-Abelian braiding of MZMs can be continuously extended to encompass Dirac fermion zero modes. The minimal Kitaev chain has been realized in coupled quantum dots [Nature 614, 445 (2023)]. Our extension, which demonstrates novel nontrivial phases with non-Abelian MZM pairs and Dirac zero modes emerging in the broader parameter regimes without fine-tuning, expands the accessible experimental parameter space and enhances the feasibility of observing non-Abelian statistics in the minimal Kitaev chain model. △ Less

Submitted 10 June, 2025; v1 submitted 8 October, 2024; originally announced October 2024.

Comments: 6 pages, 3 figures

Journal ref: Science China Physics, Mechanics & Astronomy 69, 227211 (2026)

Scaling analysis of quantum geometry in second-order nonlinear transport

Authors: Zhen-Hao Gong, Z. Z. Du, Hai-Peng Sun, Hai-Zhou Lu, X. C. Xie

Abstract: Quantum geometry encodes the structure of the Hilbert space of Bloch states and can be accessed through nonlinear transport. Yet, disorder-induced mechanisms generically contribute to nonlinear transport, making it difficult to isolate quantum-geometric contributions in experiments. Here we systematically enumerate geometric and disorder-induced mechanisms of the second-order nonlinear Hall effect… ▽ More Quantum geometry encodes the structure of the Hilbert space of Bloch states and can be accessed through nonlinear transport. Yet, disorder-induced mechanisms generically contribute to nonlinear transport, making it difficult to isolate quantum-geometric contributions in experiments. Here we systematically enumerate geometric and disorder-induced mechanisms of the second-order nonlinear Hall effect and derive a scaling law that expresses the nonlinear Hall conductivity as a polynomial of the linear longitudinal conductivity. Crucially, each mechanism carries a distinct "weight fingerprint" in the polynomial, enabling a quantitative disentanglement of quantum geometry from disorder backgrounds in existing experiments, both with and without time-reversal symmetry. Our results provide an implementable workflow for identifying quantum-geometric contributions in nonlinear-transport measurements. △ Less

Submitted 14 July, 2026; v1 submitted 7 October, 2024; originally announced October 2024.

Comments: 8 pages, 3 figures, 4 tables

Orbital-FFLO State and Josephson Vortex Lattice Melting in Layered Ising Superconductors

Authors: Hongyi Yan, Haiwen Liu, Yi Liu, Ding Zhang, X. C. Xie

Abstract: This study explores the impact of in-plane magnetic fields on the superconducting state in layered Ising superconductors, resulting in the emergence of the orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state coupled with Josephson vortices. Recent experiments have revealed an unexpected first-order phase transition in these superconductors under strong in-plane magnetic fields. Our theoretical a… ▽ More This study explores the impact of in-plane magnetic fields on the superconducting state in layered Ising superconductors, resulting in the emergence of the orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state coupled with Josephson vortices. Recent experiments have revealed an unexpected first-order phase transition in these superconductors under strong in-plane magnetic fields. Our theoretical analysis demonstrates that this phase transition is primarily driven by the formation and subsequent melting of a Josephson vortex lattice within the superconducting layers. As the magnetic field increases, the vortex lattice undergoes a transition from a solid to a liquid state, triggering the observed first-order phase transition. We calculate both the melting line and the in-plane critical field in the phase diagram, showing strong agreement with experimental results. △ Less

Submitted 30 September, 2024; originally announced September 2024.

The route of random process to ultraslow aging phenomena

Authors: Chunyan Li, Haiwen Liu, X. C. Xie

Abstract: Logarithmic aging phenomena are prevalent in various systems, including electronic materials and biological structures. This study utilizes a generalized continuous time random walk (CTRW) framework to investigate the mechanisms behind the logarithmic aging phenomena. By incorporating non-Markovian jump processes with significant memory effects, we modify traditional diffusion models to exhibit lo… ▽ More Logarithmic aging phenomena are prevalent in various systems, including electronic materials and biological structures. This study utilizes a generalized continuous time random walk (CTRW) framework to investigate the mechanisms behind the logarithmic aging phenomena. By incorporating non-Markovian jump processes with significant memory effects, we modify traditional diffusion models to exhibit logarithmic decay in both survival and return probabilities. In addition, we analyze the impact of aging on autocorrelation functions, illustrating how long-term memory behaviors affect the temporal evolution of physical properties. These results connect microscopic models to macroscopic manifestations in real-world systems, advancing the understanding of ultraslow dynamics in disordered systems. △ Less

Submitted 22 September, 2024; originally announced September 2024.

Quantum geometry in condensed matter

Authors: Tianyu Liu, Xiao-Bin Qiang, Hai-Zhou Lu, X. C. Xie

Abstract: One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of electrons in condensed matter can be characterized by the geometry of the Hilbert space of their wave functions. Such quantum geometry, comprising of Berry curvature… ▽ More One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of electrons in condensed matter can be characterized by the geometry of the Hilbert space of their wave functions. Such quantum geometry, comprising of Berry curvature and quantum metric, can thus exert profound influences on various properties of materials. The dipoles of both Berry curvature and quantum metric produce nonlinear transport. The quantum metric plays an important role in flat-band superconductors by enhancing the transition temperature. The uniformly distributed momentum-space quantum geometry stabilizes the fractional Chern insulators and results in the fractional quantum anomalous Hall effect. We here review in detail quantum geometry in condensed matter, paying close attention to its effects on nonlinear transport, superconductivity, and topological properties. Possible future research directions in this field are also envisaged. △ Less

Submitted 20 September, 2024; originally announced September 2024.

Comments: Review article accepted by National Science Review, unproofread; 17 pages, 8 figures, 1 table

Emergence of Nodal-Knot Transitions by Disorder

Authors: Ming Gong, Peng-Lu Zhao, Hai-Zhou Lu, Qian Niu, X. C. Xie

Abstract: Under certain symmetries, degenerate points in three-dimensional metals form one-dimensional nodal lines. These nodal lines sometimes exhibit intricate knotted structures and have been studied in various contexts. As one of the most common physical perturbations, disorder effects often trigger novel quantum phase transitions. For nodal-knot phases, whether disorder can drive knot transitions remai… ▽ More Under certain symmetries, degenerate points in three-dimensional metals form one-dimensional nodal lines. These nodal lines sometimes exhibit intricate knotted structures and have been studied in various contexts. As one of the most common physical perturbations, disorder effects often trigger novel quantum phase transitions. For nodal-knot phases, whether disorder can drive knot transitions remains an open and intriguing question. Employing renormalization-group calculations, we demonstrate that nodal-knot transitions emerge in the presence of weak disorder. Specifically, both chemical-potential-type and magnetic-type disorders can induce knot transitions, resulting in the emergence of distinct knot topologies. The transition can be quantitatively characterized by changes in topological invariants such as the knot Wilson loop integrals. Our findings open up a new avenue for manipulating the topology of nodal-knot phases through disorder effects. △ Less

Submitted 27 June, 2025; v1 submitted 2 September, 2024; originally announced September 2024.

Comments: 8 pages, 5 figures (+ Supplementary Materials 13 pages, 5 figures)

Journal ref: Science Bulletin, Volume 70, Issue 13, 15 July 2025, Pages 2088-2093