Showing 1–50 of 252 results for author: Held, K

Two distinct gap structures in the mid-infrared optical conductivity of the Hubbard model

Authors: Dongwook Kim, Karsten Held

Abstract: Mid-infrared (MIR) optical conductivities in cuprate superconductors show universal features. In this study, we demonstrate that these originate from two distinct gaps: the pseudogap mediated by antiferromagnetic spin fluctuations and the Mott-Hubbard gap. The MIR spectra from these two gaps show a characteristic and distinct shape and doping dependence, and can thus be distinguished. Specifically… ▽ More Mid-infrared (MIR) optical conductivities in cuprate superconductors show universal features. In this study, we demonstrate that these originate from two distinct gaps: the pseudogap mediated by antiferromagnetic spin fluctuations and the Mott-Hubbard gap. The MIR spectra from these two gaps show a characteristic and distinct shape and doping dependence, and can thus be distinguished. Specifically, the Mott-Hubbard correlations, while rendering a peak in the visible spectrum for small dopings, yield a broad optical response starting in the MIR when a ``waterfall'' develops in the one-particle spectrum at larger dopings. The numerically and analytically determined doping-dependence of both gaps consistently reproduce experiments, and provide a unified microscopic understanding of the cuprate MIR optical conductivity. △ Less

Submitted 21 August, 2026; originally announced August 2026.

Tuning crystal-fields by He-irradiation and orbital Widom line in SrVO$_3$ films

Authors: Matthias Pickem, Karsten Held, Jan M. Tomczak

Abstract: Helium-ion irradiation of epitaxial SrVO$_3$/SrTiO$_3$ films causes a metal-insulator transition, so far attributed to a Mott localization driven by a reduced kinetic energy. Using density-functional theory plus dynamical mean-field theory, we show that the driving mechanism is instead the crystal-field splitting generated by the irradiation-induced tetragonal expansion, not the interaction-to-ban… ▽ More Helium-ion irradiation of epitaxial SrVO$_3$/SrTiO$_3$ films causes a metal-insulator transition, so far attributed to a Mott localization driven by a reduced kinetic energy. Using density-functional theory plus dynamical mean-field theory, we show that the driving mechanism is instead the crystal-field splitting generated by the irradiation-induced tetragonal expansion, not the interaction-to-bandwidth ratio. The resulting $c$-axis vs. temperature phase diagram mirrors that of the one-band Hubbard model, but its critical end-point spawns an orbital Widom line, rooted in an anomalous compressibility of orbital, rather than charge occupation. At an effectively quarter filling, superexchange-like processes favor orbital over magnetic long-range order. Our results semi-quantitatively reproduce the fluence-dependent spectral gaps and transition thresholds reported experimentally, establishing ion implantation as a route to chemically expand correlated materials. △ Less

Submitted 14 August, 2026; originally announced August 2026.

Comments: 13 pages, 10 figures

Heterostructuring as Gateway to Electron Doping of Nickelate Superconductors

Authors: Chao Deng, Motoharu Kitatani, Guiwen Jiang, Siqi Guo, Niklas Witt, Ao Zhang, Wenfeng Wu, Mi Jiang, Karsten Held, Liang Si

Abstract: Despite enormous expenditures in the research field, the electron-doped side of nickelate superconductors remains uncharted territory. Substituting the trivalent rare-earth cations by a tetravalent one hitherto failed. Here, we demonstrate by first-principles calculations a disorder-free route to electron dope Ruddlesden-Popper nickelates. When intercalating wide-band-gap insulating layers such as… ▽ More Despite enormous expenditures in the research field, the electron-doped side of nickelate superconductors remains uncharted territory. Substituting the trivalent rare-earth cations by a tetravalent one hitherto failed. Here, we demonstrate by first-principles calculations a disorder-free route to electron dope Ruddlesden-Popper nickelates. When intercalating wide-band-gap insulating layers such as La$X$O$_3$ ($X$=Al, Ga, Sc) into La$_2$NiO$_4$, the extra (LaO)$^+$ layers act as electron donors, releasing carriers into the Ni-3$d$ orbitals. This electron doping puts La$_2$NiO$_4$:La$_2$AlO$_4$ naturally in the optimal region for $d_{x^2-y^2}$-wave superconductivity with T$_c$ exceeding 50 K. The same concept also allows us to electron dope La$_3$Ni$_2$O$_7$, the superconductor in the limelight. △ Less

Submitted 9 July, 2026; originally announced July 2026.

Comments: The main text spans 6 pages with 4 figures and 1 table, while the Supplemental Material contains 11 pages, 5 figures, and 3 tables. Accepted as an Editors' Suggestions in Physical Review Letters

Nodal superconductivity with spin-triplet component in a noncentrosymmetric weakly-correlated metal

Authors: Marcel Strohmeier, Andriy Smolyanyuk, Karsten Held, Michael Smidman, Geetha Balakrishnan, Wolfgang Belzig, Elke Scheer, Angelo Di Bernardo

Abstract: Although Cooper pairs in superconductors generally condense into a spin-singlet state, spin-triplet superconductivity has attracted sustained interest for dissipationless spin transport and topological quantum technologies. Noncentrosymmetric superconductors provide a promising route to triplet pairing because antisymmetric spin-orbit coupling (ASOC) can mix spin-singlet and spin-triplet states. T… ▽ More Although Cooper pairs in superconductors generally condense into a spin-singlet state, spin-triplet superconductivity has attracted sustained interest for dissipationless spin transport and topological quantum technologies. Noncentrosymmetric superconductors provide a promising route to triplet pairing because antisymmetric spin-orbit coupling (ASOC) can mix spin-singlet and spin-triplet states. To date, the strongest evidence for such mixed-parity superconductivity has been reported in heavy-fermion systems, where strong electronic correlations obscure the role of ASOC. Whether ASOC alone can support a substantial spin-triplet component therefore remains unresolved. Here we show that the weakly-correlated noncentrosymmetric superconductor Nb$_{18}$Re$_{82}$ (Nb-Re) hosts a mixed-parity superconducting state with a substantial spin-triplet contribution. Low-temperature scanning tunnelling spectroscopy on single crystals with different crystallographic orientations reveals distinct superconducting spectra. A symmetry-constrained analysis shows that the spectroscopic dataset is explained by an order parameter combining a nodal spin-singlet component with a spin-triplet contribution reaching up to half of the singlet amplitude. These findings resolve the debated pairing symmetry of Nb-Re and demonstrate that ASOC alone can foster triplet pairing. More broadly, they establish orientation-resolved tunnelling spectroscopy as a route to identifying mixed-parity superconducting states and suggest that triplet superconductivity may be more widespread among noncentrosymmetric materials than previously recognized. △ Less

Submitted 3 July, 2026; v1 submitted 3 June, 2026; originally announced June 2026.

Emergence of spin entanglement with the pseudogap onset in the Fermi-Hubbard model

Authors: Frederic Bippus, Thomas Chalopin, Gabriele Bellomia, Gergő Roósz, Titus Franz, Antoine Georges, Anna Kauch, Immanuel Bloch, Karsten Held

Abstract: Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator… ▽ More Despite decades of intense theoretical and experimental investigation, the two-dimensional Fermi-Hubbard model still resists a complete microscopic understanding. Conventional approaches typically probe global observables and locally resolved correlation functions. Here, we develop a complementary perspective based on the measurement of entanglement. Using both an ultracold-atom quantum simulator and numerical simulations based on the dynamical vertex approximation, we find that entanglement is closely tied to the onset of the enigmatic pseudogap regime: spin-singlet entanglement emerges only as the pseudogap sets in and, in contrast to classical correlations, remains confined to nearest-neighbour sites in this regime. Our results, therefore, disfavour purely classical-fluctuation theories of the pseudogap and constrain microscopic models to those that develop nearest-neighbour spin-singlet entanglement at the pseudogap onset. △ Less

Submitted 29 May, 2026; originally announced May 2026.

Comments: 8 figures, 34 pages

Beyond the conventional Emery model: crucial role of long-range hopping for cuprate superconductivity

Authors: Eric Jacob, M. O. Malcolms, Viktor Christiansson, Leonard M. Verhoff, Paul Worm, Liang Si, Philipp Hansmann, Thomas Schäfer, Karsten Held

Abstract: The Emery model is the quintessential model for cuprate superconductors. In his eponymous paper, Emery only considered the next-nearest-neighbor oxygen-copper hopping. Later, also the relevance of nearest- and next-nearest oxygen-oxygen hoppings has been pointed out. Using dynamical vertex approximation, we find a superconducting dome consistent with cuprates. However, long-range hoppings beyond t… ▽ More The Emery model is the quintessential model for cuprate superconductors. In his eponymous paper, Emery only considered the next-nearest-neighbor oxygen-copper hopping. Later, also the relevance of nearest- and next-nearest oxygen-oxygen hoppings has been pointed out. Using dynamical vertex approximation, we find a superconducting dome consistent with cuprates. However, long-range hoppings beyond the three conventional hopping parameters are necessary for the quantitatively correct phase diagram and for a proper d-wave order parameter. △ Less

Submitted 8 May, 2026; originally announced May 2026.

Comments: 4 pages, 4 figures, 2 tables

Symmetric estimator for discrete self-energy of discrete many-body systems

Authors: Aleksandrs Zacinskis, Frank T. Ebel, Mathias Pelz, Fabian B. Kugler, Karsten Held, Jan von Delft, Maurits W. Haverkort, Andreas Gleis

Abstract: We derive a discrete spectral representation of the single-particle self-energy using a discrete evaluation of Kugler's symmetric improved estimator. Our construction can be used on both the real and the complex (Matsubara) frequency axis. It is guaranteed to remain causal at the numerical level, in contrast to standard approaches that may generate unphysical negative spectral weight or require ad… ▽ More We derive a discrete spectral representation of the single-particle self-energy using a discrete evaluation of Kugler's symmetric improved estimator. Our construction can be used on both the real and the complex (Matsubara) frequency axis. It is guaranteed to remain causal at the numerical level, in contrast to standard approaches that may generate unphysical negative spectral weight or require additional broadening. Our representation can be used for any Hamiltonian; here we apply it to quantum impurity models and in dynamical mean-field theory. The latter is formulated with a discrete hybridization function throughout its self-consistency loop. In both cases and across various numerical methods, we obtain significantly improved accuracy for a range of impurity properties. △ Less

Submitted 6 May, 2026; originally announced May 2026.

Unconventional plasmon dynamics due to strong correlations in Sr$_2$RuO$_4$

Authors: Juraj Krsnik, Dino Novko, Fabian B. Kugler, Osor S. Barišić, Karsten Held

Abstract: Plasmon modes, their dispersion, and the onset of damping when approaching the electron-hole continuum are well understood when electron correlations are weak. However, we know little about how this picture is modified and what additional features emerge in strongly correlated materials. Here, we present a fully ab initio approach to plasmon excitations that combines density functional theory with… ▽ More Plasmon modes, their dispersion, and the onset of damping when approaching the electron-hole continuum are well understood when electron correlations are weak. However, we know little about how this picture is modified and what additional features emerge in strongly correlated materials. Here, we present a fully ab initio approach to plasmon excitations that combines density functional theory with dynamical mean-field theory, and we use it to reconcile controversial electron energy-loss spectroscopy results in Sr$_2$RuO$_4$. In particular, we show that electronic correlations reproduce the plasmon dispersion, while generating a large intrinsic width already below the electron-hole continuum. An additional high-energy peak reflecting transitions between incoherent features and a sharp increase of the plasmon's energy-momentum dispersion, akin to waterfalls in photoemission spectroscopy, are identified as genuine correlation effects. △ Less

Submitted 16 April, 2026; originally announced April 2026.

Comments: 5+10 pages, 4+8 figures

Substrate and cation engineering for optimizing superconductivity in infinite-layer nickelates

Authors: Viktor Christiansson, Karsten Held

Abstract: In a recent experiment [Nature 642, 58 (2025)], a new record for the superconducting critical temperature $T_c$ among infinite-layer nickelates has been reported in doped SmNiO$_2$. Here, we use the cutting-edge dynamical vertex approximation (D$Γ$A), and qualitatively as well as quantitatively reproduce the $T_c$ vs. doping dome for this compound. Encouraged by this, we go further and identify a… ▽ More In a recent experiment [Nature 642, 58 (2025)], a new record for the superconducting critical temperature $T_c$ among infinite-layer nickelates has been reported in doped SmNiO$_2$. Here, we use the cutting-edge dynamical vertex approximation (D$Γ$A), and qualitatively as well as quantitatively reproduce the $T_c$ vs. doping dome for this compound. Encouraged by this, we go further and identify a path towards realizing even higher $T_c$'s by changing the cation along the line Nd$\rightarrow$Sm$\rightarrow$Y$\rightarrow$Lu with matching substrates. The successively smaller cation radius allows for smaller lattice constants of the substrate. This in turn increases the in-plane hopping and thus eventually $T_c$. △ Less

Submitted 23 December, 2025; originally announced December 2025.

Surfaces and interfaces of infinite-layer nickelates studied by dynamical mean-field theory

Authors: Leonard M. Verhoff, Liang Si, Karsten Held

Abstract: Infinite-layer nickelate superconductors are typically synthesized as thin films and thus include, besides the more bulk-like inner layers, distinct surface and interface layers in contact with the vacuum and substrate, respectively. Here, we employ density-functional theory and dynamical mean-field theory to investigate how electronic correlations influence these surface and interface regions. Ou… ▽ More Infinite-layer nickelate superconductors are typically synthesized as thin films and thus include, besides the more bulk-like inner layers, distinct surface and interface layers in contact with the vacuum and substrate, respectively. Here, we employ density-functional theory and dynamical mean-field theory to investigate how electronic correlations influence these surface and interface regions. Our results show that electronic correlations can significantly modify the electronic structure, even driving surface layers into a Mott-insulating state with a 3$d^8$ electronic configuration. Moreover, surface termination effects induce a polar field that can shift the $Γ$ and $A$ pocket above the Fermi level, even for the undoped parent compound NdNiO$_2$. Finally, for an $n$-type interface, often synthesized experimentally, we find the Ti 3$d$ orbitals to become electron doped. △ Less

Submitted 25 November, 2025; v1 submitted 11 September, 2025; originally announced September 2025.

Lattice dynamics of the infinite-layer nickelate LaNiO$_2$

Authors: Shohei Hayashida, Vignesh Sundaramurthy, Wenfeng Wu, Pascal Puphal, Thomas Keller, Björn Fåk, Masahiko Isobe, Bernhard Keimer, Karsten Held, Liang Si, Matthias Hepting

Abstract: Infinite-layer (IL) nickelates have rapidly emerged as a new class of superconductors. However, due to the technical challenges of their topotactic synthesis, they have so far been realized primarily as thin films or polycrystalline powder samples, limiting comprehensive investigations of fundamental physical properties such as the lattice dynamics. Here, we present a time-of-flight inelastic neut… ▽ More Infinite-layer (IL) nickelates have rapidly emerged as a new class of superconductors. However, due to the technical challenges of their topotactic synthesis, they have so far been realized primarily as thin films or polycrystalline powder samples, limiting comprehensive investigations of fundamental physical properties such as the lattice dynamics. Here, we present a time-of-flight inelastic neutron scattering study on a sample composed of a large number of co-aligned bulk crystals of the IL nickelate LaNiO$_2$. We observe several dispersive phonon branches, which are in good agreement with lattice dynamical calculations based on density-functional perturbation theory. In addition, we compare the characteristics of selected LaNiO$_2$ phonon modes to those of isostructural cuprate superconductors. Our findings provide a reference point for future experimental and theoretical efforts aimed at understanding the interplay between lattice dynamics and electronic properties in IL nickelates. △ Less

Submitted 6 November, 2025; v1 submitted 3 September, 2025; originally announced September 2025.

Comments: 10 pages, 4 figures with supplemental materials

Journal ref: Phys. Rev. B 112, 205104 (2025)

Entanglement across scales: Quantics tensor trains as a natural framework for renormalization

Authors: Stefan Rohshap, Jheng-Wei Li, Alena Lorenz, Serap Hasil, Karsten Held, Anna Kauch, Markus Wallerberger

Abstract: Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information exchange between different length scales, has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-insp… ▽ More Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information exchange between different length scales, has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-inspired approach for overcoming computational bottlenecks in resource-intensive numerical calculations, as a renormalization group method by analytically expressing an exact cyclic reduction-based real-space renormalization scheme in QTT language, which serves as a natural formalism for the method. In doing so, we precisely match the QTT bond dimension, a measure of length scale entanglement, to the number of rescaled couplings generated in each coarse-graining renormalization step. While QTTs have so far been applied almost exclusively to numerical problems in physics, our analytical calculations demonstrate that they are also powerful tools for mitigating computational costs in semi-analytical treatments. We present our results for the one-dimensional tight-binding model with n-th-nearest-neighbor hopping, where the 2n rescaled couplings generated in the renormalization procedure precisely match the QTT bond dimension of the one-particle Green's function. △ Less

Submitted 18 December, 2025; v1 submitted 25 July, 2025; originally announced July 2025.

Comments: 33 pages (16 pages without appendix), 15 figures

Journal ref: Phys. Rev. Research 7, 043313 (2025)

Weyl nodes in CeRu$_4$Sn$_6$ studied by dynamical mean-field theory

Authors: Jorūnas Dobilas, Martin Brass, Frank T. Ebel, Silke Paschen, Karsten Held

Abstract: The heavy fermion compound CeRu$_4$Sn$_6$ was recently shown to exhibit a spontaneous nonlinear Hall effect, indicating its topological nature. This is consistent with the lack of inversion symmetry that allows for the existence of Weyl nodes. Here, we employ density functional theory combined with dynamical mean-field theory, which is state-of-the-art for strongly correlated materials, and study… ▽ More The heavy fermion compound CeRu$_4$Sn$_6$ was recently shown to exhibit a spontaneous nonlinear Hall effect, indicating its topological nature. This is consistent with the lack of inversion symmetry that allows for the existence of Weyl nodes. Here, we employ density functional theory combined with dynamical mean-field theory, which is state-of-the-art for strongly correlated materials, and study the topology of CeRu$_4$Sn$_6$. We find five inequivalent Weyl nodes of either type I or II, each having either eight or sixteen symmetry-related replicas. These Weyl nodes bridge the Kondo insulating gap, which is a direct but not an indirect gap. The Weyl points closest to the Fermi level are situated only 0.5 meV below it, and have a very flat dispersion. Our ab initio results establish CeRu$_4$Sn$_6$ as a model system for investigating the interplay between strong electronic correlations and nontrivial topology. These findings provide a theoretical foundation for future studies of quantum transport and interaction-driven topological phases in heavy-fermion systems. △ Less

Submitted 26 August, 2025; v1 submitted 17 July, 2025; originally announced July 2025.

Comments: 11 pages, 9 figures

Diagnosing phase transitions through time-scale entanglement

Authors: Stefan Rohshap, Hirone Ishida, Frederic Bippus, Leonard M. Verhoff, Anna Kauch, Karsten Held, Hiroshi Shinaoka, Markus Wallerberger

Abstract: Spatial entanglement of quantum states has become a central paradigm of many-body physics. Here, we unearth a fundamentally different form of entanglement, the entanglement between imaginary time scales. This time-scale entanglement is accessible through quantics tensor train diagnostics (QTTD), where the bond dimension of an $n$-particle correlator encodes the coupling between temporal scales. Ou… ▽ More Spatial entanglement of quantum states has become a central paradigm of many-body physics. Here, we unearth a fundamentally different form of entanglement, the entanglement between imaginary time scales. This time-scale entanglement is accessible through quantics tensor train diagnostics (QTTD), where the bond dimension of an $n$-particle correlator encodes the coupling between temporal scales. Our central result is that time-scale entanglement is generically enhanced in the vicinity of phase transitions and crossovers. At quantum critical points, it becomes scale-invariant. We demonstrate time-scale entanglement across a range of systems, including finite-size Hubbard rings, the transverse-field Ising model, the single-impurity Anderson model, and the Mott transition in the Hubbard model. Remarkably, the enhanced time-scale entanglement is largely independent of the specific observable, establishing QTTD as a universal and unbiased diagnostic of criticality. △ Less

Submitted 11 May, 2026; v1 submitted 15 July, 2025; originally announced July 2025.

Two-site entanglement in the two-dimensional Hubbard model

Authors: Frederic Bippus, Anna Kauch, Gergő Roósz, Christian Mayrhofer, Fakher Assaad, Karsten Held

Abstract: The study of entanglement in strongly correlated electron systems typically requires knowledge of the reduced density matrix. Here, we apply the parquet dynamical vertex approximation to study the two-site reduced density matrix at varying distance, in the Hubbard model at weak coupling. This allows us to investigate the spatial structure of entanglement in dependence of interaction strength, elec… ▽ More The study of entanglement in strongly correlated electron systems typically requires knowledge of the reduced density matrix. Here, we apply the parquet dynamical vertex approximation to study the two-site reduced density matrix at varying distance, in the Hubbard model at weak coupling. This allows us to investigate the spatial structure of entanglement in dependence of interaction strength, electron filling, and temperature. We compare results from different entanglement measures, and benchmark against quantum Monte Carlo. △ Less

Submitted 27 January, 2026; v1 submitted 11 June, 2025; originally announced June 2025.

Comments: 21 pages, 12 figures

Topotactical Hydrogen Induced Single-Band $d$-wave Superconductivity in La$_2$NiO$_4$

Authors: Ying Gao, Wenfeng Wu, Zhaoxin Liu, Karsten Held, Liang Si

Abstract: La$_2$NiO$_4$ is an antiferromagnetic insulator with a structural resemblance to its cuprate counterpart, La$_2$CuO$_4$. However, La$_2$CuO$_4$ has a Cu$^{2+}$ or 3$d^9$ electronic configuration that needs to be hole or electron doped for superconductivity, whereas La$_2$NiO$_4$ is 3$d^8$ with divalent Ni$^{2+}$. Making a cuprate analog through conventional electron doping is impractical due to th… ▽ More La$_2$NiO$_4$ is an antiferromagnetic insulator with a structural resemblance to its cuprate counterpart, La$_2$CuO$_4$. However, La$_2$CuO$_4$ has a Cu$^{2+}$ or 3$d^9$ electronic configuration that needs to be hole or electron doped for superconductivity, whereas La$_2$NiO$_4$ is 3$d^8$ with divalent Ni$^{2+}$. Making a cuprate analog through conventional electron doping is impractical due to the rarity of tetravalent substituents for trivalent La. Here, we propose an alternative route: intercalating topotactical hydrogen, which is possible through electric-field-controlled protonation and transforms La$_2$NiO$_4$ into a 3$d_{x^2-y^2}$ single-band two-dimensional antiferromagnetic Mott insulator analogous to La$_2$CuO$_4$. This we find through density-functional theory and dynamical mean-field theory calculations. The furthergoing dynamical vertex approximation predicts that H-La$_2$NiO$_4$ can host $d$-wave superconductivity under 15\% hole doping with a critical temperature above 20\,K. Our findings not only suggest a new method for tuning the electronic structure of layered nickelates but also provide theoretical evidence for a new nickelate superconductor, awaiting experimental synthesis. △ Less

Submitted 26 July, 2025; v1 submitted 30 April, 2025; originally announced April 2025.

Comments: 8 pages, 4 figures, 1 table

Journal ref: Phys. Rev. Lett. 135, 026002 (2025)

Entanglement in the pseudogap regime of cuprate superconductors

Authors: Frederic Bippus, Juraj Krsnik, Motoharu Kitatani, Luka Akšamović, Anna Kauch, Neven Barišić, Karsten Held

Abstract: We find a strongly enhanced entanglement within the pseudogap regime of the Hubbard model. This entanglement is estimated from the quantum Fisher information and, avoiding the ill-conditioned analytical continuation, the quantum variance. Both are lower bounds for the actual entanglement that can be calculated from the (antiferromagnetic) susceptibility, obtained here with the dynamical vertex app… ▽ More We find a strongly enhanced entanglement within the pseudogap regime of the Hubbard model. This entanglement is estimated from the quantum Fisher information and, avoiding the ill-conditioned analytical continuation, the quantum variance. Both are lower bounds for the actual entanglement that can be calculated from the (antiferromagnetic) susceptibility, obtained here with the dynamical vertex approximation. Our results qualitatively agree with experimental neutron scattering experiments for various cuprates. Theory predicts a $\ln(1/T)$ divergence of the entanglement for low temperatures $T$, which is however cut-off by the onset of superconductivity. △ Less

Submitted 22 August, 2025; v1 submitted 16 March, 2025; originally announced March 2025.

Comments: 13 pages, 11 figures

Two distinct quantum critical behaviors in the doped two-dimensional periodic Anderson model

Authors: M. Kitatani, T. Schäfer, A. A. Katanin, A. Toschi, K. Held

Abstract: We study quantum criticality in the doped two-dimensional periodic Anderson model with the hybridization acting as a tuning parameter. Employing the dynamical vertex approximation we find two distinct quantum critical behaviors. One is a quantum critical point between the antiferromagnetically ordered and the Kondo state, both metallic with itinerant $f$ electrons. Here, we obtained the critical e… ▽ More We study quantum criticality in the doped two-dimensional periodic Anderson model with the hybridization acting as a tuning parameter. Employing the dynamical vertex approximation we find two distinct quantum critical behaviors. One is a quantum critical point between the antiferromagnetically ordered and the Kondo state, both metallic with itinerant $f$ electrons. Here, we obtained the critical exponent $γ\approx 1$ for the temperature dependence of the antiferromagnetic susceptibility. We observe a \emph{second} quantum critical behavior with $γ=2$ above the continuing zero-temperature magnetic order, at a quantum critical point where the $f$ electrons turn from localized to itinerant. △ Less

Submitted 12 March, 2025; originally announced March 2025.

Comments: 6+2 pages, 4+2 figures

Superconducting phase diagram of finite-layer nickelates Nd$_{n+1}$Ni$_n$O$_{2n+2}$

Authors: Andreas Hausoel, Simone Di Cataldo, Motoharu Kitatani, Oleg Janson, Karsten Held

Abstract: Following the successful prediction of the superconducting phase diagram for infinite-layer nickelates, here we calculate the superconducting $T_{\mathrm{c}}$ vs. the number of layers $n$ for finite-layer nickelates using the dynamical vertex approximation. To this end, we start with density functional theory, and include local correlations non-perturbatively by dynamical mean-field theory for… ▽ More Following the successful prediction of the superconducting phase diagram for infinite-layer nickelates, here we calculate the superconducting $T_{\mathrm{c}}$ vs. the number of layers $n$ for finite-layer nickelates using the dynamical vertex approximation. To this end, we start with density functional theory, and include local correlations non-perturbatively by dynamical mean-field theory for $n=2$ to 7. For all $n$, the Ni $d_{x^2-y^2}$ orbital crosses the Fermi level, but for $n>4$ there are additional $(π, π)$ pockets or tubes that slightly enhance the layer-averaged hole doping of the $d_{x^2-y^2}$ orbitals beyond the leading $1/n$ contribution stemming from the valence electron count. We finally calculate $T_{\mathrm{c}}$ for the single-orbital $d_{x^2-y^2}$ Hubbard model by dynamical vertex approximation. △ Less

Submitted 21 July, 2025; v1 submitted 17 February, 2025; originally announced February 2025.

Comments: 6 pages + supplemental material

Journal ref: npj Quantum Mater. 10, 69 (2025)

Energy filtering-induced ultrahigh thermoelectric power factors in Ni$_3$Ge

Authors: Fabian Garmroudi, Simone Di Cataldo, Michael Parzer, Jennifer Coulter, Yutaka Iwasaki, Matthias Grasser, Simon Stockinger, Stephan Pázmán, Sandra Witzmann, Alexander Riss, Herwig Michor, Raimund Podloucky, Sergii Khmelevskyi, Antoine Georges, Karsten Held, Takao Mori, Ernst Bauer, Andrej Pustogow

Abstract: Traditional thermoelectric materials rely on low thermal conductivity to enhance their efficiency but suffer from inherently limited power factors. Novel pathways to optimize electronic transport are thus crucial. Here, we achieve ultrahigh power factors in Ni$_3$Ge through a new materials design principle. When overlapping flat and dispersive bands are engineered to the Fermi level, charge carrie… ▽ More Traditional thermoelectric materials rely on low thermal conductivity to enhance their efficiency but suffer from inherently limited power factors. Novel pathways to optimize electronic transport are thus crucial. Here, we achieve ultrahigh power factors in Ni$_3$Ge through a new materials design principle. When overlapping flat and dispersive bands are engineered to the Fermi level, charge carriers can undergo intense interband scattering, yielding an energy filtering effect similar to what has long been predicted in certain nanostructured materials. Via a multi-step DFT-based screening method developed herein, we discover a new family of L1$_2$-ordered binary compounds with ultrahigh power factors up to 11 mW m$^{-1}$ K$^{-2}$ near room temperature, which are driven by an intrinsic phonon-mediated energy filtering mechanism. Our comprehensive experimental and theoretical study of these new intriguing materials paves the way for understanding and designing high-performance scattering-tuned metallic thermoelectrics. △ Less

Submitted 8 January, 2025; originally announced January 2025.

Rise and Fall of the Pseudogap in the Emery model: Insights for Cuprates

Authors: M. O. Malcolms, Henri Menke, Yi-Ting Tseng, Eric Jacob, Karsten Held, Philipp Hansmann, Thomas Schäfer

Abstract: The pseudogap in high-temperature superconducting cuprates is an exotic state of matter, displaying emerging Fermi arcs and a momentum-selective suppression of states upon cooling. We show how these phenomena are originating in the three-band Emery model by performing cutting-edge dynamical vertex approximation calculations for its normal state. For the hole-doped parent compound our results demon… ▽ More The pseudogap in high-temperature superconducting cuprates is an exotic state of matter, displaying emerging Fermi arcs and a momentum-selective suppression of states upon cooling. We show how these phenomena are originating in the three-band Emery model by performing cutting-edge dynamical vertex approximation calculations for its normal state. For the hole-doped parent compound our results demonstrate the formation of a pseudogap due to short-ranged commensurate antiferromagnetic fluctuations. At larger doping values, progressively, incommensurate correlations and a metallic regime appear. Our results are in qualitative agreement with the normal state of cuprates, and, hence, represent a crucial step towards the uniform description of their phase diagrams within a single theoretical framework. △ Less

Submitted 31 January, 2025; v1 submitted 19 December, 2024; originally announced December 2024.

Comments: 8 pages, 4 figures; Supplemental Material: 10 pages, 7 figures

Ladder equation for the three-particle vertex and its approximate solution

Authors: Patrick Kappl, Tin Ribic, Anna Kauch, Karsten Held

Abstract: We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels. However, as we do not have this three-particle irreducible vertex at hand, we approximate this building block for the ladder by the sum of two-particle irreducib… ▽ More We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels. However, as we do not have this three-particle irreducible vertex at hand, we approximate this building block for the ladder by the sum of two-particle irreducible vertices each connecting two fermionic lines. The comparison to the exact solution shows that this approximation is only good for rather weak interactions and even than only qualitatively - at least for the non-linear response function analyzed. △ Less

Submitted 27 November, 2024; originally announced December 2024.

Comments: 20 pages, 23 figures + Supplemental Material

Boosting the transparency of metallic SrNbO3 through Ti doping

Authors: Shammi Kumar, Liang Si, Karsten Held, Sankar Dhar, Rakesh Kumar, Priya Johari

Abstract: In recent years, various materials have been developed to reduce the reliance of industries on Indium, a primary component of transparent conducting oxides (TCOs) used in the current generation of devices. The leading candidates for indium free TCOs are strontium vanadates, niobates and molybdates -- strongly correlated perovskite systems that exhibit high intrinsic electrical conductivity and opt… ▽ More In recent years, various materials have been developed to reduce the reliance of industries on Indium, a primary component of transparent conducting oxides (TCOs) used in the current generation of devices. The leading candidates for indium free TCOs are strontium vanadates, niobates and molybdates -- strongly correlated perovskite systems that exhibit high intrinsic electrical conductivity and optimal transparency. In this work, we focus on the strontium niobate thin films and manipulate its optical conductivity by Ti doping, which shifts the plasma frequency and reduces electronic correlations. This allows us to achieve a low resistance for Ti doped SNO thin films, while maintaining a high transparency in the visible spectrum. We obtain the optimal figure-of-merit (FOM) of 10.3 ($10^{-3}Ω^{-1}$) for $x = 0.3$. This FOM significantly outperforms the optoelectronic capabilities of Tin-doped Indium oxide (ITO) and several other proposed transparent conductor materials. Our research paves the way for designing the next generation of transparent conductors, guided by insights from density-functional theory (DFT) and dynamical mean-field theory (DMFT). △ Less

Submitted 4 October, 2024; originally announced October 2024.

Comments: 35 pages, 14 figure including supplementary figures

Pairing boost from enhanced spin-fermion coupling in the pseudogap regime

Authors: Yang Yu, Sergei Iskakov, Emanuel Gull, Karsten Held, Friedrich Krien

Abstract: We perform a fluctuation analysis of the pairing interaction in the hole-doped Hubbard model within the dynamical cluster approximation. Our analysis reveals that spin-fluctuation-mediated pairing differs qualitatively in the over- and underdoped regimes. In the underdoped regime, spin fluctuations open a pseudogap. We show that in this regime the spin-fermion coupling mediates a giant attraction… ▽ More We perform a fluctuation analysis of the pairing interaction in the hole-doped Hubbard model within the dynamical cluster approximation. Our analysis reveals that spin-fluctuation-mediated pairing differs qualitatively in the over- and underdoped regimes. In the underdoped regime, spin fluctuations open a pseudogap. We show that in this regime the spin-fermion coupling mediates a giant attraction between antinodal fermions. This explains why superconductivity survives at underdoping in the Hubbard model and cuprates, despite the lack of coherent fermionic quasiparticles in the pseudogap regime. △ Less

Submitted 1 July, 2025; v1 submitted 2 October, 2024; originally announced October 2024.

Comments: 7 pages, 2 figures

Journal ref: Phys. Rev. B 112, L041105 (2025)

Analytical expression for $π$-ton vertex contributions to the optical conductivity

Authors: Juraj Krsnik, Anna Kauch, Karsten Held

Abstract: Vertex corrections from the transversal particle-hole channel, so-called $π$-tons, are generic in models for strongly correlated electron systems and can lead to a displaced Drude peak (DDP). Here, we derive the analytical expression for these $π$-tons, and how they affect the optical conductivity as a function of correlation length $ξ$, fermion lifetime $τ$, temperature $T$, and coupling strength… ▽ More Vertex corrections from the transversal particle-hole channel, so-called $π$-tons, are generic in models for strongly correlated electron systems and can lead to a displaced Drude peak (DDP). Here, we derive the analytical expression for these $π$-tons, and how they affect the optical conductivity as a function of correlation length $ξ$, fermion lifetime $τ$, temperature $T$, and coupling strength to spin or charge fluctuations $g$. In particular, for $T\rightarrow T_c$, the critical temperature for antiferromagnetic or charge ordering, the dc vertex correction is algebraic $σ_{VERT}^{dc}\propto ξ\sim (T-T_c)^{-ν}$ in one dimension and logarithmic $σ_{VERT}^{dc}\propto \lnξ\sim ν\ln (T-T_c)$ in two dimensions. Here, $ν$ is the critical exponent for the correlation length. If we have the exponential scaling $ξ\sim e^{1/T}$ of an ideal two-dimensional system, the DDP becomes more pronounced with increasing $T$ but fades away at low temperatures where only a broadening of the Drude peak remains, as it is observed experimentally, with the dc resistivity exhibiting a linear $T$ dependence at low temperatures. Further, we find the maximum of the DPP to be given by the inverse lifetime: $ω_{DDP} \sim 1/τ$. These characteristic dependencies can guide experiments to evidence $π$-tons in actual materials. △ Less

Submitted 28 April, 2025; v1 submitted 17 September, 2024; originally announced September 2024.

Comments: 27 pages, 7 figures

Magnetic quantum criticality: The role of the Fermi surface geometry

Authors: D. R. Fus, S. Adler, M. O. Malcolms, A. Vock, K. Held, A. A. Katanin, T. Schäfer, A. Toschi

Abstract: We investigate magnetic quantum phase-transitions in bulk correlated metals. To this end, we focus on the Hubbard model on different cubic lattices as a function of temperature and electronic density, determining the relevant regimes around its quantum magnetic transition, i.e. classical, quantum critical, and quantum disordered, as well as the corresponding (thermal/non-thermal) quantum critical… ▽ More We investigate magnetic quantum phase-transitions in bulk correlated metals. To this end, we focus on the Hubbard model on different cubic lattices as a function of temperature and electronic density, determining the relevant regimes around its quantum magnetic transition, i.e. classical, quantum critical, and quantum disordered, as well as the corresponding (thermal/non-thermal) quantum critical exponents. Our numerical results, based on dynamical mean-field theory, together with supporting analytical derivations, rigorously demonstrate how and why the presence of different kinds of Kohn anomalies on the underlying Fermi surface (i) drives the quantum critical behavior above the quantum critical point and (ii) shapes the whole phase diagram around it. Our findings highlight the importance of an explicit inclusion of such Fermi surface geometrical properties into the universality class definition for magnetic quantum phase-transitions in correlated metals. △ Less

Submitted 2 August, 2026; v1 submitted 6 September, 2024; originally announced September 2024.

Comments: 8 pages (including references) + 2 pages of (newly added) End Matter section, 4 figures

Closing in on possible scenarios for infinite-layer nickelates: comparison of dynamical mean-field theory with angular-resolved photoemission spectroscopy

Authors: Liang Si, Eric Jacob, Wenfeng Wu, Andreas Hausoel, Juraj Krsnik, Paul Worm, Simone Di Cataldo, Oleg Janson, Karsten Held

Abstract: Conflicting theoretical scenarios for infinite-layer nickelate superconductors have been hotly debated, particularly regarding whether {only} a single Ni-3$d_{x^2-y^2}$ band is relevant at low energies besides electron pockets or whether multi-orbital physics including Ni-3$d_{z^2}$ is instead essential. The first scenario has emerged from density-functional theory plus dynamical mean-field theory… ▽ More Conflicting theoretical scenarios for infinite-layer nickelate superconductors have been hotly debated, particularly regarding whether {only} a single Ni-3$d_{x^2-y^2}$ band is relevant at low energies besides electron pockets or whether multi-orbital physics including Ni-3$d_{z^2}$ is instead essential. The first scenario has emerged from density-functional theory plus dynamical mean-field theory (DFT+DMFT) calculations. Comparing the previous DFT+DMFT spectra to recent angular-resolved photoemission spectroscopy (ARPES) experiments, we find excellent agreement for both the Fermi surface and the strongly renormalized quasi-particle bands, supporting the first scenario. Our key findings further suggest that the "waterfalls" observed in ARPES might emerge from the quasi-particle--to--Hubbard-band crossover, and that additional spectral weight close to the $A$-pocket {likely} originates from the Ni-3$d_{xy}$ orbital. △ Less

Submitted 24 November, 2024; v1 submitted 23 August, 2024; originally announced August 2024.

Comments: 8 pages, 4 figures

Journal ref: Phys. Rev. Research 6, 043104 (2024)

Local correlations necessitate waterfalls as a connection between quasiparticle band and developing Hubbard bands

Authors: Juraj Krsnik, Karsten Held

Abstract: Waterfalls are anomalies in the angle-resolved photoemission spectrum where the energy-momentum dispersion is almost vertical, and the spectrum strongly smeared out. These anomalies are observed at relatively high energies, among others, in superconducting cuprates and nickelates. The prevalent understanding is that they originate from the coupling to some boson, with spin fluctuations and phonons… ▽ More Waterfalls are anomalies in the angle-resolved photoemission spectrum where the energy-momentum dispersion is almost vertical, and the spectrum strongly smeared out. These anomalies are observed at relatively high energies, among others, in superconducting cuprates and nickelates. The prevalent understanding is that they originate from the coupling to some boson, with spin fluctuations and phonons being the usual suspects. Here, we show that waterfalls occur naturally in the process where a Hubbard band develops and splits off from the quasiparticle band. Our results for the Hubbard model with $\textit{ab initio}$ determined parameters well agree with waterfalls in cuprates and nickelates, providing a natural explanation for these spectral anomalies observed in correlated materials. △ Less

Submitted 7 November, 2024; v1 submitted 23 August, 2024; originally announced August 2024.

Comments: 7 pages, 4 figures, 1 mp4 file, Supplementary Information contains comparisons of DMFT and D$Γ$A

Embedded multi-boson exchange: A step beyond quantum cluster theories

Authors: Dominik Kiese, Nils Wentzell, Igor Krivenko, Olivier Parcollet, Karsten Held, Friedrich Krien

Abstract: We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the length scale of the cluster, while long-ranged correlations are recovered from a set of diagrammatic equations for the Hedin three-leg vertex. By virtue of the… ▽ More We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the length scale of the cluster, while long-ranged correlations are recovered from a set of diagrammatic equations for the Hedin three-leg vertex. By virtue of the crossing symmetry, the Fierz decoupling ambiguity of the Hubbard interaction is resolved exactly. Our benchmarks for the half-filled Hubbard model on the square lattice are in very good agreement with numerically exact diagrammatic Monte Carlo simulations. △ Less

Submitted 21 June, 2024; originally announced June 2024.

Comments: 16 pages, 14 figures

Weyl nodes in Ce$_3$Bi$_4$Pd$_3$ revealed by dynamical mean-field theory

Authors: Martin Braß, Jan M. Tomczak, Karsten Held

Abstract: Experimental studies have found unusual transport properties in Ce$_3$Bi$_4$Pd$_3$ which are potentially a consequence of the interplay between band-structure topology and electronic correlations. Based on these measurements, the existence of Weyl points in strongly renormalized, flat quasiparticle bands has been postulated. However, so far, there has been neither a direct spectroscopic observatio… ▽ More Experimental studies have found unusual transport properties in Ce$_3$Bi$_4$Pd$_3$ which are potentially a consequence of the interplay between band-structure topology and electronic correlations. Based on these measurements, the existence of Weyl points in strongly renormalized, flat quasiparticle bands has been postulated. However, so far, there has been neither a direct spectroscopic observation of these, nor a calculation from first principles that would confirm their existence close to the Fermi energy. Here, we present density functional theory (DFT) and dynamical mean field theory (DMFT) calculations and study the low-energy excitations and their topological properties. We find that the Kondo effect promotes two out of the six angular momentum $J=5/2$ states, with the other four pushed to higher energies. Further, we find Weyl nodes close to the Fermi energy as previously suggested for explaining the observed giant spontaneous Hall effect in Ce$_3$Bi$_4$Pd$_3$, as well as nodal lines. △ Less

Submitted 26 April, 2024; originally announced April 2024.

High thermoelectric power factor through topological flat bands

Authors: Fabian Garmroudi, Illia Serhiienko, Simone Di Cataldo, Michael Parzer, Alexander Riss, Matthias Grasser, Simon Stockinger, Sergii Khmelevskyi, Kacper Pryga, Bartlomiej Wiendlocha, Karsten Held, Takao Mori, Ernst Bauer, Andrej Pustogow

Abstract: Thermoelectric (TE) materials are useful for applications such as waste heat harvesting or efficient and targeted cooling. While various strategies towards superior thermoelectrics through a reduction of the lattice thermal conductivity have been developed, a path to enhance the power factor is pressing. Here, we report large power factors up to 5 mW m$^{-1}$ K$^{-2}$ at room temperature in the ka… ▽ More Thermoelectric (TE) materials are useful for applications such as waste heat harvesting or efficient and targeted cooling. While various strategies towards superior thermoelectrics through a reduction of the lattice thermal conductivity have been developed, a path to enhance the power factor is pressing. Here, we report large power factors up to 5 mW m$^{-1}$ K$^{-2}$ at room temperature in the kagome metal Ni$_3$In$_{1-x}$Sn$_x$. This system is predicted to feature almost dispersionless flat bands in conjunction with highly dispersive Dirac-like bands in its electronic structure around the Fermi energy $E_\text{F}$ [L. Ye et al., Nature Physics 1-5 (2024)]. Within this study, we experimentally and theoretically showcase that tuning this flat band precisely below $E_\text{F}$ by chemical doping $x$ boosts the Seebeck coefficient and power factor, as highly mobile charge carriers scatter into the flat-band states. Our work demonstrates the prospect of engineering extremely flat and highly dispersive bands towards the Fermi energy in kagome metals and introduces topological flat bands as a novel tuning knob for thermoelectrics. △ Less

Submitted 11 April, 2024; originally announced April 2024.

Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions

Authors: Selina Dirnböck, Seung-Sup B. Lee, Fabian B. Kugler, Sebastian Huber, Jan von Delft, Karsten Held, Markus Wallerberger

Abstract: Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imag… ▽ More Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from NRG.Due to the overcompleteness, we achieve only qualitative agreement. △ Less

Submitted 8 April, 2024; originally announced April 2024.

Comments: 9 pages, 4 figures

Journal ref: Phys. Rev. Research 6, 043228 (2024)

Displaced Drude peak from $π$-ton vertex corrections

Authors: J. Krsnik, O. Simard, P. Werner, A. Kauch, K. Held

Abstract: Correlated electron systems often show strong bosonic fluctuations, e.g., of antiferromagnetic nature, around a large wave vector such as $\mathbf{q}=(π,π\ldots)$. These fluctuations can give rise to vertex corrections to the optical conductivity through the (transversal) particle-hole channel, coined $π$-ton contributions. Previous numerical results differed qualitatively on how such vertex corre… ▽ More Correlated electron systems often show strong bosonic fluctuations, e.g., of antiferromagnetic nature, around a large wave vector such as $\mathbf{q}=(π,π\ldots)$. These fluctuations can give rise to vertex corrections to the optical conductivity through the (transversal) particle-hole channel, coined $π$-ton contributions. Previous numerical results differed qualitatively on how such vertex corrections alter the optical conductivity. Here, we clarify that $π$-ton vertex corrections lead to a displaced Drude peak for correlated metals. The proximity and enhancement of the effect when approaching a phase transition of, e.g., antiferromagnetic nature can be utilized for discriminating $π$-tons in experiments from other physics leading to a displaced Drude peak. △ Less

Submitted 25 February, 2024; originally announced February 2024.

Comments: 12 pages, 7 figures

Unambiguous fluctuation decomposition of the self-energy: pseudogap physics beyond spin fluctuations

Authors: Yang Yu, Sergei Iskakov, Emanuel Gull, Karsten Held, Friedrich Krien

Abstract: Correlated electron systems may give rise to multiple effective interactions whose combined impact on quasiparticle properties can be difficult to disentangle. We introduce an unambiguous decomposition of the electronic self-energy which allows us to quantify the contributions of various effective interactions simultaneously. We use this tool to revisit the hole-doped Hubbard model within the dyna… ▽ More Correlated electron systems may give rise to multiple effective interactions whose combined impact on quasiparticle properties can be difficult to disentangle. We introduce an unambiguous decomposition of the electronic self-energy which allows us to quantify the contributions of various effective interactions simultaneously. We use this tool to revisit the hole-doped Hubbard model within the dynamical cluster approximation, where commonly spin fluctuations are considered to be the origin of the pseudogap. While our fluctuation decomposition confirms that spin fluctuations indeed suppress antinodal electronic spectral weight, we show that they alone can not capture the pseudogap self-energy quantitatively. Nonlocal multi-boson Feynman diagrams yield substantial contributions and are needed for a quantitative description of the pseudogap. △ Less

Submitted 26 May, 2024; v1 submitted 16 January, 2024; originally announced January 2024.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 132, 216501 (2024)

Fermi and Luttinger arcs: two concepts, realized on one surface

Authors: Paul Worm, Matthias Reitner, Karsten Held, Alessandro Toschi

Abstract: We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces the results of numerically demanding many-body calculations, here obtained using the dynamical vertex approximation. Our analytical theory pro… ▽ More We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces the results of numerically demanding many-body calculations, here obtained using the dynamical vertex approximation. Our analytical theory provides a transparent description of a precise mechanism, capable to drive the formation of disconnected segments along the Fermi surface (the highly debated "Fermi arcs") as well as of the opening of a pseudogap at hole- and electron-doping. This occurs through a specific mechanism: The electronic states on the Fermi arcs remain intact, while the Fermi surface part where the gap opens transforms into a Luttinger arc. △ Less

Submitted 17 October, 2024; v1 submitted 29 December, 2023; originally announced December 2023.

Comments: 6 pages, 4 figures, suppl. mat

Journal ref: Phys. Rev. Letter 133, 166501 (2024)

Two-site reduced density matrix from one- and two-particle Green's functions

Authors: Gergő Roósz, Anna Kauch, Frederic Bippus, Daniel Wieser, Karsten Held

Abstract: Strongly correlated electron systems are challenging to calculate, and entanglement in such systems is not widely analyzed. We present an approach that can be used as a post-processing step for calculating the two-site reduced density matrix and from it entanglement measures such as the mutual information and entanglement negativity. Input is only the one- and two-particle Green's function which… ▽ More Strongly correlated electron systems are challenging to calculate, and entanglement in such systems is not widely analyzed. We present an approach that can be used as a post-processing step for calculating the two-site reduced density matrix and from it entanglement measures such as the mutual information and entanglement negativity. Input is only the one- and two-particle Green's function which is the output of numerous many-body methods. As an illustration, we present results for a toy model, the Hubbard model on a $2\times2$ cluster and a $6$ site ring. △ Less

Submitted 27 May, 2024; v1 submitted 21 December, 2023; originally announced December 2023.

Comments: 19 pages, 15 figures

Spin fluctuations sufficient to mediate superconductivity in nickelates

Authors: Paul Worm, Qisi Wang, Motoharu Kitatani, Izabela Biało, Qiang Gao, Xiaolin Ren, Jaewon Choi, Diana Csontosová, Ke-Jin Zhou, Xingjiang Zhou, Zhihai Zhu, Liang Si, Johan Chang, Jan M. Tomczak, Karsten Held

Abstract: Infinite-layer nickelates show high-temperature superconductivity, and the experimental phase diagram agrees well with the one simulated within the dynamical vertex approximation (D$Γ$A). Here, we compare the spin-fluctuation spectrum behind these calculations to resonant inelastic X-ray scattering experiments. The overall agreement is good. This independent cross-validation of the strength of spi… ▽ More Infinite-layer nickelates show high-temperature superconductivity, and the experimental phase diagram agrees well with the one simulated within the dynamical vertex approximation (D$Γ$A). Here, we compare the spin-fluctuation spectrum behind these calculations to resonant inelastic X-ray scattering experiments. The overall agreement is good. This independent cross-validation of the strength of spin fluctuations strongly supports the scenario, advanced by D$Γ$A, that spin-fluctuations are the mediator of the superconductivity observed in nickelates. △ Less

Submitted 13 December, 2023; originally announced December 2023.

Comments: 13 pages, 8 figures

Unconventional superconductivity without doping: infinite-layer nickelates under pressure

Authors: Simone Di Cataldo, Paul Worm, Jan Tomczak, Liang Si, Karsten Held

Abstract: High-temperature unconventional superconductivity quite generically emerges from doping a strongly correlated parent compound, often (close to) an antiferromagnetic insulator. The recently developed dynamical vertex approximation is a state-of-the-art technique that has quantitatively predicted the superconducting dome of nickelates. Here, we apply it to study the effect of pressure in the infinit… ▽ More High-temperature unconventional superconductivity quite generically emerges from doping a strongly correlated parent compound, often (close to) an antiferromagnetic insulator. The recently developed dynamical vertex approximation is a state-of-the-art technique that has quantitatively predicted the superconducting dome of nickelates. Here, we apply it to study the effect of pressure in the infinite-layer nickelate Sr$_x$Pr$_ {1-x}$NiO$_2$. We reproduce the increase of the critical temperature ($T_c$) under pressure found in experiment up to 12 GPa. According to our results, $T_c$ can be further increased with higher pressures. Even without Sr-doping the parent compound, PrNiO$_2$, will become a high-temperature superconductor thanks to a strongly enhanced self-doping of the \nidxsqysq{} orbital under pressure. With a maximal \Tc{} of 100\,K around 100\,GPa, nickelate superconductors can reach that of the best cuprates. △ Less

Submitted 10 November, 2023; originally announced November 2023.

Comments: Main text: 6 pages, 4 figures. Supplementary information: 18 pages, 16 figures

Journal ref: Nature Communications 5, 3952 (2024)

Weyl points and spin-orbit coupling in copper-substituted lead phosphate apatite

Authors: Martin Braß, Liang Si, Karten Held

Abstract: We study the impact of spin-orbit coupling on the topological band-properties of copper-substituted lead phosphate apatite using a combination of group-theoretical analysis and full-relativistic density-functional theory calculations. We characterize Weyl points at time-reversal invariant momenta and find that a band-inversion due to spin-orbit coupling leads to additional Weyl points close to the… ▽ More We study the impact of spin-orbit coupling on the topological band-properties of copper-substituted lead phosphate apatite using a combination of group-theoretical analysis and full-relativistic density-functional theory calculations. We characterize Weyl points at time-reversal invariant momenta and find that a band-inversion due to spin-orbit coupling leads to additional Weyl points close to the Fermi-edge at general momenta. To determine the position of the altogether 66 Weyl points in the Brilouin-zone, we develop an algorithm that follows a Berry-curvature-derived vector field to its monopole: the Weyl point. The emerging surface Fermi-arcs and their spin-polarization reveal avoided crossings and a Fermi-loop detached from the Weyl points. △ Less

Submitted 12 October, 2023; originally announced October 2023.

No superconductivity in Pb$_9$Cu$_1$(PO$_4$)$_6$O found in orbital and spin fluctuation exchange calculations

Authors: Niklas Witt, Liang Si, Jan M. Tomczak, Karsten Held, Tim O. Wehling

Abstract: Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an $\textit{ab initio}$ derived two-ba… ▽ More Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an $\textit{ab initio}$ derived two-band model of the Cu $e_g$ orbitals for which we determine interaction values from the constrained random phase approximation (cRPA). For this two-band model we perform calculations in the fluctuation exchange (FLEX) approach to assess the strength of orbital and spin fluctuations. We scan over a broad range of parameters and enforce no magnetic or orbital symmetry breaking. Even under optimized conditions for superconductivity, spin and orbital fluctuations turn out to be too weak for superconductivity anywhere near to room-temperature. We contrast this finding to non-self-consistent RPA, where it is possible to induce spin-singlet $d$-wave superconductivity at $T_{\mathrm{c}}\geq300$ K if the system is put close enough to a magnetic instability. △ Less

Submitted 26 October, 2023; v1 submitted 14 August, 2023; originally announced August 2023.

Comments: 14 pages, 3 figures; revised submission to SciPost Physics

Journal ref: SciPost Phys. 15, 197 (2023)

Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O: a Mott or charge transfer insulator in need of further doping for (super)conductivity

Authors: Liang Si, Markus Wallerberger, Andriy Smolyanyuk, Simone di Cataldo, Jan M. Tomczak, Karsten Held

Abstract: We briefly review the status quo of research on the putative superconductor Pb$_9$Cu(PO$_4$)$_6$O also known as LK-99. Further, we provide {\em ab initio} derived tight-binding parameters for a two- and five-band model, and solve these in dynamical-mean-field theory. The ratio interaction-to-bandwidth makes LK-99 a Mott or charge transfer insulator. Electron or hole doping (which is different from… ▽ More We briefly review the status quo of research on the putative superconductor Pb$_9$Cu(PO$_4$)$_6$O also known as LK-99. Further, we provide {\em ab initio} derived tight-binding parameters for a two- and five-band model, and solve these in dynamical-mean-field theory. The ratio interaction-to-bandwidth makes LK-99 a Mott or charge transfer insulator. Electron or hole doping (which is different from substituting Pb by Cu and thus differs from LK-99) is required to make it metallic and potentially superconducting. △ Less

Submitted 9 August, 2023; v1 submitted 8 August, 2023; originally announced August 2023.

Comments: 7 figures, 9 pages, 2 tables. Version 2 is the same as version 1 except for additional DMFT and DFT+U results in Secs. IV and V

Electronic structure of the putative room-temperature superconductor Pb$_9$Cu(PO$_4$)$_6$O

Authors: Liang Si, Karsten Held

Abstract: A recent paper [Lee {\em et al.}, J. Korean Cryt. Growth Cryst. Techn. {\bf 33}, 61 (2023)] provides some experimental indications that Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O with $x\approx 1$, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory calculations show lattice parameters and a volume contraction with $x$ -- very similar to experiment. The… ▽ More A recent paper [Lee {\em et al.}, J. Korean Cryt. Growth Cryst. Techn. {\bf 33}, 61 (2023)] provides some experimental indications that Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O with $x\approx 1$, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory calculations show lattice parameters and a volume contraction with $x$ -- very similar to experiment. The DFT electronic structure shows Cu$^{2+}$ in a $3d^9$ configuration with two flat Cu bands crossing the Fermi energy. This puts Pb$_{9}$Cu(PO$_4$)$_6$O in an ultra-correlated regime and suggests that, without doping, it is a Mott or charge transfer insulator. If doped such an electronic structure might support flat-band superconductivity or an correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results. △ Less

Submitted 25 September, 2023; v1 submitted 1 August, 2023; originally announced August 2023.

Comments: 10 pages, 7 figures and 4 tables including supplementary materials

Journal ref: Physical Review B 108, L121110 (2023)

Chiral magnetism and ordering of oxygen vacancies in SrTiO$_{2.5}$

Authors: Liang Si, Xiaochao Wang, Paul Worm, Wei Peng, Minjae Kim, Lingfei Wang, Karsten Held

Abstract: Oxygen vacancies in the perovskite insulator SrTiO$_3$ free electrons that couple with other physical degrees of freedom such as lattice, orbital, and spin. This leads to the emergence of exotic quantum states such as superconductivity and unusual ferromagnetism. We perform density-functional theory and dynamical mean-field theory calculations and demonstrate that the orientation and ordering of t… ▽ More Oxygen vacancies in the perovskite insulator SrTiO$_3$ free electrons that couple with other physical degrees of freedom such as lattice, orbital, and spin. This leads to the emergence of exotic quantum states such as superconductivity and unusual ferromagnetism. We perform density-functional theory and dynamical mean-field theory calculations and demonstrate that the orientation and ordering of the TiO$_5$ pentahedra plays a crucial role. Specifically, for vacancy-rich SrTiO$_{3-δ}$ ($δ\sim$0.5), we find a chiral ordering of the TiO$_5$ pentahedra in a sixfold superlattice. This chiral structure is accompanied by a chiral magnetic state with a net moment in the (111) direction at room temperature, which can explain several experimental observations. △ Less

Submitted 12 June, 2023; originally announced June 2023.

Comments: 10 pages, 8 figures including supplementary materials

Strain-Tuned Magnetic Frustration in a Square Lattice $J_1$-$J_2$ Material

Authors: I. Biało, L. Martinelli, G. De Luca, P. Worm, A. Drewanowski, J. Choi, M. Garcia-Fernandez, S. Agrestini, Ke-Jin Zhou, K. Kummer, N. B. Brookes, L. Guo, A. Edgeton, C. B. Eom, J. M. Tomczak, K. Held, M. Gibert, Qisi Wang, J. Chang

Abstract: Magnetic frustration is a route that can lead to the emergence of novel ground states, including spin liquids and spin ices. Such frustration can be introduced through either the geometry of lattice structures or by incompatible exchange interactions. Identifying suitable strategies to control the degree of magnetic frustration in real systems is an active field of research. In this study, we devi… ▽ More Magnetic frustration is a route that can lead to the emergence of novel ground states, including spin liquids and spin ices. Such frustration can be introduced through either the geometry of lattice structures or by incompatible exchange interactions. Identifying suitable strategies to control the degree of magnetic frustration in real systems is an active field of research. In this study, we devise a design principle for the tuning of frustrated magnetism on the square lattice through the manipulation of nearest (NN) and next-nearest neighbor (NNN) antiferromagnetic (AF) exchange interactions. By studying the magnon excitations in epitaxially-strained La$_2$NiO$_4$ films using resonant inelastic x-ray scattering (RIXS) we show that, in contrast to the cuprates, the dispersion peaks at the AF zone boundary. This indicates the presence of an AF-NNN spin interaction. Using first principles simulations and an effective spin-model, we demonstrate the AF-NNN coupling to be a consequence of the two-orbital nature of La$_2$NiO$_4$. Our results demonstrate that compressive strain can enhance this coupling, providing a design principle for the tunability of frustrated magnetism on a square lattice. △ Less

Submitted 13 August, 2024; v1 submitted 9 June, 2023; originally announced June 2023.

Journal ref: Commun. Phys. 7, 230 (2024)

A functional-analysis derivation of the parquet equation

Authors: Christian J. Eckhardt, Patrick Kappl, Anna Kauch, Karsten Held

Abstract: The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all diagrams of the two-particle Green's function in terms of their (ir)reducibility properties. In this work we provide a derivation of the parquet equation solely… ▽ More The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all diagrams of the two-particle Green's function in terms of their (ir)reducibility properties. In this work we provide a derivation of the parquet equation solely employing techniques of functional analysis namely functional Legendre transformations and functional derivatives. The advantage of a derivation in terms of a straightforward calculation is twofold: (i) the quantities appearing in the calculation have a clear mathematical definition and interpretation as derivatives of the Luttinger--Ward functional; (ii) analogous calculations to the ones that lead to the parquet equation may be performed for higher-order Green's functions potentially leading to a classification of these in terms of their (ir)reducible components. △ Less

Submitted 15 September, 2023; v1 submitted 25 May, 2023; originally announced May 2023.

Comments: Submission to SciPost

Journal ref: SciPost Phys. 15, 203 (2023)

Absence of electron-phonon-mediated superconductivity in hydrogen-intercalated nickelates

Authors: Simone Di Cataldo, Paul Worm, Liang Si, Karsten Held

Abstract: A recent experiment [X. Ding et al., Nature 615, 50 (2023)] indicates that superconductivity in nickelates is restricted to a narrow window of hydrogen concentration: 0.22 < x < 0.28 in Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$H$_{x}$. This reported necessity of hydrogen suggests that it plays a crucial role for superconductivity, as it does in the vast field of hydride superconductors. Using density-function… ▽ More A recent experiment [X. Ding et al., Nature 615, 50 (2023)] indicates that superconductivity in nickelates is restricted to a narrow window of hydrogen concentration: 0.22 < x < 0.28 in Nd$_{0.8}$Sr$_{0.2}$NiO$_{2}$H$_{x}$. This reported necessity of hydrogen suggests that it plays a crucial role for superconductivity, as it does in the vast field of hydride superconductors. Using density-functional theory and its extensions, we explore the effect of topotactic hydrogen on the electronic structure and phonon-mediated superconductivity in nickelate superconductors. Our calculations show that the electron-phonon coupling in hydrogen-intercalated nickelates is not strong enough to drive the electron pairing, and thus cannot explain the reported superconductivity. △ Less

Submitted 7 April, 2023; originally announced April 2023.

Comments: 3 figures, 1 table

Transition from Diffusive to Superdiffusive Transport in Carbon Nanotube Networks via Nematic Order Control

Authors: Michael Wais, Filchito Renee G. Bagsican, Natsumi Komatsu, Weilu Gao, Kazunori Serita, Hironaru Murakami, Karsten Held, Iwao Kawayama, Junichiro Kono, Marco Battiato, Masayoshi Tonouchi

Abstract: The one-dimensional confinement of quasiparticles in individual carbon nanotubes (CNTs) leads to extremely anisotropic electronic and optical properties. In a macroscopic ensemble of randomly oriented CNTs, this anisotropy disappears together with other properties that make them attractive for certain device applications. The question however remains if not only anisotropy, but other types of beha… ▽ More The one-dimensional confinement of quasiparticles in individual carbon nanotubes (CNTs) leads to extremely anisotropic electronic and optical properties. In a macroscopic ensemble of randomly oriented CNTs, this anisotropy disappears together with other properties that make them attractive for certain device applications. The question however remains if not only anisotropy, but other types of behaviours are suppressed by disorder. Here, we compare the dynamics of quasiparticles under strong electric fields in aligned and random CNT networks using a combination of terahertz emission and photocurrent experiments and out-of-equilibrium numerical simulations. We find that the degree of alignment strongly influences the excited quasiparticles' dynamics, rerouting the thermalisation pathways. This is, in particular, evidenced in the high-energy, high-momentum electronic population (probed through the formation of low energy excitons via exciton impact ionization) and the transport regime evolving from diffusive to superdiffusive. △ Less

Submitted 11 May, 2023; v1 submitted 3 March, 2023; originally announced March 2023.

Comments: 17 pages, 5 figures

Non-linear responses and three-particle correlators in correlated electron systems exemplified by the Anderson impurity model

Authors: Patrick Kappl, Friedrich Krien, Clemens Watzenböck, Karsten Held

Abstract: Three-particle correlators are relevant for, among others, Raman, Hall and non-linear responses. They are also required for the next order of approximations extending dynamical mean-field theory diagrammatically. We present a general formalism on how to treat these three-particle correlators and susceptibilities, and calculate the local three-particle response of the Anderson impurity model numeri… ▽ More Three-particle correlators are relevant for, among others, Raman, Hall and non-linear responses. They are also required for the next order of approximations extending dynamical mean-field theory diagrammatically. We present a general formalism on how to treat these three-particle correlators and susceptibilities, and calculate the local three-particle response of the Anderson impurity model numerically. We find that genuine three-particle vertex corrections are sizable. In particular, it is not sufficient to just take the bare bubble terms or corrections based on the two-particle vertex. The full three-particle vertex must be considered. △ Less

Submitted 9 May, 2023; v1 submitted 22 December, 2022; originally announced December 2022.

Comments: 18 pages, 18 figures

Journal ref: Phys. Rev. B 107, 205108 (2023)

Aberration of the Green's function estimator in hybridization expansion continuous-time quantum Monte Carlo

Authors: Andreas Hausoel, Markus Wallerberger, Josef Kaufmann, Karsten Held, Giorgio Sangiovanni

Abstract: We describe an aberration of the resampling estimator for the Green's function customarily used in hybridization expansion continuous-time quantum Monte Carlo. It occurs due to Pauli principle constraints in calculations of Anderson impurity models with baths consisting of a discrete energy spectrum. We identify the missing Feynman diagrams, characterize the affected models and discuss implication… ▽ More We describe an aberration of the resampling estimator for the Green's function customarily used in hybridization expansion continuous-time quantum Monte Carlo. It occurs due to Pauli principle constraints in calculations of Anderson impurity models with baths consisting of a discrete energy spectrum. We identify the missing Feynman diagrams, characterize the affected models and discuss implications as well as solutions. This issue does not occur when using worm sampling or in the presence of continuous baths. However certain energy spectra can be inherently close to a discrete limit, and we explain why autocorrelation times can become very large in these cases. △ Less

Submitted 11 November, 2022; originally announced November 2022.

Topotactic-hydrogen forms chains in $AB$O$_2$ nickelate superconductors

Authors: Liang Si, Paul Worm, Dachuan Chen, Karsten Held

Abstract: Despite enormous experimental and theoretical efforts, obtaining generally accepted conclusions regarding the intrinsic magnetic and electronic properties of superconducting nickelates remains exceptionally challenging. Experiments show a significant degree of uncertainty, indicating hidden factors in the synthesized films, which call for further investigations. One of those "hidden factors" is th… ▽ More Despite enormous experimental and theoretical efforts, obtaining generally accepted conclusions regarding the intrinsic magnetic and electronic properties of superconducting nickelates remains exceptionally challenging. Experiments show a significant degree of uncertainty, indicating hidden factors in the synthesized films, which call for further investigations. One of those "hidden factors" is the possibility of intercalating hydrogen during the chemical reduction process from Nd(La)NiO$_3$ to Nd(La)NiO$_2$ using CaH$_2$. While hydrogen has been detected in experimental samples, not much is known about its distribution through the crystal and its influence on the electronic environment. Here, we show the tendency toward the formation of one-dimensional hydrogen chains in infinite-layers LaNiO$_2$ superconductors using density-functional theory (DFT) supplemented by dynamical mean-field theory (DMFT). The formation of such hydrogen chains induces a coexistence of different oxidation states of Ni and competing magnetic phases, and possibly explains the recently observed charge order states in nickelate superconductors. Furthermore, it contributes to the difficulty of synthesizing homogeneous nickelates and determining their ground states. The smoking gun to detect excess hydrogen in nickelates are flat phonon modes, which are infrared active and quite insensitive to the exact arrangement of the H atoms. △ Less

Submitted 3 March, 2023; v1 submitted 23 August, 2022; originally announced August 2022.

Comments: 19 pages, 13 figures, under PRB review