Showing 1–50 of 135 results for author: Koshino, M

Second-harmonic generation in twisted double bilayer graphene: Double-resonant enhancement from moiré flat bands

Authors: Takaaki V. Joya, Takuto Kawakami, Mikito Koshino

Abstract: We theoretically investigate second-harmonic generation (SHG) in twisted double bilayer graphene (TDBG) with AB--AB and AB--BA stacking configurations using a perturbative approach based on an effective continuum Hamiltonian. We present a systematic analysis of the SHG response as a function of twist angle, vertical bias voltage, Fermi energy, and stacking configuration. We find that the SHG signa… ▽ More We theoretically investigate second-harmonic generation (SHG) in twisted double bilayer graphene (TDBG) with AB--AB and AB--BA stacking configurations using a perturbative approach based on an effective continuum Hamiltonian. We present a systematic analysis of the SHG response as a function of twist angle, vertical bias voltage, Fermi energy, and stacking configuration. We find that the SHG signal is strongly enhanced at small twist angles due to the emergence of moiré flat bands and the associated increase in the joint density of states. Beyond this conventional enhancement mechanism, we demonstrate that the reduced bandwidth enables a pronounced double-resonant process, in which optical transitions at both $ω$ and $2ω$ are simultaneously satisfied over extended regions of the moiré Brillouin zone. This mechanism leads to a substantial amplification of the SHG response, analogous to the enhancement observed in systems with discrete energy levels, but realised here in a tuneable moiré band structure. Furthermore, we show that the AB--AB and AB--BA configurations exhibit a systematic $π$ phase shift in the SHG response at large bias voltages, reflecting their distinct symmetry and electronic structure. Our results identify double-resonance effects as a generic mechanism for enhancing SHG in moiré systems and provide a unified framework for understanding and controlling nonlinear optical responses in tuneable flat-band materials. △ Less

Submitted 3 August, 2026; originally announced August 2026.

Twist-configured moire-moire reconstruction governs diverse commensurate double-moire phases in twisted bilayer graphene on h-BN

Authors: Yuta Seo, Naoto Nakatsuji, Jimpei Kawase, Naoto Hishida, Kenji Watanabe, Takashi Taniguchi, Takuto Kawakami, Mikito Koshino, Tomoki Machida

Abstract: The coexistence of multiple moire lattices in van der Waals heterostructures raises a fundamental question: how do distinct moire patterns interact and reconstruct? Here, we investigate twisted bilayer graphene (tBG) on hexagonal boron nitride (h-BN), where tBG and graphene/h-BN moire structures coexist, using conductive atomic force microscopy combined with continuum-model simulations. We show th… ▽ More The coexistence of multiple moire lattices in van der Waals heterostructures raises a fundamental question: how do distinct moire patterns interact and reconstruct? Here, we investigate twisted bilayer graphene (tBG) on hexagonal boron nitride (h-BN), where tBG and graphene/h-BN moire structures coexist, using conductive atomic force microscopy combined with continuum-model simulations. We show that reconstruction between these moire lattices-moire-moire reconstruction-manifests across multiple length scales, giving rise to diverse commensurate double-moire phases. Locally, the stacking registry between the two moire lattices is uniquely selected by the global twist configuration (helical or alternate), mediated by rotational relaxation of the shared graphene layer. This registry, together with twist angle and strain, governs commensurate domains from C3z-symmetric to strained symmetry-modified structures. These results establish moire-moire reconstruction as a general framework for engineering structural and electronic order -- including theoretically predicted topological flat bands below the magic angle -- in multilayer moire materials. △ Less

Submitted 2 July, 2026; originally announced July 2026.

Comments: Main(26 pages, 5 figures), SI(20 pages, 8 figures, 3 tables)

Landau levels and magneto-optics in 30$^\circ$ quasi-periodic twisted bilayer graphene

Authors: Masaru Hitomi, Takuto Kawakami, Mikito Koshino

Abstract: We develop a theoretical framework for Landau levels in quasi-periodic twisted bilayer graphene at a $30^\circ$ twist angle, a system without translational symmetry but possessing 12-fold rotational symmetry. Using a quasi-band formalism, we incorporate the magnetic field through a conventional momentum substitution in the zero-field Hamiltonian. This approach provides a transparent physical inter… ▽ More We develop a theoretical framework for Landau levels in quasi-periodic twisted bilayer graphene at a $30^\circ$ twist angle, a system without translational symmetry but possessing 12-fold rotational symmetry. Using a quasi-band formalism, we incorporate the magnetic field through a conventional momentum substitution in the zero-field Hamiltonian. This approach provides a transparent physical interpretation by directly relating the Landau levels to the quasi-band structure, allowing them to be understood as quantized orbits of quasi-band pockets. By using this method, we reveal distinctive spectral features, including nearly flat bands with weak magnetic-field dependence and highly degenerate levels arising from twelve off-center pockets. The resulting Landau levels are classified by two quantum numbers: the Landau-level index and the angular momentum associated with the underlying quasicrystalline symmetry. We also compute the magneto-optical conductivity and show that optical transitions follow angular-momentum selection rules enforced by the 12-fold symmetry. Our approach provides a symmetry-based and computationally efficient framework for bulk quantum magneto-optics in quasicrystalline van der Waals systems, predicting spectroscopic signatures accessible in high-field infrared and THz experiments. △ Less

Submitted 20 April, 2026; originally announced April 2026.

Comments: 12 pages, 6 figures

One-Dimensional Electronic States in a Moiré Superlattice of Twisted Bilayer WTe2

Authors: Takuto Kawakami, Hayato Tateish, Daiki Yoshida, Xiaohan Yang, Naoto Nakatsuji, Limi Chen, Kohei Aso, Yukiko Yamada-Takamura, Yoshifumi Oshima, Yijin Zhang, Tomoki Machida, Koichiro Kato, Mikito Koshino

Abstract: One-dimensional (1D) moiré superlattices provide a new route to engineering reduced-dimensional electronic states in van der Waals materials, yet their electronic structure and microscopic origin remain largely unexplored. Here, we investigate the structural relaxation and electronic properties of a 1D moiré superlattice formed in twisted bilayer 1T$'$-WTe$_2$ using density functional theory calcu… ▽ More One-dimensional (1D) moiré superlattices provide a new route to engineering reduced-dimensional electronic states in van der Waals materials, yet their electronic structure and microscopic origin remain largely unexplored. Here, we investigate the structural relaxation and electronic properties of a 1D moiré superlattice formed in twisted bilayer 1T$'$-WTe$_2$ using density functional theory calculations, complemented by high-angle annular dark-field scanning transmission electron microscopy. We show that lattice relaxation strongly reconstructs the moiré stripes, leading to stacking-dependent stripe widths that are in excellent agreement with experimental observations. The relaxed structure hosts quasi-one-dimensional electronic bands near the Fermi level, characterized by strong dispersion along the stripe direction and nearly flat dispersion in the perpendicular direction. By comparing the full bilayer with isolated relaxed layers, we establish that these 1D electronic states are governed predominantly by an intralayer moiré potential induced by in-plane lattice relaxation, rather than by interlayer hybridization. We extract this position-dependent moiré potential directly from DFT calculations and construct an effective tight-binding model that reproduces both the band dispersion and the real-space localization of the electronic wave functions. Our results identify lattice relaxation as the key mechanism underlying 1D electronic states in 1D moiré superlattices. %and establish twisted bilayer WTe$_2$ as a promising platform for exploring emergent one-dimensional moiré physics. The framework developed here provides a unified theoretical basis for realizing and exploring one-dimensional moiré physics in a broad class of anisotropic two-dimensional materials. △ Less

Submitted 16 August, 2026; v1 submitted 28 January, 2026; originally announced January 2026.

Comments: 18 pages, 14 figures

Journal ref: Phys. Rev. B 114, 105407 (2026)

Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons

Authors: Kazuki Yamamoto, Takuto Kawakami, Mikito Koshino

Abstract: We investigate a ferroelectric instability of a magnon Bose-Einstein condensate, mediated by its interaction with an electric field through a geometric Aharonov-Casher (AC) phase. A distinct feature of the system is the positive feedback loop in which an electric field induces magnon orbital motion via the AC phase, generating electric polarization that in turn enhances the original field. Based o… ▽ More We investigate a ferroelectric instability of a magnon Bose-Einstein condensate, mediated by its interaction with an electric field through a geometric Aharonov-Casher (AC) phase. A distinct feature of the system is the positive feedback loop in which an electric field induces magnon orbital motion via the AC phase, generating electric polarization that in turn enhances the original field. Based on bosonic Bogoliubov-de Gennes (BdG) mean-field theory, we show that this feedback drives a spontaneous ferroelectric transition in the magnon superfluid, accompanied by a persistent magnon supercurrent. In the resulting ferroelectric phase, the quasiparticle excitation spectrum becomes nonreciprocal, reflecting spontaneous breaking of spatial inversion symmetry. At the critical point of the transition, the bosonic BdG Hamiltonian exhibits a global coalescence of both eigenvalues and eigenvectors, forming exceptional points throughout the entire Brillouin zone. The corresponding eigenvector is an equally weighted superposition of bosonic quasiparticle and quasihole states and is invariant under particle-hole transformation, allowing it to be interpreted as a bosonic analog of a Majorana fermion. △ Less

Submitted 2 July, 2026; v1 submitted 26 December, 2025; originally announced December 2025.

Comments: 13 pages, 5 figures

Journal ref: Physical Review B 114, 034501 (2026)

Emergent electronic insulating states in a one-dimensional moiré superlattice

Authors: Jianfeng Bi, Masaki Minamikawa, Ruige Dong, DongJun Kang, Zihan Weng, Shaoqi Sun, Kenji Watanabe, Takashi Taniguchi, Ryosuke Okumura, Huizhen Wu, Naoto Nakatsuji, SeokJae Yoo, Mikito Koshino, Sihan Zhao

Abstract: Two-dimensional (2D) van der Waals (vdW) moiré superlattices have provided a powerful knob to engineer a plethora of new quantum states. However, extending such moiré engineering to one-dimensional (1D) vdW systems has remained challenging. Here we report the moiré-engineered electronic insulating states in a new 1D moiré superlattice, by crystallographically aligning an armchair single-walled car… ▽ More Two-dimensional (2D) van der Waals (vdW) moiré superlattices have provided a powerful knob to engineer a plethora of new quantum states. However, extending such moiré engineering to one-dimensional (1D) vdW systems has remained challenging. Here we report the moiré-engineered electronic insulating states in a new 1D moiré superlattice, by crystallographically aligning an armchair single-walled carbon nanotube (SWNT) to 2D hexagonal boron nitride (hBN) substrate. Remarkably, we observe the emergence of pronounced insulating states at charge neutrality point (CNP), full and half moiré fillings in lattice-aligned armchair SWNT/hBN heterostructures by low-temperature electrical transport measurements. In strong contrast, armchair SWNT devices without hBN alignment do not show any of these insulating behaviors, providing compelling evidence for the significant 1D moiré effect. Our density functional theory (DFT) and tight-binding calculations reveal that synergetic nanotube partial flattening and in-plane lattice reconstruction at 1D moiré interface expand the most stable AB' stacking regions (carbon on top of boron) and open sizable band gaps at both CNP and full moiré fillings at the single-particle level. Our one-body theory predicts no band gaps at half moiré fillings, suggesting that electron correlation and/or electron-phonon interaction may give rise to these emergent insulating behaviors in our 1D moiré systems. Our work establishes a new and definite moiré engineering route for 1D vdW materials and opens an exciting avenue for exploring interaction-induced quantum phases in 1D. △ Less

Submitted 13 November, 2025; originally announced November 2025.

Comments: 28 pages; 4 figures, 13 supplementary data figures, etc

Journal ref: Phys. Rev. Lett. 137, 066201 Published 6 August, 2026

One-dimensional moiré engineering in zigzag graphene nanoribbons on hBN

Authors: Ryosuke Okumura, Naoto Nakatsuji, Takuto Kawakami, Mikito Koshino

Abstract: We study the structural relaxation and electronic properties of a one-dimensional (1D) moiré system composed of a zigzag graphene nanoribbon (GNR) placed on a hexagonal boron nitride (hBN) substrate. Using an effective grid model derived from continuum elasticity theory, we calculate the relaxed atomic structure of the GNR/hBN system for various twist angles and ribbon widths. The relaxation gives… ▽ More We study the structural relaxation and electronic properties of a one-dimensional (1D) moiré system composed of a zigzag graphene nanoribbon (GNR) placed on a hexagonal boron nitride (hBN) substrate. Using an effective grid model derived from continuum elasticity theory, we calculate the relaxed atomic structure of the GNR/hBN system for various twist angles and ribbon widths. The relaxation gives rise to a characteristic 1D domain structure consisting of alternating commensurate AB$'$ regions and two distinct types of domain boundaries. At finite twist angles, the ribbon adopts a wavy shape, locally tracing the hBN zigzag direction but occasionally sliding to adjacent atomic rows. The resulting moiré potential strongly modulates the electronic structure: the zero-energy zigzag edge states are modulated by the local stacking, leading to densely packed subbands in the AB$'$ domains and sharply localized domain-wall states in the energy gaps between domain plateaus, which together realize gate-tunable one-dimensional arrays of quantum-confined electronic states. Our results demonstrate that moiré modulation in GNR/hBN heterostructures provides a versatile platform for electronic structure engineering and the design of 1D moiré nanodevices. △ Less

Submitted 24 October, 2025; originally announced October 2025.

Comments: 13 pages, 8 figures

Journal ref: Phys. Rev. B 113, 115411 (2026)

Resonant Structure of Second Harmonic Generation in Multilayer Graphene Polytypes

Authors: Patrick Johansen Sarsfield, Takaaki V. Joya, Takuto Kawakami, Mikito Koshino, Vladimir Fal'ko

Abstract: Second harmonic generation (SHG) is a powerful optical tool for identifying non-centrosymmetric crystalline structures. Here, we analyze SHG in multilayer graphenes (MLG), with a focus on its dependence on the stacking order, encapsulation environment and biasing which break inversion symmetry in multilayers, as well as the SHG sensitivity to the electron-hole asymmetry in the MLG spectra and dopi… ▽ More Second harmonic generation (SHG) is a powerful optical tool for identifying non-centrosymmetric crystalline structures. Here, we analyze SHG in multilayer graphenes (MLG), with a focus on its dependence on the stacking order, encapsulation environment and biasing which break inversion symmetry in multilayers, as well as the SHG sensitivity to the electron-hole asymmetry in the MLG spectra and doping. In particular, we identify stacking-order-dependent resonant features in the SHG spectra for trilayers and tetralayers, suggesting that infra-red range SHG offers a non-invasive characterization method for distinguishing between MLG polytypes, as well as optical identification of crystallographic direction in MLG films. △ Less

Submitted 24 March, 2026; v1 submitted 21 August, 2025; originally announced August 2025.

Comments: 8 pages, 4 figures

Twist-angle tunable Josephson junctions in three-dimensional superconductors

Authors: Tenta Tani, Takuto Kawakami, Mikito Koshino

Abstract: We theoretically investigate the superconducting phase and perpendicular Josephson supercurrent in twisted three-dimensional (3D) superconductors, where two layered 3D materials are stacked with a relative twist. We formulate the Bogoliubov-de Gennes Hamiltonian and develop a self-consistent method to calculate the superconducting order parameter and the resulting supercurrent. Applying this frame… ▽ More We theoretically investigate the superconducting phase and perpendicular Josephson supercurrent in twisted three-dimensional (3D) superconductors, where two layered 3D materials are stacked with a relative twist. We formulate the Bogoliubov-de Gennes Hamiltonian and develop a self-consistent method to calculate the superconducting order parameter and the resulting supercurrent. Applying this framework to a toy model with Fermi surfaces located near the Brillouin zone corners, we demonstrate a phase discontinuity at the twisted interface, indicating that a Josephson junction is formed purely by the twist. Our calculations reveal that the interface supports a finite critical current even when the Fermi surfaces of the two superconductors are completely separated, unlike in the case of a twisted normal-metal interface. We further show that the critical current can be effectively controlled by the twist angle, transitioning from a high-transparency regime at small angles to a low-transparency regime at larger angles. △ Less

Submitted 13 January, 2026; v1 submitted 13 August, 2025; originally announced August 2025.

Comments: 16 pages, 11 figures

Journal ref: Phys. Rev. B 113, 035418 (2026)

Non-Abelian Chern band in rhombohedral graphene multilayers

Authors: Taketo Uchida, Takuto Kawakami, Mikito Koshino

Abstract: Moiré flat bands in rhombohedral multilayer graphene provide a platform for exploring interaction-driven topological phases, where a single isolated band often forms a Chern band. However, non-Abelian degenerate Chern bands with internal symmetries such as $\mathrm{SU}(N)$ have so far been realized only in highly engineered systems. Here, we show that a doubly degenerate non-Abelian Chern band wit… ▽ More Moiré flat bands in rhombohedral multilayer graphene provide a platform for exploring interaction-driven topological phases, where a single isolated band often forms a Chern band. However, non-Abelian degenerate Chern bands with internal symmetries such as $\mathrm{SU}(N)$ have so far been realized only in highly engineered systems. Here, we show that a doubly degenerate non-Abelian Chern band with Chern number $|C|=1$ emerges spontaneously at filling $ν=2$ in rhombohedral 3-, 4-, and 5-layer graphene, regardless of the presence of an hBN substrate. Using self-consistent Hartree-Fock calculations, we map out phase diagrams as functions of displacement field and electronic periodicity, and analytically demonstrate that the Fock term drives spontaneous symmetry breaking and generates non-Abelian Berry curvature. We further show that this non-Abelian topology is characterized by $\mathrm{SU}(2)$ gauge flux threading the noncontractible cycles of the Brillouin zone, leading to a global non-Abelian holonomy. Our findings unveil a new class of interaction-driven non-Abelian topological phases, distinct from quantum anomalous Hall and fractional Chern phases. △ Less

Submitted 14 April, 2026; v1 submitted 10 August, 2025; originally announced August 2025.

Journal ref: Phys. Rev. Lett. 136, 156602 (2026)

Direct observation of locally modified excitonic effect within a moiré unit cell in twisted bilayer graphene

Authors: Ming Liu, Ryosuke Senga, Masanori Koshino, Yung-Chang Lin, Kazu Suenaga

Abstract: Bilayer graphene, forming moiré superlattices, possesses distinct electronic and optical properties derived from the hybridization of energy band and the emergence of van Hove singularities depending on its twist angle. Extensive research has been conducted on the global characteristics of moiré superlattice induced by long-range periodicity. However, limited attention has been given to the local… ▽ More Bilayer graphene, forming moiré superlattices, possesses distinct electronic and optical properties derived from the hybridization of energy band and the emergence of van Hove singularities depending on its twist angle. Extensive research has been conducted on the global characteristics of moiré superlattice induced by long-range periodicity. However, limited attention has been given to the local properties within a moiré unit cell, which undoubtedly differ due to the variations in three-dimensional atomic arrangement. Here we demonstrate the highly localized excitations of carbon 1s electrons to unoccupied van Hove singularities in a twisted bilayer graphene using an electron energy loss spectroscopy based on a monochromated transmission electron microscope. The core-level excitations associated with the van Hove singularities show a systematic twist angle dependence which is analogous to the optical excitations. Furthermore, local variations in those core-level van Hove singularity peaks within a moiré unit cell have been corroborated for the first time, which can originate from core-exciton lifetimes and band modifications influenced by the local stacking geometry. △ Less

Submitted 7 July, 2025; originally announced July 2025.

Comments: 33 pages with 4 figures for maintext and 5 pages with 3 figures for supporting information

Journal ref: ACS Nano 17 (2023) 18433-18440

Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction

Authors: Takuto Kawakami, Yuji Igarashi, Mikito Koshino

Abstract: We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a pair of degenerate flat bands touching a dispersive band. We derive a three-orbital effective continuum model that captures the essential features near the band… ▽ More We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a pair of degenerate flat bands touching a dispersive band. We derive a three-orbital effective continuum model that captures the essential features near the band-touching point. Within this framework, we identify the point-like topological singularity on a planar manifold defined by the degenerate flat band eigenvectors. This singularity strongly influences the quantum geometry and results in a characteristic Landau level structure, where the levels spread over a finite energy range. We show that this structure reflects the underlying band reconstruction due to the orbital Zeeman effect, which lifts the flat band degeneracy and induces the Weyl-semimetal-like dispersion near the singularity. Our analysis reveals that the range of Landau level spreading is proportional to the quantum metric of each Zeeman-split band. We further demonstrate that adding a small dispersion via longer-range . Finally, we show that our approach extends naturally to systems with higher orbital angular momentum, indicating the robustness of these features in a broad class of three-dimensional flat band models. △ Less

Submitted 29 January, 2026; v1 submitted 16 June, 2025; originally announced June 2025.

Comments: 19 pages, 13 figures

Journal ref: Phys. Rev. B 112, 125202 (2025)

Moiré Band Engineering in Twisted Trilayer WSe2

Authors: Naoto Nakatsuji, Takuto Kawakami, Hayato Tateishi, Koichiro Kato, Mikito Koshino

Abstract: We present a systematic theoretical study on the structural and electronic properties of twisted trilayer transition metal dichalcogenide (TMD) WSe$_2$, where two independent moiré patterns form between adjacent layers. Using a continuum approach, we investigate the optimized lattice structure and the resulting energy band structure, revealing fundamentally different electronic behaviors between h… ▽ More We present a systematic theoretical study on the structural and electronic properties of twisted trilayer transition metal dichalcogenide (TMD) WSe$_2$, where two independent moiré patterns form between adjacent layers. Using a continuum approach, we investigate the optimized lattice structure and the resulting energy band structure, revealing fundamentally different electronic behaviors between helical and alternating twist configurations. In helical trilayers, lattice relaxation induces $αβ$ and $βα$ domains, where the two moiré patterns shift to minimize overlap, while in alternating trilayers, $αα'$ domains emerge with aligned moiré patterns. A key feature of trilayer TMDs is the summation of moiré potentials from the top and bottom layers onto the middle layer, effectively doubling the potential depth. In helical trilayers, this mechanism generates a Kagome lattice potential in the $αβ$ domains, giving rise to flat bands characteristic of Kagome physics. In alternating trilayers, the enhanced potential confinement forms deep triangular quantum wells, distinct from those found in bilayer systems. Furthermore, we demonstrate that a moderate perpendicular electric field can switch the layer polarization near the valence band edge, providing an additional degree of tunability. In particular, it enables tuning of the hybridization between orbitals on different layers, allowing for the engineering of diverse and controllable electronic band structures. Our findings highlight the unique role of moiré potential summation in trilayer systems, offering a broader platform for designing moiré-based electronic and excitonic phenomena beyond those achievable in bilayer TMDs. △ Less

Submitted 29 April, 2025; originally announced April 2025.

Comments: 24 pages, 17 figures

Shift current response in twisted double bilayer graphenes

Authors: Takaaki V. Joya, Takuto Kawakami, Mikito Koshino

Abstract: We calculate the shift current response in twisted double bilayer graphenes (TDBG) by applying the perturbative approach to the effective continuum Hamiltonian. We have performed a systematic study of the shift current in AB-AB and AB-BA stacked TDBG, where we have investigated the dependence of the signal on the twist angle, the vertical bias voltage and the Fermi level. The numerical analyses de… ▽ More We calculate the shift current response in twisted double bilayer graphenes (TDBG) by applying the perturbative approach to the effective continuum Hamiltonian. We have performed a systematic study of the shift current in AB-AB and AB-BA stacked TDBG, where we have investigated the dependence of the signal on the twist angle, the vertical bias voltage and the Fermi level. The numerical analyses demonstrate that the signal is greatly enhanced as the twist angle is reduced. Notably, we also found that there is a systematic sign reversal of the signal in the two stacking configurations below the charge neutrality point for large bias voltages. We qualitatively explain the origin of this sign reversal by studying the shift current response in AB-stacked bilayer graphene. △ Less

Submitted 11 July, 2025; v1 submitted 9 March, 2025; originally announced March 2025.

Electronic properties of stacking faults in Bernal graphite

Authors: Patrick Johansen Sarsfield, Sergey Slizovskiy, Mikito Koshino, Vladimir Fal'ko

Abstract: Using the tight-binding model of graphite, incorporating all Slonczewski-Weiss-McClure parameters, we compute the spectrum of two-dimensional states of electrons bound to a stacking fault in Bernal graphite. We find that those bands retain characteristic features of the low-energy bands of a rhombohedral graphene trilayer, which actually represents the lattice structure the fault. Based on the sel… ▽ More Using the tight-binding model of graphite, incorporating all Slonczewski-Weiss-McClure parameters, we compute the spectrum of two-dimensional states of electrons bound to a stacking fault in Bernal graphite. We find that those bands retain characteristic features of the low-energy bands of a rhombohedral graphene trilayer, which actually represents the lattice structure the fault. Based on the self-consistent analysis of charge and potential distribution across the fault layers, we determine the shape of the Fermi contour for the 2D band, which has the form of three pockets with a hole-like conic dispersion and Dirac points above the Fermi level. The computed frequency of Shubnikov-de Haas oscillations and the cyclotron mass of the fault-bound charge carriers (at the Fermi level) are sufficiently different from the corresponding bulk values in graphite, making such stacking faults identifiable by quantum transport and cyclotron resonance measurements. △ Less

Submitted 9 December, 2024; originally announced December 2024.

Comments: 5 pages, 5 figures (main text). 7 pages, 9 figures (supplementary text)

Electromagnetic response in dipole superfluids: vortex lattices and singular domain walls

Authors: Kazuki Yamamoto, Takuto Kawakami, Mikito Koshino

Abstract: Among the most significant macroscopic quantum phenomena in condensed matter physics is the Meissner effect observed in superconductivity, which arises from the unique interaction between superfluids of charged particles and electromagnetic fields. However, superfluids can also emerge from particles possessing distinct electromagnetic properties. In particular, there has been growing interest in s… ▽ More Among the most significant macroscopic quantum phenomena in condensed matter physics is the Meissner effect observed in superconductivity, which arises from the unique interaction between superfluids of charged particles and electromagnetic fields. However, superfluids can also emerge from particles possessing distinct electromagnetic properties. In particular, there has been growing interest in superfluids composed of charge-neutral particles with magnetic or electric dipole moments, such as Bose-Einstein condensates of magnons or excitons. Despite this interest, the electromagnetic response of dipole superfluids, including potential analogs or contrasts to the Meissner effect, remains poorly understood. In this work, we develop a Ginzburg-Landau phenomenological theory to describe magnetic and electric dipole superfluids subjected to pseudo-magnetic fields induced by geometric phases. For magnetic dipole superfluids interacting with the Aharonov-Casher (AC) phase, we find that they form vortex lattices with sharply localized pseudo-magnetic fields along hexagonal domain walls, leading to singular and discontinuous change of physical variables at these boundaries. For electric dipole superfluids influenced by the He-McKellar-Wilkens (HMW) phase, in contrast, we identify vortex lattices where the pseudo-magnetic field and supercurrent are concentrated at vortex cores, resembling superconductors. These results reveal strikingly different electromagnetic responses in dipole superfluids, opening new directions for exploring superfluid systems with unconventional electromagnetic responses. △ Less

Submitted 15 January, 2025; v1 submitted 22 October, 2024; originally announced October 2024.

Comments: 17 pages, 8 figures

Journal ref: Commun. Phys. 8, 171 (2025)

Manipulating moires by controlling heterostrain in van der Waals devices

Authors: Ian Sequeira, Andrew Z. Barabas, Aaron H Barajas-Aguilar, Michaela G Bacani, Naoto Nakatsuji, Mikito Koshino, Takashi Taniguichi, Kenji Watanabe, Javier D. Sanchez-Yamagishi

Abstract: Van der Waals (vdW) moires offer tunable superlattices that can strongly manipulate electronic properties. We demonstrate the in-situ manipulation of moire superlattices via heterostrain control in a vdW device. By straining a graphene layer relative to its hexagonal boron nitride substrate, we modify the shape and size of the moire. Our sliding-based technique achieves uniaxial heterostrain value… ▽ More Van der Waals (vdW) moires offer tunable superlattices that can strongly manipulate electronic properties. We demonstrate the in-situ manipulation of moire superlattices via heterostrain control in a vdW device. By straining a graphene layer relative to its hexagonal boron nitride substrate, we modify the shape and size of the moire. Our sliding-based technique achieves uniaxial heterostrain values exceeding 1%, resulting in distorted moires that are larger than those achievable without strain. The stretched moire is evident in transport measurements, resulting in shifted superlattice resistance peaks and Landau fans consistent with an enlarged superlattice unit cell. Electronic structure calculations reveal how heterostrain shrinks and distorts the moire Brillouin zone, resulting in a reduced electronic bandwidth as well as the appearance of highly anisotropic and quasi-1-dimensional Fermi surfaces. Our heterostrain control approach opens a wide parameter space of moire lattices to explore beyond what is possible by twist angle control alone. △ Less

Submitted 11 September, 2024; originally announced September 2024.

Low-temperature thermal transport in moiré superlattices

Authors: Lukas P. A. Krisna, Takuto Kawakami, Mikito Koshino

Abstract: We calculate the phonon thermal conductivity of various moiré bilayer systems using a continuum approach and the semiclassical transport theory. When the twist angle is close to 0, we observe a significant reduction of thermal conductivity in a particular low-temperature regime. This reduction is attributed to a moiré-induced reconstruction of acoustic phonon bands and associated decrease of the g… ▽ More We calculate the phonon thermal conductivity of various moiré bilayer systems using a continuum approach and the semiclassical transport theory. When the twist angle is close to 0, we observe a significant reduction of thermal conductivity in a particular low-temperature regime. This reduction is attributed to a moiré-induced reconstruction of acoustic phonon bands and associated decrease of the group velocity. Conversely, in the zero temperature limit, the thermal conductivity is enhanced by moiré effect, surpassing the original values in non-moiré counterparts. These changes result in a characteristic temperature dependence which deviates from the quadratic behavior in intrinsic two-dimensional systems. △ Less

Submitted 7 February, 2025; v1 submitted 1 May, 2024; originally announced May 2024.

Comments: 12 pages, 10 figures

Journal ref: J. Phys. Soc. Jpn. 94, 044602 (2025)

A Microscopic study of Magnetic monopoles in Topological Insulators

Authors: Shoto Aoki, Hidenori Fukaya, Naoto Kan, Mikito Koshino, Yoshiyuki Matsuki

Abstract: In this article, we analyze a magnetic monopole in topological insulators. The monopole obtain a fractional electric charge because of the Witten effect. We consider this system with a microscopic view by adding the Wilson term to the ordinary Dirac Hamiltonian. The Wilson term yields the positive mass shift to the effective mass of the electrons, then the curved domain-wall is dynamically generat… ▽ More In this article, we analyze a magnetic monopole in topological insulators. The monopole obtain a fractional electric charge because of the Witten effect. We consider this system with a microscopic view by adding the Wilson term to the ordinary Dirac Hamiltonian. The Wilson term yields the positive mass shift to the effective mass of the electrons, then the curved domain-wall is dynamically generated around the monopole. The zero-modes of the electrons are localized on the domain-wall, which can be identified as the source of the electric charge. △ Less

Submitted 11 January, 2024; originally announced January 2024.

Comments: 9 pages, contribution to the 40th International Symposium on Lattice Field Theory (Lattice2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

Report number: OU-HET-1212

Non-linear Landau fan diagram for graphene electrons exposed to a moiré potential

Authors: Pilkyung Moon, Youngwook Kim, Mikito Koshino, Takashi Taniguchi, Kenji Watanabe, Jurgen H. Smet

Abstract: Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and magnetic field. This fan looks identical irrespective of the electron dispersion details that determines the field dependence of the Landau level energy. This is… ▽ More Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and magnetic field. This fan looks identical irrespective of the electron dispersion details that determines the field dependence of the Landau level energy. This is no surprise, since the position of conductance minima solely depends on the level degeneracy which is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they too create just linear fans for the same reason. Here, we report on conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule of flux linearity and attribute the anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown. △ Less

Submitted 27 November, 2023; originally announced November 2023.

Journal ref: Nano Letters (2024)

Perpendicular electronic transport and moiré-induced resonance in twisted interfaces of three-dimensional graphite

Authors: Tenta Tani, Takuto Kawakami, Mikito Koshino

Abstract: We calculate the perpendicular electrical conductivity in twisted three-dimensional graphite (rotationally stacked graphite pieces) by using the effective continuum model and the recursive Green's function method. In the low twist angle regime $(θ\lesssim 2^\circ)$, the conductivity shows a nonmonotonic dependence with a peak and dip structure as a function of the twist angle. By analyzing the mom… ▽ More We calculate the perpendicular electrical conductivity in twisted three-dimensional graphite (rotationally stacked graphite pieces) by using the effective continuum model and the recursive Green's function method. In the low twist angle regime $(θ\lesssim 2^\circ)$, the conductivity shows a nonmonotonic dependence with a peak and dip structure as a function of the twist angle. By analyzing the momentum-resolved conductance and the local density of states, this behavior is attributed to the Fano resonance between continuum states of bulk graphite and interface-localized states, which is a remnant of the flat band in the magic-angle twisted bilayer graphene. We also apply the formulation to the high-angle regime near the commensurate angle $θ\approx 21.8^\circ$, and reproduce the conductance peak observed in the experiment. △ Less

Submitted 25 October, 2023; v1 submitted 7 August, 2023; originally announced August 2023.

Comments: 15 pages, 13 figures

Journal ref: Phys. Rev. B 108, 165422 (2023)

Multi-scale lattice relaxation in general twisted trilayer graphenes

Authors: Naoto Nakatsuji, Takuto Kawakami, Mikito Koshino

Abstract: We present comprehensive theoretical studies on the lattice relaxation and the electronic structures in general non-symemtric twisted trilayer graphenes. By using an effective continuum model, we show that the relaxed lattice structure forms a patchwork of moiré-of-moiré domains, where a moiré pattern given by layer 1 and 2 and another pattern given by layer 2 and 3 become locally commensurate. Th… ▽ More We present comprehensive theoretical studies on the lattice relaxation and the electronic structures in general non-symemtric twisted trilayer graphenes. By using an effective continuum model, we show that the relaxed lattice structure forms a patchwork of moiré-of-moiré domains, where a moiré pattern given by layer 1 and 2 and another pattern given by layer 2 and 3 become locally commensurate. The atomic configuration inside the domain exhibits a distinct contrast between chiral and alternating stacks, which are determined by the relative signs of the two twist angles. In the chiral case, the electronic band calculation reveals a wide energy window ($>$ 50 meV) with low density of states, featuring sparsely distributed highly one-dimensional electron bands. These one-dimensional states exhibit a sharp localization at the boundaries between super-moiré domains, and they are identified as a topological boundary state between distinct Chern insulators. The alternating trilayer exhibits a coexistence of the flat bands and a monolayer-like Dirac cone, and it is attributed to the formation of moiré-of-moiré domains equivalent to the mirror-symmetric twisted trilayer graphene. △ Less

Submitted 6 June, 2023; v1 submitted 22 May, 2023; originally announced May 2023.

Comments: 18 pages, 16 figures

Why magnetic monopole becomes dyon in topological insulators

Authors: Shoto Aoki, Hidenori Fukaya, Naoto Kan, Mikito Koshino, Yoshiyuki Matsuki

Abstract: The Witten effect predicts that a magnetic monopole acquires a fractional electric charge inside topological insulators. In this work, we give a microscopic description of this phenomenon, as well as an analogous two-dimensional system with a vortex. We solve the Dirac equation of electron field both analytically in continuum and numerically on a lattice, by adding the Wilson term and smearing t… ▽ More The Witten effect predicts that a magnetic monopole acquires a fractional electric charge inside topological insulators. In this work, we give a microscopic description of this phenomenon, as well as an analogous two-dimensional system with a vortex. We solve the Dirac equation of electron field both analytically in continuum and numerically on a lattice, by adding the Wilson term and smearing the gauge field within a finite range to regularize the short-distance behavior of the system. Our results reveal that the Wilson term induces a strong positive mass shift, creating a domain-wall around the monopole/vortex. This small, yet finite-sized domain-wall localizes the chiral zero modes and ensures their stability through the Atiyah-Singer index theorem, whose cobordism invariance is crucial in explaining why the electric charge is fractional. △ Less

Submitted 20 May, 2024; v1 submitted 27 April, 2023; originally announced April 2023.

Comments: 40 pages, 10 figures, minor corrections, references added, published version

Report number: OU-HET-1181

Topological Domain Walls in Graphene Nanoribbons with Carrier Doping

Authors: Takuto Kawakami, Gen Tamaki, Mikito Koshino

Abstract: We theoretically study magnetic ground states of doped zigzag graphene nanoribbons and the emergence of topological domain walls. Using the Hartree-Fock mean-field approach and an effective continuum model, we demonstrated that the carrier doping stabilizes a magnetic structure with alternating antiferromagnetic domains, where the doped carriers are accommodated in topological bound states localiz… ▽ More We theoretically study magnetic ground states of doped zigzag graphene nanoribbons and the emergence of topological domain walls. Using the Hartree-Fock mean-field approach and an effective continuum model, we demonstrated that the carrier doping stabilizes a magnetic structure with alternating antiferromagnetic domains, where the doped carriers are accommodated in topological bound states localized at the domain wall. The energy spectrum exhibits a Hofstadter-like fractal spectral evolution as a function of the carrier density, where minigaps are characterized by the Chern number associated with the adiabatic charge pump in moving domain walls. A systematic analysis for nanoribbons with different widths revealed that the ferromagnetic domain-wall phase emerges in relatively wide ribbons, while the colinear domain-wall phase arises in narrower ribbons. △ Less

Submitted 17 March, 2023; originally announced March 2023.

Comments: 14 pages, 11 figures

Mechanical properties of 2D metal-organic and covalent-organic frameworks with non trivial topological band dispersion

Authors: Priyadarshini Kapri, Takuto Kawakami, Mikito Koshino

Abstract: Using density functional theory (DFT), we investigate mechanical properties of a few 2D metal-organic frameworks (MOFs) and covalent-organic frameworks (COFs) having Dirac and flat bands. These porous materials have become a subject of great captivation because of their physical stability, distinctive structural characteristics and large surface to volume ratio. The inherent porosity of these fram… ▽ More Using density functional theory (DFT), we investigate mechanical properties of a few 2D metal-organic frameworks (MOFs) and covalent-organic frameworks (COFs) having Dirac and flat bands. These porous materials have become a subject of great captivation because of their physical stability, distinctive structural characteristics and large surface to volume ratio. The inherent porosity of these frameworks gives rise to many fascinating and occasionally surprising phenomena, which makes them potential candidates for technological applications. For reliable usage of MOFs/COFs in functional nanodevice and practical application, it is quite imperative to investigate their mechanical properties. Thus, herein a particular attention is paid to study elastic deformation of few 2D MOFs and COFs having non trivial topological band dispersion in the regime with linear dependency of stress upon strain. Specially, we consider different types of deformation and find all the components of elastic tensor from the stress-strain and energy-strain curves. These findings may provide useful information to fabricate the MOFs/COFs based devices by lowering the number of experiments. △ Less

Submitted 14 March, 2023; originally announced March 2023.

Comments: 26 Pages, 9 figures

Moiré phonons in graphene/hexagonal boron nitride moiré superlattice

Authors: Lukas P. A. Krisna, Mikito Koshino

Abstract: We theoretically study in-plane acoustic phonons of graphene/hexagonal boron nitride moiré superlattice by using a continuum model. We demonstrate that the original phonon bands of individual layers are strongly hybridized and reconstructed into moiré phonon bands consisting of dispersive bands and flat bands. The phonon band structure can be effectively described by a spring-mass network model to… ▽ More We theoretically study in-plane acoustic phonons of graphene/hexagonal boron nitride moiré superlattice by using a continuum model. We demonstrate that the original phonon bands of individual layers are strongly hybridized and reconstructed into moiré phonon bands consisting of dispersive bands and flat bands. The phonon band structure can be effectively described by a spring-mass network model to simulate the motion of moiré domain walls, where the flat-band modes are interpreted as vibrations of independent, decoupled strings. We also show that the moiré phonon has angular momentum due to the inversion symmetry breaking by hBN, with high amplitudes concentrated near narrow gap region. Finally, we apply the same approach to twisted bilayer graphene, and we find a notable difference between the origins of the flat-band modes in G/hBN and TBG, reflecting distinct geometric structures of domain pattern. △ Less

Submitted 2 March, 2023; v1 submitted 7 October, 2022; originally announced October 2022.

Comments: 15 pages, 11 figures

Journal ref: Phys. Rev. B 107, 115301 (2023)

Spontaneous spin-valley polarization in NbSe2 at a van der Waals interface

Authors: Hideki Matsuoka, Tetsuro Habe, Yoshihiro Iwasa, Mikito Koshino, Masaki Nakano

Abstract: A proximity effect at a van der Waals (vdW) interface enables creation of an emergent quantum electronic ground state. Here we demonstrate that an originally-superconducting two-dimensional (2D) NbSe2 forms a ferromagnetic ground state with spontaneous spin polarization at a vdW interface with a 2D ferromagnet V5Se8. We investigated the anomalous Hall effect (AHE) of the NbSe2/V5Se8 magnetic vdW h… ▽ More A proximity effect at a van der Waals (vdW) interface enables creation of an emergent quantum electronic ground state. Here we demonstrate that an originally-superconducting two-dimensional (2D) NbSe2 forms a ferromagnetic ground state with spontaneous spin polarization at a vdW interface with a 2D ferromagnet V5Se8. We investigated the anomalous Hall effect (AHE) of the NbSe2/V5Se8 magnetic vdW heterostructures, and found that the sign of the AHE was reversed as the number of the V5Se8 layer was thinned down to the monolayer limit. Interestingly, the AHE signal of those samples was enhanced with the in-plane magnetic fields, suggesting an additional contribution to the AHE signal other than magnetization. This unusual behavior is well reproduced by band structure calculations, where the emergence of the Berry curvature along the spin-degenerate nodal lines in 2D NbSe2 by the in-plane magnetization plays a key role, unveiling a unique interplay between magnetism and Zeeman-type spin-orbit interaction in a non-centrosymmetric 2D quantum material. △ Less

Submitted 30 August, 2022; v1 submitted 28 August, 2022; originally announced August 2022.

Comments: accepted to Nature Communications

Perfect one-dimensional interface states in a twisted stack of three-dimensional topological insulators

Authors: Manato Fujimoto, Takuto Kawakami, Mikito Koshino

Abstract: We theoretically study the electronic structure of interface states in twisted stacks of three-dimensional topological insulators. When the center of the surface Dirac cone is located at a midpoint of a side of BZ boundary, we find that an array of nearly-independent one-dimensional channels is formed by the interface hybridization of the surface states, even when the moiré pattern itself is isotr… ▽ More We theoretically study the electronic structure of interface states in twisted stacks of three-dimensional topological insulators. When the center of the surface Dirac cone is located at a midpoint of a side of BZ boundary, we find that an array of nearly-independent one-dimensional channels is formed by the interface hybridization of the surface states, even when the moiré pattern itself is isotropic. The two counter-propagating channels have opposite spin polarization, and they are robust against scattering by spin-independent impurities. The coupling between the parallel channels can be tuned by the twist angle.The unique 1D states can be understood as effective Landau levels where the twist angle works as a fictitious magnetic field. △ Less

Submitted 27 June, 2022; originally announced June 2022.

Comments: 12 pages, 9 figures

Moiré disorder effect in twisted bilayer graphene

Authors: Naoto Nakatsuji, Mikito Koshino

Abstract: We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moiré patterns. By using an extended continuum model incorporating non-uniform lattice distortion, we find that the local density of states of the flat band is hardly broadened, but splits into upper and lower subbands in most places. The spatial dependence of the splitting energy is almost excl… ▽ More We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moiré patterns. By using an extended continuum model incorporating non-uniform lattice distortion, we find that the local density of states of the flat band is hardly broadened, but splits into upper and lower subbands in most places. The spatial dependence of the splitting energy is almost exclusively determined by the local value of the effective vector potential induced by heterostrain, whereas the variation of local twist angle and local moiré period give relatively minor effects on the electronic structure. We explain the exclusive dependence on the local vector potential by a pseudo Landau level picture for the magic-angle flat band, and we obtain an analytic expression of the splitting energy as a function of the strain amplitude. △ Less

Submitted 13 April, 2022; originally announced April 2022.

Comments: 11 pages, 6 figures

Momentum-dependent oscillator strength crossover of excitons and plasmons in two-dimensional PtSe2

Authors: Jinhua Hong, Mark Kamper Svendsen, Masanori Koshino, Thomas Pichler, Hua Xu, Kazu Suenaga, Kristian Sommer Thygesen

Abstract: The 1T-phase layered PtX2 chalcogenides has attracted widespread interest due to its thickness dependent metal-semiconductor transition driven by strong interlayer coupling. While the ground state properties of this paradigmatic material system have been widely explored, its fundamental excitation spectrum remains poorly understood. Here we combine first principles calculations with momentum (q) r… ▽ More The 1T-phase layered PtX2 chalcogenides has attracted widespread interest due to its thickness dependent metal-semiconductor transition driven by strong interlayer coupling. While the ground state properties of this paradigmatic material system have been widely explored, its fundamental excitation spectrum remains poorly understood. Here we combine first principles calculations with momentum (q) resolved electron energy loss spectroscopy (q-EELS) to study the collective excitations in 1T-PtSe2 from the monolayer limit to the bulk. At finite momentum transfer all the spectra are dominated by two distinct interband plasmons that disperse to higher energy with increasing q. Interestingly, the absence of long-range screening in the two-dimensional (2D) limit, inhibits the formation of long wavelength plasmons. Consequently, in the small-q limit, excitations in monolayer PtSe2 are exclusively of excitonic nature, and the loss spectrum coincides with the optical spectrum. Our work unravels the excited state spectrum of layered 1T-PtSe2 and establishes the qualitatively different momentum dependence of excitons and plasmons in 2D materials. △ Less

Submitted 9 March, 2022; originally announced March 2022.

Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals

Authors: Kazuki Yamamoto, Mikito Koshino

Abstract: We study the topological gap labeling of general 3D quasicrystals and we find that every gap in the spectrum is characterized by a set of the third Chern numbers. We show that a quasi-periodic structure has multiple Brillouin zones defined by redundant wavevectors, and the number of states below a gap is quantized as an integer linear combination of volumes of these Brillouin zones. The associated… ▽ More We study the topological gap labeling of general 3D quasicrystals and we find that every gap in the spectrum is characterized by a set of the third Chern numbers. We show that a quasi-periodic structure has multiple Brillouin zones defined by redundant wavevectors, and the number of states below a gap is quantized as an integer linear combination of volumes of these Brillouin zones. The associated quantum numbers to characterize energy gaps can be expressed as third Chern numbers by considering a formal relationship between an adiabatic charge pumping under cyclic deformation of the quasi-periodic potential and a topological nonlinear electromagnetic response in 6D insulators. △ Less

Submitted 13 January, 2022; originally announced January 2022.

Comments: 8 pages, 2 figures

Topological edge and corner states and fractional corner charges in blue phosphorene

Authors: Tenta Tani, Masaru Hitomi, Takuto Kawakami, Mikito Koshino

Abstract: We theoretically study emergent edge and corner states in monolayer blue phosphorus (blue phosphorene) using the first-principles calculation and tight-binding model. We show that the existence of the Wannier orbitals at every bond center yields edge states both in zigzag and armchair nanoribbons. The properties of the edge states can be well described by a simple effective Hamiltonian for uncoupl… ▽ More We theoretically study emergent edge and corner states in monolayer blue phosphorus (blue phosphorene) using the first-principles calculation and tight-binding model. We show that the existence of the Wannier orbitals at every bond center yields edge states both in zigzag and armchair nanoribbons. The properties of the edge states can be well described by a simple effective Hamiltonian for uncoupled edge orbitals, where the structural relaxation near the boundary significantly affects the edge band structure. For corner states, we examine two types of corner structures consisting of zigzag and armchair edges, where we find that multiple corner states emerge in the bulk gap as a consequence of hybridization of edge and corner uncoupled orbitals. In the armchair corner, in particular, we demonstrate that corner states appear right at the Fermi energy, which leads to the emergence of fractional corner charge due to filling anomaly. Finally, we discuss the relationship between blue phosphorene and black phosphorene, and show that two systems share the equivalent Wannier orbital positions and similar edge/corner state properties even though their atomic structures are totally different. △ Less

Submitted 7 February, 2022; v1 submitted 22 December, 2021; originally announced December 2021.

Comments: 15 pages, 10 figures

Journal ref: Phys. Rev. B 105, 075407 (2022)

Topological invariants in two-dimensional quasicrystals

Authors: Mikito Koshino, Hiroki Oka

Abstract: We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones defined in the redundant periodicities. T… ▽ More We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones defined in the redundant periodicities. These integers can be expressed as the second Chern numbers, by considering an adiabatic charge pumping under a relative slide of different periodicities, and using a formal relationship to the four-dimensional quantum Hall effect. The integers are independent of commensurability of the multiple periods, and invariant under arbitrary continuous deformations such as a relative rotation of twisted periodicities. △ Less

Submitted 27 September, 2021; originally announced September 2021.

Comments: 17 pages, 12 figures

Interlayer interactions in one-dimensional van der Waals moiré superlattices

Authors: Sihan Zhao, Ryo Kitaura, Pilkyung Moon, Mikito Koshino, Feng Wang

Abstract: Different atomistic registry between the layers forming the inner and outer nanotubes can form one-dimensional (1D) van der Waals (vdW) moiré superlattices. Unlike the two-dimensional (2D) vdW moiré superlattices, effects of 1D vdW moiré superlattices on electronic and optical properties in 1D moiré superlattices are not well understood, and they are often neglected. In this Perspective, we summar… ▽ More Different atomistic registry between the layers forming the inner and outer nanotubes can form one-dimensional (1D) van der Waals (vdW) moiré superlattices. Unlike the two-dimensional (2D) vdW moiré superlattices, effects of 1D vdW moiré superlattices on electronic and optical properties in 1D moiré superlattices are not well understood, and they are often neglected. In this Perspective, we summarize new experimental observations and theoretical perspectives related to interlayer interactions in double-walled carbon nanotubes (DWNTs), a representative 1D vdW moiré system. Our discussion will focus on new optical features emerging from the interlayer electronic interactions in DWNTs. Exciting correlated physics and exotic phases of matter are anticipated to exist in 1D vdW moiré superlattices, analogous with those discovered in the 2D vdW moiré superlattices. We further discuss the future directions in probing and uncovering interesting physical phenomena in 1D moiré superlattices. △ Less

Submitted 29 July, 2021; originally announced July 2021.

Comments: 28 pages

Multiorbital edge and corner states in black phosphorene

Authors: Masaru Hitomi, Takuto Kawakami, Mikito Koshino

Abstract: We theoretically study emergent edge/corner localized states in monolayer black phosphorene. Using the tight-binding model based on the density functional theory, we find that the multi-orbital band structure due to the non-planar puckered geometry plays an essential role in the formation of the boundary localized modes. In particular, we demonstrate that edge states emerge at a boundary along an… ▽ More We theoretically study emergent edge/corner localized states in monolayer black phosphorene. Using the tight-binding model based on the density functional theory, we find that the multi-orbital band structure due to the non-planar puckered geometry plays an essential role in the formation of the boundary localized modes. In particular, we demonstrate that edge states emerge at a boundary along an arbitrary crystallographic direction, and it can be understood from the fact that the Wannier orbitals associated with $3p_x$, $3p_y$, $3p_z$ orbitals occupy all the bond centers of phosphorene. At a corner where two edges intersect, we show that multiple corner-localized states appear due to hybridization of higher-order topological corner state and the edge states nearby. These characteristic properties of the edge and corner states can be intuitively explained by a simple topologically-equivalent model where all the bond angles are deformed to $90^{\circ}$. △ Less

Submitted 21 September, 2021; v1 submitted 11 May, 2021; originally announced May 2021.

Comments: 15 pages, 15 figures

Journal ref: Phys. Rev. B 104, 125302 (2021)

Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moiré systems

Authors: Hiroki Oka, Mikito Koshino

Abstract: We calculate the electronic structure in quasiperiodic double-moiré systems of graphene sandwiched by hexagonal boron nitride, and identify the topological invariants of energy gaps. We find that the electronic spectrum contains a number of minigaps, and they exhibit a recursive fractal structure similar to the Hofstadter butterfly when plotted against the twist angle. Each of the energy gaps can… ▽ More We calculate the electronic structure in quasiperiodic double-moiré systems of graphene sandwiched by hexagonal boron nitride, and identify the topological invariants of energy gaps. We find that the electronic spectrum contains a number of minigaps, and they exhibit a recursive fractal structure similar to the Hofstadter butterfly when plotted against the twist angle. Each of the energy gaps can be characterized by a set of integers, which are associated with an area in the momentum space. The corresponding area is geometrically interpreted as a quasi Brillouin zone, which is a polygon enclosed by multiple Bragg planes of the composite periods and can be uniquely specified by the plain wave projection in the weak potential limit. △ Less

Submitted 11 May, 2021; originally announced May 2021.

Comments: 17 pages, 11 figures

Journal ref: Phys. Rev. B 104, 035306 (2021)

Deciphering the Intense Post-Gap Absorptions of Monolayer Transition Metal Dichalcogenides

Authors: Jinhua Hong, Masanori Koshino, Ryosuke Senga, Thomas Pichler, Hua Xu, Kazu Suenaga

Abstract: Rich valleytronics and diverse defect-induced or interlayer pre-bandgap excitonics have been extensively studied in transition metal dichalcogenides (TMDCs), a system with fascinating optical physics. However, more intense high-energy absorption peaks (~ 3 eV) above the bandgaps used to be long ignored and their underlying physical origin remains to be unveiled. Here, we employ momentum resolved e… ▽ More Rich valleytronics and diverse defect-induced or interlayer pre-bandgap excitonics have been extensively studied in transition metal dichalcogenides (TMDCs), a system with fascinating optical physics. However, more intense high-energy absorption peaks (~ 3 eV) above the bandgaps used to be long ignored and their underlying physical origin remains to be unveiled. Here, we employ momentum resolved electron energy loss spectroscopy to measure the dispersive behaviors of the valley excitons and intense higher-energy peaks at finite momenta. Combined with accurate Bethe Salpeter equation calculations, non-band-nesting transitions at Q valley and at midpoint of KM are found to be responsible for the high-energy broad absorption peaks in tungsten dichalcogenides and present spin polarizations similar to A excitons, in contrast with the band-nesting mechanism in molybdenum dichalcogenides. Our experiment-theory joint research will offer insights into the physical origins and manipulation of the intense high-energy excitons in TMDCs-based optoelectronic devices. △ Less

Submitted 1 April, 2021; originally announced April 2021.

Fractal defect states in the Hofstadter butterfly

Authors: Yoshiyuki Matsuki, Kazuki Ikeda, Mikito Koshino

Abstract: We investigate the electronic properties in the Bloch electron on a square lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to the system creates a defect energy level in every single innumerable fractal energy gap in the Hofstadter butterfly. The wavefunctions of different defect levels have all different localization lengths depending on their f… ▽ More We investigate the electronic properties in the Bloch electron on a square lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to the system creates a defect energy level in every single innumerable fractal energy gap in the Hofstadter butterfly. The wavefunctions of different defect levels have all different localization lengths depending on their fractal generations, and they can be described by a single universal function after an appropriate fractal scaling. We also show that each defect state has its own characteristic orbital magnetic moment, which is exactly correlated to the gradient of the energy level in the Hofstadter diagram. Probing the spatial nature of the defect-localized states provides a powerful way to elucidate the fractal nature of the Hofstadter butterfly. △ Less

Submitted 24 February, 2021; originally announced February 2021.

Comments: 10 pages, 10 figures

Report number: OU-HET-1092

Journal ref: Phys. Rev. B 104, 035305 (2021)

Moiré edge states in twisted bilayer graphene and their topological relation to quantum pumping

Authors: Manato Fujimoto, Mikito Koshino

Abstract: We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relativ… ▽ More We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relatively slid with respect to the other layer, the edge states are transferred from a single band to another across the band gap, and the number of the edge states pumped in a sliding cycle is shown to be equal to the sliding Chern number of the band gap. The relationship can be viewed as a manifestation of the bulk-edge correspondence inherent in moiré bilayer systems. △ Less

Submitted 4 December, 2020; originally announced December 2020.

Comments: 7 pages, 5 figures

Journal ref: Phys. Rev. B 103, 155410 (2021)

Dirac Fermion kinetics in three-dimensionally curved graphene

Authors: Yoichi Tanabe, Yoshikazu Ito, Katsuaki Sugawara, Mikito Koshino, Shojiro Kimura, Tomoya Naito, Isaac Johnson, Takashi Takahashi, Mingwei Chen

Abstract: Three dimensionally curved graphene with a wide range of curvature radii from 25 nm to 1000 nm demonstrates that nano-scale curvature is a new degree of freedom to tune the transport properties of graphene by manipulating 2D electron kinetics on 3D curved surfaces. Three dimensionally curved graphene with a wide range of curvature radii from 25 nm to 1000 nm demonstrates that nano-scale curvature is a new degree of freedom to tune the transport properties of graphene by manipulating 2D electron kinetics on 3D curved surfaces. △ Less

Submitted 9 October, 2020; v1 submitted 7 October, 2020; originally announced October 2020.

Electronic properties of graphyne-$N$ monolayer and its multilayer: even-odd effect and topological nodal line semimetalic phases

Authors: Takuto Kawakami, Takafumi Nomura, Mikito Koshino

Abstract: We study the electronic structure and topological properties of monolayer and ABC-stacked multilayer of graphyne-$N$, which are a family of planar carbon sheets consisting of $sp$ and $sp_2$-bonding. By using the density-functional theory and the effective continuum model, we find a striking even-odd effect in the dependence of the band structure on $N$ (the number of carbon-carbon triple bonds be… ▽ More We study the electronic structure and topological properties of monolayer and ABC-stacked multilayer of graphyne-$N$, which are a family of planar carbon sheets consisting of $sp$ and $sp_2$-bonding. By using the density-functional theory and the effective continuum model, we find a striking even-odd effect in the dependence of the band structure on $N$ (the number of carbon-carbon triple bonds between neighboring benzene rings). Specifically, even-$N$ graphyne monolayer has doubly-degenerate conduction and valence bands near the Fermi energy, and in its ABC multilayer, the band inversion of the doubly-degenerate bands leads to a nodal-line semimetal phase with non-trivial $\mathbb{Z}_2$ monopole charge. In contrast, odd-$N$ monolayer has singly-degenerate bands in separate valleys, and its ABC multilayer can have only $\mathbb{Z}_2$-trivial nodal lines. ABC graphynes with larger $N$ tend to be trivial insulators because of smaller interlayer coupling, while the external pressure induces a topological phase transition from the trivial phase to the nodal line semimetal phase. △ Less

Submitted 22 September, 2020; v1 submitted 11 August, 2020; originally announced August 2020.

Comments: 16 pages, 13 figures, 4 tables

Journal ref: Phys. Rev. B 102, 115421 (2020)

Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphenes

Authors: J. A. Crosse, Naoto Nakatsuji, Mikito Koshino, Pilkyung Moon

Abstract: We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system, we calculate the energy spectrum and quantized Hall conductivities at each spectral gap… ▽ More We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system, we calculate the energy spectrum and quantized Hall conductivities at each spectral gap by using a continuum Hamiltonian that satisfies the magneto-translation condition. We show that the Hofstadter butterfly spectra of AB-AB and AB-BA stackings differ significantly, even though their zero magnetic field band structures closely resemble; the spectrum of AB-AB has valley degeneracy, which can be lifted by applying interlayer potential asymmetry, while the spectrum of AB-BA has no such degeneracy in any case. We explain the origin of the difference from the perspectives of lattice symmetry and band topology. △ Less

Submitted 13 May, 2020; originally announced May 2020.

Comments: 10 pages, 4 figures

Journal ref: Phys. Rev. B 102, 035421 (2020)

Topological junction states and their crystalline network in chiral-symmetric systems: application to graphene nanoribbons

Authors: Gen Tamaki, Takuto Kawakami, Mikito Koshino

Abstract: We develop a general theoretical framework based on $Z$-classification to count the number of topological bound states at a junction of chiral-symmetric one-dimensional systems. The formulation applies to general multiway junctions composed of an arbitrary number of channels and an arbitrary joint structure. By using the formula, we calculate the zero-energy bound states in various types of two-wa… ▽ More We develop a general theoretical framework based on $Z$-classification to count the number of topological bound states at a junction of chiral-symmetric one-dimensional systems. The formulation applies to general multiway junctions composed of an arbitrary number of channels and an arbitrary joint structure. By using the formula, we calculate the zero-energy bound states in various types of two-way and three-way junctions of semiconducting graphene nanoribbons. We then consider periodic two-dimensional networks of graphene nanoribbons, and show that the topological junction states form isolated energy bands inside the bulk energy gap, which can be viewed as a two-dimensional crystal of the effective atoms. Depending on the $Z$ number of a single junction, we have a different set of effective atomic orbitals, resulting in various types of nanoscale metamaterials, which are often accompanied by flat bands. The system would provide an ideal platform for quantum simulator to emulate a strongly-interacting fermion system on various types of lattices. △ Less

Submitted 27 May, 2020; v1 submitted 9 April, 2020; originally announced April 2020.

Comments: 11 pages, 12 figures

Journal ref: Phys. Rev. B 101, 205311 (2020)

Perfect one-dimensional chiral states in biased twisted bilayer graphene

Authors: Bonnie Tsim, Nguyen N. T. Nam, Mikito Koshino

Abstract: We theoretically study the electronic structure of small-angle twisted bilayer graphene with a large potential asymmetry between the top and bottom layers. We show that the emergent helical states known to appear on the triangular AB-BA domain boundary do not actually form a percolating network, but instead they provide independent, perfect one-dimensional channels propagating in three different d… ▽ More We theoretically study the electronic structure of small-angle twisted bilayer graphene with a large potential asymmetry between the top and bottom layers. We show that the emergent helical states known to appear on the triangular AB-BA domain boundary do not actually form a percolating network, but instead they provide independent, perfect one-dimensional channels propagating in three different directions. Using the continuum-model Hamiltonian, we demonstrate that an applied bias causes two well-defined energy windows which contain sparsely distributed one-dimensional channels. The origin of these energy windows can be understood using a two-band model of the intersecting electron and hole bands of single layer graphene. We also use the tight-binding model to implement the lattice deformations in twisted bilayer graphene, and discuss the effect of lattice relaxation on the one-dimensional channels. △ Less

Submitted 22 January, 2020; v1 submitted 17 January, 2020; originally announced January 2020.

Comments: 9 pages, 7 figures

Journal ref: Phys. Rev. B 101, 125409 (2020)

Topological charge pumping by sliding moiré pattern

Authors: Manato Fujimoto, Henri Koschke, Mikito Koshino

Abstract: We study the adiabatic topological charge pumping driven by interlayer sliding in the moiré superlattices. We show that, when we slide a single layer of the twisted bilayer system relatively to the other, a moiré pattern flow and a quantized transport of electrons occurs. When the Fermi energy is in a spectral gap, the number of pumped charges in the interlayer sliding process is quantized to a sl… ▽ More We study the adiabatic topological charge pumping driven by interlayer sliding in the moiré superlattices. We show that, when we slide a single layer of the twisted bilayer system relatively to the other, a moiré pattern flow and a quantized transport of electrons occurs. When the Fermi energy is in a spectral gap, the number of pumped charges in the interlayer sliding process is quantized to a sliding Chern number, which obeys a Diophantine equation analogous to the quantum Hall effect. We apply the argument to the twisted bilayer graphene, and find that energy gaps above and below the nearly-flat bands has non-zero sliding Chern numbers. When the Fermi energy is in either of those gaps, the slide-driven topological pumping occurs perpendicularly to the sliding direction. △ Less

Submitted 10 October, 2019; originally announced October 2019.

Comments: 6 pages, 3 figures

Journal ref: Phys. Rev. B 101, 041112 (2020)

Continuum model for relaxed twisted bilayer graphenes and moiré electron-phonon interaction

Authors: Mikito Koshino, Nguyen N. T. Nam

Abstract: We construct an analytic continuum model to describe the electronic structure and the electron-phonon interaction in twisted bilayer graphenes with arbitrary lattice deformation. Starting from the tight-binding model, we derive the interlayer Hamiltonian in the presence of general lattice displacement, and obtain a long-wavelength continuum expression for smooth deformation. We show that the conti… ▽ More We construct an analytic continuum model to describe the electronic structure and the electron-phonon interaction in twisted bilayer graphenes with arbitrary lattice deformation. Starting from the tight-binding model, we derive the interlayer Hamiltonian in the presence of general lattice displacement, and obtain a long-wavelength continuum expression for smooth deformation. We show that the continuum model correctly describes the band structures of the lattice-relaxed twisted bilayer graphenes. We apply the formula to the phonon vibration, and derive an explicit expression of the electron-phonon matrix elements between the moiré band states and the moiré phonon modes. By numerical calculation, we find that the electron-phonon coupling and phonon mediated electron-electron interaction are significantly enhanced in low twist angles due to the superlattice hybridization. △ Less

Submitted 21 February, 2020; v1 submitted 24 September, 2019; originally announced September 2019.

Comments: 13 pages, 5 figures

Journal ref: Phys. Rev. B 101, 195425 (2020)

Mapping the twist angle and unconventional Landau levels in magic angle graphene

Authors: Aviram Uri, Sameer Grover, Yuan Cao, J. A. Crosse, Kousik Bagani, Daniel Rodan-Legrain, Yuri Myasoedov, Kenji Watanabe, Takashi Taniguchi, Pilkyung Moon, Mikito Koshino, Pablo Jarillo-Herrero, Eli Zeldov

Abstract: The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $θ_M \approx 1.1°$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$°$, little information is currently… ▽ More The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $θ_M \approx 1.1°$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$°$, little information is currently available on the distribution of the local twist angles in actual magic angle twisted bilayer graphene (MATBG) transport devices. Here we map the local $θ$ variations in hBN encapsulated devices with relative precision better than 0.002$°$ and spatial resolution of a few moir$é$ periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MATBG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local $θ$. We find that even state-of-the-art devices, exhibiting high-quality global MATBG features including superconductivity, display significant variations in the local $θ$ with a span close to 0.1$°$. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived $θ$ maps reveal substantial gradients and a network of jumps. We show that the twist angle gradients generate large unscreened electric fields that drastically change the quantum Hall state by forming edge states in the bulk of the sample, and may also significantly affect the phase diagram of correlated and superconducting states. The findings call for exploration of band structure engineering utilizing twist-angle gradients and gate-tunable built-in planar electric fields for novel correlated phenomena and applications. △ Less

Submitted 13 August, 2019; originally announced August 2019.

Journal ref: Nature 581, 47 (2020)

Observation of drastic electronic structure change in one-dimensional moiré crystals

Authors: Sihan Zhao, Pilkyung Moon, Yuhei Miyauchi, Kazunari Matsuda, Mikito Koshino, Ryo Kitaura

Abstract: We report the first experimental observation of strong coupling effect in one-dimensional moiré crystals. We study one-dimensional double-wall carbon nanotubes (DWCNTs) in which van der Waals-coupled two single nanotubes form one-dimensional moiré superlattice. We experimentally combine Rayleigh scattering spectroscopy and electron beam diffraction on the same individual DWCNTs to probe the optica… ▽ More We report the first experimental observation of strong coupling effect in one-dimensional moiré crystals. We study one-dimensional double-wall carbon nanotubes (DWCNTs) in which van der Waals-coupled two single nanotubes form one-dimensional moiré superlattice. We experimentally combine Rayleigh scattering spectroscopy and electron beam diffraction on the same individual DWCNTs to probe the optical transitions of structure-identified DWCNTs in the visible spectral range. Among more than 30 structure-identified DWCNTs examined, we experimentally observed and identified a drastic change of optical transition spectrum in DWCNT with chirality (12,11)@(17,16). The origin of the marked change is attributed to the strong intertube coupling effect in a moiré superlattice formed by two nearly-armchair nanotubes. Our numerical simulation is consistent to these experimental findings. △ Less

Submitted 27 June, 2019; v1 submitted 22 June, 2019; originally announced June 2019.

Journal ref: Phys. Rev. Lett. 124, 106101 (2020)

Films of rhombohedral graphite as two-dimensional topological semimetals

Authors: Sergey Slizovskiy, Edward McCann, Mikito Koshino, Vladimir I. Fal'ko

Abstract: Topologically non-trivial states characterized by Berry curvature appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene, despite a zero total Chern number for the entire Brillouin zone, Berry curvature with different signs concentrated in different valleys can affect the observable m… ▽ More Topologically non-trivial states characterized by Berry curvature appear in a number of materials ranging from spin-orbit-coupling driven topological insulators to graphene. In multivalley conductors, such as mono- and bilayer graphene, despite a zero total Chern number for the entire Brillouin zone, Berry curvature with different signs concentrated in different valleys can affect the observable material's transport characteristics. Here we consider thin films of rhombohedral graphite, which appear to retain truly two-dimensional properties up to tens of layers of thickness and host two-dimensional electron states with a large Berry curvature, accompanied by a giant intrinsic magnetic moment carried by electrons. The size of Berry curvature and magnetization in the vicinity of each valley can be controlled by electrostatic gating leading to a tuneable anomalous Hall effect and a peculiar structure of the two-dimensional Landau level spectrum. △ Less

Submitted 27 November, 2019; v1 submitted 30 May, 2019; originally announced May 2019.

Comments: 24 pages, 7 figures

Journal ref: Commun Phys 2, 164 (2019)

Moiré phonons in the twisted bilayer graphene

Authors: Mikito Koshino, Young-Woo Son

Abstract: We study the in-plane acoustic phonons in twisted bilayer graphenes using the effective continuum approach. We calculate the phonon modes by solving the continuum equation of motion for infinitesimal vibration around the static relaxed state with triangular domain structure. We find that the moiré interlayer potential only affects the in-plane asymmetric modes, where the original linear dispersion… ▽ More We study the in-plane acoustic phonons in twisted bilayer graphenes using the effective continuum approach. We calculate the phonon modes by solving the continuum equation of motion for infinitesimal vibration around the static relaxed state with triangular domain structure. We find that the moiré interlayer potential only affects the in-plane asymmetric modes, where the original linear dispersion is broken down into miniphonon bands separated by gaps, while the in-plane symmetric modes with their linear dispersion are hardly affected. The phonon wave functions of asymmetric modes are regarded as collective vibrations of the domain-wall network, and the low-energy phonon band structure can be qualitatively described by an effective moiré-scale lattice model. △ Less

Submitted 16 August, 2019; v1 submitted 23 May, 2019; originally announced May 2019.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. B 100, 075416 (2019)