arXiv subjects

Mikito Koshino

Publications and source records attributed to Mikito Koshino.

At least 55 records · Page 3Linked to original sources

arXiv2020

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

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.

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arXiv2020

Dirac Fermion kinetics in three-dimensionally curved graphene

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.

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arXiv2020

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

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.

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arXiv2020

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

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.

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arXiv2020

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

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.

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arXiv2020

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

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.

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arXiv2020

Perfect one-dimensional chiral states in biased twisted bilayer graphene

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.

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arXiv2019

Films of rhombohedral graphite as two-dimensional topological semimetals

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.

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arXiv2019

Topological charge pumping by sliding moiré pattern

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.

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arXiv2019

Moiré phonons in the twisted bilayer graphene

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.

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arXiv2019

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

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.

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arXiv2019

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

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.

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arXiv2019

Band structure and topological property of twisted double bilayer graphenes

We study the electronic band structure and the topological property of the twisted double bilayer graphene, or a pair of AB-stacked bilayer graphenes rotationally stacked on top of each other. We consider two different arrangements, AB-AB and AB-BA, which differ in the relative orientation. For each system, we calculate the energy band and the valley Chern number using the continuum Hamiltonian. We show that the AB-AB and the AB-BA have similar band structures, while the Chern numbers associated with the corresponding bands are completely different. In the absence of the perpendicular electric field, in particular, the AB-AB system is a trivial insulator when the Fermi energy is in a gap, while the AB-BA is a valley Hall insulator. Also, the lowest electron and hole bands of the AB-AB are entangled by the symmetry protected band touching points, while they are separated in the AB-BA. In both cases, the perpendicular electric field immediately opens an energy gap at the charge neutral point, where the electron branch becomes much narrower than the hole branch, due to the significant electron-hole asymmetry.

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arXiv2019

Diamagnetic levitation and thermal gradient driven motion of graphite

We theoretically study the diamagnetic levitation and the thermal-driven motion of graphite. Using the quantum-mechanically derived magnetic susceptibility, we compute the equilibrium position of levitating graphite over a periodic arrangement of magnets, and investigate the dependence of the levitation height on the susceptibility and the geometry. We find that the levitation height is maximized at a certain period of the magnets, and the maximum height is then linearly proportional to the susceptibility of the levitating object. We compare the ordinary AB-stacked graphite and a randomly stacked graphite, and show that the latter exhibits a large levitation length particularly in low temperatures, because of its diamagnetism inversely proportional to the temperature. Finally, we demonstrate that the temperature gradient moves the levitating object towards the high temperature side, and estimate the generated force as a function of susceptibility.

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arXiv2019

Quasicrystalline electronic states in 30$^\circ$ rotated twisted bilayer graphene

The recently realized bilayer graphene system with a twist angle of $30^\circ$ offers a new type of quasicrystal which unites the dodecagonal quasicrystalline nature and graphene's relativistic properties. Here, we introduce a concise theoretical framework that fully respects both the dodecagonal rotational symmetry and the massless Dirac nature, to describe the electronic states of the system. We find that the electronic spectrum consists of resonant states labeled by 12-fold quantized angular momentum, together with the extended relativistic states. The resulting quasi-band structure is composed of the nearly flat bands with spiky peaks in the density of states, where the wave functions exhibit characteristic patterns which fit to the fractal inflations of the quasicrystal tiling. We also demonstrate that the 12-fold resonant states appear as spatially-localized states in a finite-size geometry, which is another hallmark of quasicrystal. The theoretical method introduced here is applicable to a broad class of "extrinsic quasicrystals" composed of a pair of two-dimensional crystals overlaid on top of the other with incommensurate configurations.

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arXiv2019

Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides

We theoretically study the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides monolayer stacked with arbitrary twist angles. We find that the relative rotation greatly enhances the spin splitting of graphene, typically by a few to ten times compared to the non-rotated geometry,and the maximum splitting is achieved around $20^\circ$. The induced SOC can be changed from the Zeeman-type to the Rashba-type by rotation. The spin-splitting is also quite sensitive to the gate-induced potential, and it sharply rises when the graphene's Dirac point is shifted toward the TMDC band. The theoretical method does not need the exact lattice matching and it is applicable to any incommensurate bilayer systems. It is useful for the twist-angle engineering of a variety of van der Waals proximity effects.

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arXiv2019

Quantum Hall effect in three-dimensional graphene

We theoretically study the electronic band structure and the Hall effect in the negatively-curved three-dimensional (3D) graphene network in magnetic fields. We found that special energy regions appear above and below the zero-energy Landau level, where the 3D Hall conductivity is quantized even though the spectrum is not fully gapped. The energy regions are dominated by the chiral snake states traveling along the zero magnetic field contour on the 3D surface, and the quantization of the Hall conductivity crucially depends on the topology of the contour. The exclusive energy region for the chiral states is found to be a universal feature of 3D graphene systems.

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arXiv2018

Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We found the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per super cell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which would possibly lead to an unconventional many-body state.

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