Mikito Koshino

The transport properties of a bilayer graphene are studied theoretically within a self-consistent Born approximation. The electronic spectrum is composed of $k$-linear dispersion in the low-energy region and $k$-square dispersion as in an ordinary two-dimensional metal at high energy, leading to a crossover between different behaviors in the conductivity on changing the Fermi energy or disorder strengths. We find that the conductivity approaches $2{e}^{2}∕{\ensuremath{\pi}}^{2}\ensuremath{\hbar}

The electronic band structure of ABC-stacked multilayer graphene is studied within an effective mass approximation. The electron and hole bands touching at zero energy support chiral quasiparticles characterized by Berry's phase $N\ensuremath{\pi}$ for $N$ layers, generalizing the low-energy band structure of monolayer and bilayer graphene. We investigate the trigonal-warping deformation of the energy bands and show that the Lifshitz transition, in which the Fermi circle breaks up into separate

We present a theoretical study on the orbital magnetism in multilayer graphenes within the effective mass approximation. The Hamiltonian and thus susceptibility can be decomposed into contributions from subsystems equivalent to monolayer or bilayer graphene. The monolayer-type subband exists only in odd layers and exhibits a delta-function susceptibility at ${\ensuremath{\epsilon}}_{F}=0$. The bilayer-type subband appearing in every layer number gives a singular structure in the vicinity of ${\e

We study the effect of perpendicular electric fields on the band structures of $ABA$ and $ABC$ graphene multilayers, and find that the electronic screening effect is significantly different between them. In $ABA$ multilayers, the field produces a band overlap and gives a linear screening, while in $ABC$ multilayers, in contrast, it opens an energy gap in the surface-state band at low energy, leading to a strong screening effect essentially nonlinear to the field amplitude. The energy gap of a la

The magneto-optical absorption properties of graphene multilayers are theoretically studied. It is shown that the spectrum can be decomposed into sub-components effectively identical to the monolayer or bilayer graphene, allowing us to understand the spectrum systematically as a function of the layer number. Odd-layered graphenes always exhibit absorption peaks which shifts in proportion to $\sqrt{B}$, with $B$ being the magnetic field, due to the existence of an effective monolayer-like subband

The orbital diamagnetic susceptibility is calculated in monolayer and bilayer graphenes with band gap as well as in three-dimensional Dirac systems. It is demonstrated that the pseudospin degree of freedom such as valleys produces paramagnetic susceptibility analogous to contribution from real spin, and it dominates over the Landau diamagnetism. The pseudospin paramagnetism explains the origin of a singular diamagnetism which is present only in the band-gap region and disappears rapidly inside t

We study the electronic band structure and the topological properties 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 associat

We calculate the electronic band structure of ABA-stacked trilayer graphene in the presence of external gates, using a self-consistent Hartree approximation to take account of screening. In the absence of a gate potential, there are separate pairs of linear and parabolic bands at low energy. A gate field perpendicular to the layers breaks mirror reflection symmetry with respect to the central layer and hybridizes the linear and parabolic low-energy bands, leaving a chiral Hamiltonian essentially

We present a general theoretical formulation to describe the interlayer interaction in incommensurate bilayer systems with arbitrary crystal structures. By using the generic tight-binding description, we show that the interlayer coupling, which is highly complex in the real space, can be simply written in terms of generalized Umklapp process in the reciprocal space. The formulation is useful to describe the interaction in the two-dimensional interface of different materials with arbitrary lattic

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 moir\'e 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 t

We study spatial symmetry in general $ABA$-stacked multilayer graphene to illustrate how electronic spectra at the two valleys are related in a magnetic field. We show that the lattice of multilayers with an even number of layers as well as that of monolayer graphene satisfy spatial inversion symmetry, which rigorously guarantees valley degeneracy in the absence of time-reversal symmetry. A multilayer with an odd number of layers (three or more) lacks inversion symmetry, but there is another tra

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.

For a three-dimensional (3D) lattice in magnetic fields we have shown that the hopping along the third direction, which normally smears out the Landau quantization gaps, can rather give rise to a Hofstadter's butterfly specific to 3D when a criterion is fulfilled by anisotropic (quasi-one-dimensional) systems. In 3D the angle of the magnetic field plays the role of the field intensity in 2D, so that the butterfly can occur in much smaller fields. We have also calculated the Hall conductivity in

We study the magnetic susceptibility in various three-dimensional gapless systems, including Dirac and Weyl semimetals, and a line-node semimetal. The susceptibility is decomposed into the orbital term, the spin term and also the spin-orbit cross term, which is caused by the spin-orbit interaction. We show that the orbital susceptibility logarithmically diverges at the band touching energy in the point-node case, while it exhibits a stronger $\ensuremath{\delta}$-function singularity in the line

The orbital magnetism is studied in graphene monolayer within the effective-mass approximation. In models of short-range and long-range disorders, the magnetization is calculated with self-consistent Born approximation. In the zero-field limit, the susceptibility becomes highly diamagnetic around zero energy, while it has a long tail proportional to the inverse of the Fermi energy. We demonstrated how the magnetic oscillation vanishes and converges to the susceptibility, in going from a strong-f