Kentaro Nomura

Quantum transport of massless Dirac fermions.

Motivated by recent graphene transport experiments, we undertake a numerical study of the conductivity of disordered two-dimensional massless Dirac fermions. Our results reveal distinct differences between the cases of short-range and Coulomb randomly distributed scatterers. We speculate that this behavior is related to the Boltzmann transport theory prediction of dirty-limit behavior for Coulomb scatterers.

Quantum Hall Ferromagnetism in Graphene

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. When Zeeman and spin-orbit interactions are neglected, its Landau levels are fourfold degenerate, explaining the 4e2/h separation between quantized Hall conductivity values seen in recent experiments. In this Letter we derive a criterion for the occurrence of interaction-driven quantum Hall effects near intermediate integer values of e2/h due to charge gaps in broken symmetry states.

Surface-quantized anomalous Hall current and the magnetoelectric effect in magnetically disordered topological insulators.

We study theoretically the role of quenched magnetic disorder at the surface of topological insulators by numerical simulation and scaling analysis based on the massive Dirac fermion model. This addresses the problem of Anderson localization on chiral anomaly. It is found that all the surface states are localized, while the transverse conductivity is quantized to be ±e2/2h as long as the Fermi energy is within the bulk gap. This greatly facilitates the realization of the topological magnetoelectric effect proposed by Qi et al. [Phys. Rev. B 78, 195424 (2008)] with the surface magnetization direction being controlled by the simultaneous application of magnetic and electric fields.

Topological delocalization of two-dimensional massless Dirac fermions

The beta function of a two-dimensional massless Dirac Hamiltonian subject to a random scalar potential, which, e.g., underlies theoretical descriptions of graphene, is computed numerically. Although it belongs to, from a symmetry standpoint, the two-dimensional symplectic class, the beta function monotonically increases with decreasing conductance. We also provide an argument based on the spectral flows under twisting boundary conditions, which shows that none of the states of the massless Dirac Hamiltonian can be localized.

Intra-Landau-level cyclotron resonance in bilayer graphene.

Interaction driven integer quantum-Hall effects are anticipated in graphene bilayers because of the near degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate k3/2 dispersion. We speculate on the possibility of unusual localization physics associated with these modes.

Edge spin accumulation in semiconductor two-dimensional hole gases

The controlled generation of localized spin densities is a key enabler of semiconductor spintronics In this work, we study spin Hall effect induced edge-spin accumulation in a two-dimensional hole gas with strong spin orbit interactions. We argue that it is an intrinsic property, in the sense that it is independent of the strength of disorder scattering. We show numerically that the spin polarization near the edge induced by this mechanism can be large, and that it becomes larger and more strongly localized as the spin-orbit coupling strength increases, and is independent of the width of the conducting strip once this exceeds the elastic scattering mean-free-path. Our experiments in two-dimensional hole gas microdevices confirm this remarkable spin Hall effect phenomenology. Achieving comparable levels of spin polarization by external magnetic fields would require laboratory equipment whose physical dimensions and operating electrical currents are a million times larger than those of our spin Hall effect devices.

Electric charging of magnetic textures on the surface of a topological insulator

A three-dimensional topological insulator manifests gapless surface modes, described by two-dimensional Dirac equation. We study magnetic textures, such as domain walls and vortices, in a ferromagnetic thin film deposited on a three-dimensional topological insulator. It is shown that these textures can be electrically charged, ascribed to the proximity effect with the Dirac surface states. We derive a general relation between the electric and the magnetic charges. As a physical consequence, we discuss domain-wall motion driven by an applied electric field, which promises magnetic devices with high thermal efficiency.

Cross-correlated responses of topological superconductors and superfluids.

We study nontrivial responses of topological superconductors and superfluids to the temperature gradient and rotation of the system. In two-dimensional gapped systems, the Strěda formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the orbital angular momentum and thermal polarization (entropy polarization). These results can be naturally related to the gravitoelectromagnetism description of three-dimensional topological superconductors and superfluids, analogous to the topological magnetoelectric effect in Z(2) topological insulators.

Field-induced Kosterlitz-Thouless transition in the n=0 Landau level of graphene.

At the charge neutral point, graphene exhibits a very unusual high-resistance metallic state and a transition to a complete insulating phase in a strong magnetic field. We propose that the current carriers in this state are the charged vortices of the XY valley-pseudospin order parameter, a situation which is dual to a conventional thin superconducting film. We study energetics and the stability of this phase in the presence of disorder.

Fractional Quantum Hall Effects in Graphene and Its Bilayer

Single-layer and Bilayer of graphene are new classes of two-dimensional electron systems with unconventional band structures and valley degrees of freedom. The ground states and excitations in the integer and fractional quantum Hall regimes are investigated on torus and spherical geometries with the use of the density matrix renormalization group (DMRG) method. At nonzero Landau level indices, the ground states at effective filling factors 1, 1/3, 2/3 and 2/5 are valley polarized both in single-layer and bilayer graphenes. We examine the elementary charge excitations which could couple with the valley degrees of freedom (so called valley skyrmions). The excitation gaps are calculated and extrapolated to the thermodynamic limit. The largest excitation gap at effective filling 1/3 is obtained in bilayer graphene, which is a good candidate for experimental observation of fractional quantum Hall effect.