Takahiro Morimoto

Quantum Faraday and Kerr rotations in graphene

Graphene, a monolayer sheet of carbon atoms, exhibits intriguing electronic properties that arise from its massless Dirac dispersion of electrons. A striking example is the half-integer quantum Hall effect, which endorses the presence of Dirac cones or, equivalently, a non-zero (π) Berrys (topological) phase. It is curious how these anomalous features of Dirac electrons would affect optical properties. Here we observe the quantum magneto-optical Faraday and Kerr effects in graphene in the terahertz frequency range. Our results detect the quantum plateaus in the Faraday and Kerr rotations at precisely the quantum Hall steps that hallmark the Dirac electrons, with the rotation angle defined by the fine-structure constant. The robust quantum Hall plateaus in the optical regime, besides being conceptually interesting, may open avenues for new graphene-based optoelectronic applications.

Optical Hall Conductivity in Ordinary and Graphene Quantum Hall Systems

We reveal from numerical study that the optical Hall conductivity sigma(xy)(omega) has a characteristic feature even in the ac ( approximately THz) regime in that the Hall plateaus are retained both in the ordinary two-dimensional electron gas and in graphene in the quantum Hall regime, although the plateau height is no longer quantized in ac. In graphene sigma(xy)(omega) reflects the unusual Landau level structure. The effect remains unexpectantly robust against the significant strength of disorder, which we attribute to an effect of localization. We predict the ac quantum Hall measurements are feasible through the Faraday rotation characterized by the fine-structure constant alpha.

Topological classification with additional symmetries from Clifford algebras

We classify topological insulators and superconductors in the presence of additional symmetries such as reflection or mirror symmetries. For each member of the 10 Altland-Zirnbauer symmetry classes, we have a Clifford algebra defined by operators of the generic (time-reversal, particle-hole, or chiral) symmetries and additional symmetries, together with gamma matrices in Dirac Hamiltonians representing topological insulators and superconductors. Following Kitaevs approach, we classify gapped phases of non-interacting fermions under additional symmetries by examining all possible distinct Dirac mass terms which can be added to the set of generators of the Clifford algebra. We find that imposing additional symmetries in effect changes symmetry classes and causes shifts in the periodic table of topological insulators and superconductors. Our results are in agreement with the classification under reflection symmetry recently reported by Chiu et al. Several examples are discussed including a topological crystalline insulator with mirror Chern numbers and mirror superconductors.

Classification of Interacting Topological Floquet Phases in One Dimension

Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting fermionic and bosonic quantum systems subject to periodic driving, which we dub Floquet SPTs (FSPTs). For physical realizations of interacting FSPTs, many-body localization by disorder is a crucial ingredient, required to obtain a stable phase that does not catastrophically heat to infinite temperature. We demonstrate that bosonic and fermionic FSPTs phases are classified by the same criteria as equilibrium phases, but with an enlarged symmetry group

Optical Hall effect in the integer quantum Hall regime.

\tilde G

Cyclotron radiation and emission in graphene

, that now includes discrete time translation symmetry associated with the Floquet evolution. In particular, 1D bosonic FSPTs are classified by projective representations of the enlarged symmetry group

Quantized circular photogalvanic effect in Weyl semimetals

H^2({\tilde G},U(1))

Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals

. We construct explicit lattice models for a variety of systems, and then formalize the classification to demonstrate the completeness of this construction. We also derive general constraints on localization and symmetry based on the representation theory of the symmetry group, and show that symmetry-preserving localized phases are possible only for Abelian symmetry groups. In particular, this rules out the possibility of many-body localized SPTs with continuous spin symmetry.

Topological nature of nonlinear optical effects in solids

Optical Hall conductivity σ{xy}(ω) is measured from the Faraday rotation for a GaAs/AlGaAs heterojunction quantum Hall system in the terahertz-frequency regime. The Faraday rotation angle (∼ fine-structure constant ∼ mrad) is found to significantly deviate from the Drude-like behavior to exhibit a plateaulike structure around the Landau-level filling ν=2. The result, which fits with the behavior expected from the carrier localization effect in the ac regime, indicates that the plateau structure, although not quantized, still exists in the terahertz regime.

Breakdown of the topological classificationZfor gapped phases of noninteracting fermions by quartic interactions

Peculiarity in the cyclotron radiation and emission in graphene is theoretically examined in terms of the optical conductivity and relaxation rates to propose that graphene in magnetic fields can be a candidate to realize the Landau level laser, proposed decades ago [H. Aoki, Appl. Phys. Lett. {\bf 48}, 559 (1986)].