Disorder effect on the localization/delocalization in incommensurate potential

The interplay between incommensurate (IC) and random potentials is studied in a two-dimensional symplectic model with the focus on localization/delocalization problem. With the IC potential only, there appear wavefunctions localized along the IC wavevector while extended perpendicular to it. Once the disorder potential is introduced, these turn into two-dimensional anisotropic metallic states beyond the scale of the elastic mean free path, and eventually becomes localized in both directions at a critical strength of the disorder. Implications of these results to the experimental observation of the IC-induced localization is discussed.Comment: 4 pages, 3 figures (7 files), RevTe

Dynamics of localized spins coupled to the conduction electrons with charge/spin currents

The effects of the charge/spin currents of conduction electrons on the dynamics of the localized spins are studied in terms of the perturbation in the exchange coupling $J_{K}$ between them. The equations of motion for the localized spins are derived exactly up to $O(J_{K}^2)$, and the equations for the two-spin system is solved numerically. It is found that the dynamics depends sensitively upon the relative magnitude of the charge and spin currents, i.e., it shows steady state, periodic motion, and even chaotic behavior. Extension to the multi-spin system and its implications including possible ``spin current detector'' are also discussed.Comment: 5 pages, 4 figures, REVTe

Localization in a quantum spin Hall system

Localization problem of electronic states in a two-dimensional quantum spin Hall system (QSH - a symplectic model with a non-trivial topological structure) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair-annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent $\nu$ for the divergence of the localization length is estimated as $\nu \cong 1.6$ which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. This strongly suggests a different universality class related to the non-trivial topology of the QSH system.Comment: 5 pages, 4 figures, REVTe

Topological Photonic Media and the Possibility of Toroidal Electromagnetic Wavepackets

This study aims to present a theoretical investigation of a feasible electromagnetic wavepacket with toroidal-type dual vortices. The paper begins with a discussion on geometric phases and angular momenta of electromagnetic vortices in free space and periodic structures, and introduces topological photonic media with a review on topological phenomena of electron systems in solids, such as quantum Hall systems and topological insulators. Representative simulations demonstrate both the characteristics of electromagnetic vortices in a periodic structure and of exotic boundary modes of a topological photonic crystal, on a Y-shaped waveguide configuration. Those boundary modes stem from photonic helical surface modes, i.e., a photonic analog of electronic helical surface states of topological insulators. Then, we discuss the possibility of toroidal electromagnetic wavepackets via topological photonic media, based on the dynamics of an electronic wavepacket around the boundary of a topological insulator and a correspondence relation between electronic helical surface states and photonic helical surface modes. Finally, after introducing a simple algorithm for the construction of wavepacket solutions to Maxwell\u27s equations with multiple types of vortices, we examine the stability of a toroidal electromagnetic wavepacket against reflection and refraction, and further discuss the transformation laws of its topological properties in the corresponding processes

Tuning phase transition between quantum spin Hall and ordinary insulating phases

An effective theory is constructed for analyzing a generic phase transition between the quantum spin Hall and the insulator phases. Occurrence of degeneracies due to closing of the gap at the transition are carefully elucidated. For systems without inversion symmetry the gap-closing occurs at \pm k_0(\neq G/2) while for systems with inversion symmetry, the gap can close only at wave-numbers k=G/2, where G is a reciprocal lattice vector. In both cases, following a unitary transformation which mixes spins, the system is represented by two decoupled effective theories of massive two-component fermions having masses of opposite signs. Existence of gapless helical modes at a domain wall between the two phases directly follows from this formalism. This theory provides an elementary and comprehensive phenomenology of the quantum spin Hall system.Comment: 6 pages, 2 figures, to appear in Phys. Rev.

Photonic analog of graphene model and its extension -- Dirac cone, symmetry, and edge states --

This paper presents a theoretical analysis on bulk and edge states in honeycomb lattice photonic crystals with and without time-reversal and/or space-inversion symmetries. Multiple Dirac cones are found in the photonic band structure and the mass gaps are controllable via symmetry breaking. The zigzag and armchair edges of the photonic crystals can support novel edge states that reflect the symmetries of the photonic crystals. The dispersion relation and the field configuration of the edge states are analyzed in detail in comparison to electronic edge states. Leakage of the edge states to free space is inherent in photonic systems and is fully taken into account in the analysis. A topological relation between bulk and edge, which is analogous to that found in quantum Hall systems, is also verified.Comment: 9 pages, 7 figure

Effective mass staircase and the Fermi liquid parameters for the fractional quantum Hall composite fermions

Effective mass of the composite fermion in the fractional quantum Hall system, which is of purely interaction originated, is shown, from a numerical study, to exhibit a curious nonmonotonic behavior with a staircase correlated with the number (=2,4,...) of attached flux quanta. This is surprising since the usual composite-fermion picture predicts a smooth behavior. On top of that, significant interactions are shown to exist between composite fermions, where the excitation spectrum is accurately reproduced in terms of Landau's Fermi liquid picture with negative (i.e., Hund's type) orbital and spin exchange interactions.Comment: 4 pages, 3 figures, REVTe

Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets - Quantum Hall Effect from Metal -

We study the effect of disorder on the anomalous Hall effect (AHE) in two-dimensional ferromagnets. The topological nature of AHE leads to the integer quantum Hall effect from a metal, i.e., the quantization of $\sigma_{xy}$ induced by the localization except for the few extended states carrying Chern number. Extensive numerical study on a model reveals that Pruisken's two-parameter scaling theory holds even when the system has no gap with the overlapping multibands and without the uniform magnetic field. Therefore the condition for the quantized AHE is given only by the Hall conductivity $\sigma_{xy}$ without the quantum correction, i.e., $|\sigma_{xy}| > e^2/(2h)$.Comment: 5 pages, 4 figures, REVTe