小林 浩二

The magnetotransport properties of disordered ferromagnetic kagome layers are investigated numerically. We show that a large domain-wall magnetoresistance or negative magnetoresistance can be realized in kagome layered materials (e.g., Fe3Sn2, Co3Sn2S2, and Mn3Sn), which show the quantum anomalous Hall effect. The kagome layers show a strong magnetic anisotropy and a large magnetoresistance depending on their magnetic texture. These domain-wall magnetoresistances are expected to be robust against disorder and observed irrespective of the domain-wall thickness, in contrast to conventional domain-wall magnetoresistance in ferromagnetic metals.

The magnetotransport properties of disordered ferromagnetic Weyl semimetals are investigated numerically. We found an extraordinarily stable and huge magnetoresistance effect in domain walls of Weyl semimetals. This effect originates from the helicity mismatch of Weyl fermions and is a specific property of Weyl semimetals. Although conventional magnetoresistance effects are strongly suppressed in domain walls where local magnetization varies gradually, the helicity-protected magnetoresistance in Weyl semimetals maintains almost 100% of the magnetoresistance ratio for any kind of thick domain walls, even in the presence of disorder. The contribution of surface Fermi arcs to the magnetoresistance is also discussed.

We theoretically study the anisotropic magnetotransport in Dirac-Weyl magnetic junctions where a doped ferromagnetic Weyl semimetal is sandwiched between doped Dirac semimetals. We calculate the conductance using the Landauer formula and find that the system exhibits extraordinarily large anisotropic magnetoresistance (AMR). The AMR depends on the ratio of the Fermi energy to the strength of the exchange interaction. The origin of the AMR is the shift of the Fermi surface in the Weyl semimetal, and the mechanism is completely different from the conventional AMR originating from the spin dependent scattering and the spin-orbit interaction.

Regarding three-dimensional (3D) topological insulators and semimetals as a stack of constituent twodimensional (2D) topological (or sometimes nontopological) systems is a useful viewpoint. Here, we perform a comparative study of the paradigmatic 3D topological phases: Weyl semimetal (WSM), strong and weak topological insulators (STI/WTI), and Chern insulator (CI). By calculating the Z and Z(2) indices for the thin films of such 3D topological phases, we follow dimensional evolution of topological properties from 2D to 3D. It is shown that the counterparts of STI and WTI in the time-reversal symmetry broken CI system are, respectively, WSM and CI phases. The number N-D of helical Dirac cones emergent on the surface of a topological insulator is shown to be identical to the number N-W of the pairs of Weyl cones in the corresponding WSM phase: N-D = N-W. To test the robustness of this scenario against disorder, we have studied the transport property of disordered WSM thin films, taking into account both the bulk and surface contributions.

We show how the two-dimensional (2D) topological insulator evolves, by stacking, into a strong or weak topological insulator with different topological indices, proposing a new conjecture that goes beyond an intuitive picture of the crossover from quantum spin Hall to weak topological insulator. Studying the conductance under different boundary conditions, we demonstrate the existence of two conduction regimes in which conduction happens through either surface or edge conduction channels. We show that the two conduction regimes are complementary and exclusive. Conductance maps in the presence and absence of disorder are introduced, together with 2D Z(2)-index maps, describing the dimensional crossover of the conductance from the 2D to the 3D limit. Stacking layers is an effective way to invert the gap, an alternative to controlling the strength of spin-orbit coupling. The emerging quantum spin Hall insulator phase is not restricted to the case of odd numbers of layers.

We numerically demonstrate a practical means of systematically controlling topological transport on the surface of a three-dimensional topological insulator, by introducing strong disorder in a layer of depth d extending inward from the surface of the topological insulator. The dependence on d of the density of states, conductance, scattering time, scattering length, diffusion constant, and mean Fermi velocity are investigated. The proposed control via disorder depth d requires that the disorder strength be near the large value which is necessary to drive the topological insulator into the nontopological phase. If d is patterned using masks, gates, ion implantation, etc., then integrated circuits may be fabricated. This technique will be useful for experiments and for device engineering.

The concept of the topological insulator (TI) has introduced a new point of view to condensedmatter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some classes of nodal superconductors, superfluid He-3, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of a disordered Z(2) topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent nu and the dynamical critical exponent z are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.

A global phase diagram of disordered weak and strong topological insulators is established numerically. As expected, the location of the phase boundaries is renormalized by disorder, a feature recognized in the study of the so-called topological Anderson insulator. Here, we report unexpected quantization, i.e., robustness against disorder of the conductance peaks on these phase boundaries. Another highlight of the work is on the emergence of two subregions in the weak topological insulator phase under disorder. According to the size dependence of the conductance, the surface states are either robust or "defeated" in the two subregions. The nature of the two distinct types of behavior is further revealed by studying the Lyapunov exponents.

We have estimated the critical exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The critical exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known to be consistent with that of topologically trivial symplectic systems. However, the precise estimation of the critical exponent for the metal-quantum spin Hall insulator transition proved to be problematic because of the existence, in this case, of edge states in the localized phase. We have overcome this difficulty by analyzing the second smallest positive Lyapunov exponent instead of the smallest positive Lyapunov exponent. We find a value for the critical exponent nu = 2.73 +/- 0.02 that is consistent with that for topologically trivial symplectic systems.

The Anderson transition is a disorder driven quantum phase transition between metallic and insulating phases. In contrast to the common belief that two dimensional (2D) systems are always insulating and that the Anderson transition does not occur in 2D, in certain universality classes 2D systems can be metallic. We review the recent development of the theory of the Anderson transition in 2D. There are ten universality classes: three Wigner-Dyson classes, three chiral universality classes, and four Bogoliubov-de Gennes classes. We report results for critical exponents and distributions of conductance for the symplectic universality class. We emphasize that, on the one hand, the existence of a topological insulating phase does not alter the value of the critical exponent, while on the other, it strongly affects the form of the conductance distribution at the transition.

We study numerically the charge conductance distributions of disordered quantum spin-Hall (QSH) systems using a quantum network model. We have found that the conductance distribution at the metal-QSH insulator transition is clearly different from that at the metal-ordinary insulator transition. Thus the critical conductance distribution is sensitive not only to the boundary condition but also to the presence of edge states in the adjacent insulating phase. We have also calculated the point-contact conductance. Even when the two-terminal conductance is approximately quantized, we find large fluctuations in the point-contact conductance. Furthermore, we have found a semicircular relation between the average of the point-contact conductance and its fluctuation.

We study the transport properties of disordered two-dimensional electron systems with a perfectly conducting channel. We introduce an asymmetric Chalker-Coddington network model and numerically investigate the point-contact conductance. We find that the behavior of the conductance in this model is completely different from that in the symmetric model. Even in the limit of a large distance between the contacts, we find a broad distribution of conductance and a non-trivial power law dependence of the averaged conductance on the system width. Our results are applicable to systems such as zigzag graphene nano-ribbons where the numbers of left- and right-going channels are different.

We study the transport properties of disordered electron systems that contain perfectly conducting channels. Two quantum network models that belong to different universality classes, unitary and symplectic, are simulated numerically. The perfectly conducting channel in the unitary class can be realized in zigzag graphene nano-ribbons and that in the symplectic class is known to appear in metallic carbon nanotubes. The existence of a perfectly conducting channel leads to novel conductance distribution functions and a shortening of the conductance decay length.