Ai Yamakage

Spin-orbit effects in a graphene bipolar pn junction

A graphene pn junction is studied theoretically in the presence of both intrinsic and Rashba spin-orbit couplings. We show that a crossover from perfect reflection to perfect transmission is achieved at normal incidence by tuning the perpendicular electric field. By further studying angular-dependent transmission, we demonstrate that perfect reflection at normal incidence can be clearly distinguished from trivial band gap effects. We also investigate how spin-orbit effects modify the conductance and the Fano factor associated with a potential step in both nn and np cases.

Zigzag edge modes in a Z2 topological insulator : Reentrance and completely flat spectrum

The spectrum and wave function of helical edge modes in Z_2 topological insulator are derived on a square lattice using Bernevig-Hughes-Zhang (BHZ) model. The BHZ model is characterized by a mass term M (k) that is parameterized as M (k) = Delta - B k^2. A topological insulator realizes when the parameters Delta and B fall on the regime, either 0 4 of the 1D Brillouin zone. In the (1,1)-edge geometry, the group velocity at the zone center changes sign at Delta /B = 4 where the spectrum becomes independent of the momentum, i.e. flat, over the whole 1D Brillouin zone. Furthermore, for Delta/B < 1.354..., the edge mode starting from the zone center vanishes in an intermediate region of the 1D Brillouin zone, but reenters near the zone boundary, where the energy of the edge mode is marginally below the lowest bulk excitations. On the other hand, the behavior of reentrant mode in real space is indistinguishable from an ordinary edge mode.

Z2 Topological Anderson Insulator

Effects of disorder on a two-dimensional Z2 topological insulator are studied numerically. We propose and study the phase diagram of a variant of Bernevig-Hughes-Zhang model, which takes account of the sz non-conserving spin-orbit coupling. Using scaling analyses, we determine the phase boundary and the critical exponent characterizing the transition between metallic and the topologically insulating phases.

Flat edge modes of graphene and of Z2 topological insulator.

A graphene nano-ribbon in the zigzag edge geometry exhibits a specific type of gapless edge modes with a partly flat band dispersion. We argue that the appearance of such edge modes are naturally understood by regarding graphene as the gapless limit of a Z2 topological insulator. To illustrate this idea, we consider both Kane-Mele (graphene-based) and Bernevig-Hughes-Zhang models: the latter is proposed for HgTe/CdTe 2D quantum well. Much focus is on the role of valley degrees of freedom, especially, on how they are projected onto and determine the 1D edge spectrum in different edge geometries.

Spin-orbit effects in graphene p - n junction

A graphene p - n junction is studied theoretically in the presence of both intrinsic and extrinsic (Rashba) spin-orbit interactions. It is shown that a crossover from perfect reflection to perfect transmission is achieved at normal incidence by tuning the perpendicular electric field. We also study angular-dependent transmission for demonstrating that perfect reflection at normal incidence can be clearly distinguished from trivial band gap effects. We clarify how spin-orbit effects modify the conductance and the Fano factor associated with a potential step in both nn and np cases.