Engineering Dirac electrons emergent on the surface of a topological insulator

The concept of topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some classes of nodal superconductors and superfluid $^3$He, etc. From a technological point of view, topological insulator is expected to serve as a platform for realizing dissipationless transport in a non-superconducting context. The topological insulator 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 contrast the cases of weak and strong TIs. We study robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new perspective of research in the field.

Manipulating quantum channels in weak topological insulator nanoarchitectures

In $strong$ topological insulators protected surface states are always manifest, while in $weak$ topological insulators (WTI) the corresponding metallic surface states are either manifest or hidden, depending on the orientation of the surface. One can design a nanostep on the surface of WTI such that a protected helical channel appears along it. In a more generic WTI nanostructure, multiple sets of such quasi-1D channels emerge and are coupled to each other. We study the response of the electronic spectrum associated with such quasi-1D surface modes against a magnetic flux piercing the system in the presence of disorder, and find a non-trivial, connected spectral flow as a clear signature indicating the immunity of the surface modes to disorder. We propose that the WTI nanoarchitecture is a promising platform for realizing topologically protected nanocircuits immune to disorder.

Characterizing the weak topological properties: Berry phase point of view

We propose classification schemes for characterizing two-dimensional topological phases with nontrivial weak indices. Here, weak implies that the Chern number in the corresponding phase is trivial, while the system shows edge states along specific boundaries. As concrete examples, we analyze differen