Transport properties of some topological insulators and topological superconductors in two dimensions

Abstract

Topology has found its widespread applications in condensed matter physics ever since the proposal of quantum spin Hall insulator based on graphene. The quantum spin Hall insulator, also known as two-dimensional topological insulator, is an insulator that has topologically nontrivial band properties unlike conventional insulators. The most vivid consequence of nontrivial band structures of topological insulators is the existence of gapless excitations at open boundaries. Furthermore, applications of topology to superconductors with a full superconducting gap and even to semimetals without band gap give rise to topological superconductors and topological semimetals respectively. In topological superconductors the low-energy property of boundary excitations is governed by Majorana equation, which suggests that Majorana fermions are promising to be realized in condensed matter physics. Similarly, Weyl (Dirac) semimetals can support Weyl (Dirac) fermions. Searching for these new fermions and studying their related transport signatures have become an imperative trend in condensed matter physics.

In the presented thesis we investigated the transport properties of some two dimensional topological systems including graphene, topological insulator based on the InAs/GaSb quantum wells, and chiral topological superconductor based on the quantum anomalous Hall/superconductor hybrid device. After a brief introductory chapter, a detailed description of Green’s function method for mesoscopic transport is presented in Chapter 2. The remaining chapters will present the main results of this thesis. In Chapter 3, the concept of chiral anomaly is extended to graphene. Graphene is actually a semimetal in two dimensions. By confining the zigzag graphene nanoribbons, genuine chiral bands evolved from edge states can be realized and hence the nonconservation of chiral current (chiral anomaly) happens. The width of the graphene nanoribbons serves as an effective magnetic field in this case. As a consequence, finite-size conductivity has characteristic quadratic dependence on the effective magnetic field, which is treated as a signature of chiral anomaly. In Chapter 4, we address the robust quantum edge transport of topological insulators in InAs/GaSb quantum wells. Recent experimental results show that the quantized conductance from helical edge states is very robust against in-plane magnetic fields up to 12 Tesla. By reexamination of band structures, we construct a six-band effective model for the description of the quantum spin Hall effect in InAs/GaSb quantum wells.It is shown that the hidden edge Dirac point in this effective model may give reasonable explanations for the experimental results of robust edge transport. In Chapter 5, we investigate the interference effect of chiral Majorana fermions in quantum anomalous Hall insulator/superconductor hybrid device. Experimentally the half-quantized two-terminal conductance is treated as a solid evidence of chiral Majorana modes in this system. Other possible interpretations, however, may also account for the half-quantized conductance plateau. Therefore, we propose a Majorana-Josephson interferometer to demonstrate the coherent transport of chiral Majorana fermions utilizing the interference effect. From the scattering theory, the characteristic phase-dependent transport properties, including current, conductance, and noise power, can provide a smoking gun evidence to the existence of chiral Majorana fermions. More interestingly, the interferometer may provide an avenue to braid the Majorana modes.