Related papers: Robust integer and fractional helical modes in the…
We review our recent theoretical works on the the quantum spin Hall effect. First we compare edge states in various 2D systems, and see whether they are robust or fragile against perturbations. Through the comparisons we see the robust…
We consider a helical spin liquid system which shows majorana fermion modes at the edge. The interaction between the quasiparticles in this system induces phase transition, Majorana-Ising transition. We comply the density matrix…
We give field theory descriptions of the time-reversal invariant quantum spin Hall insulator in 2+1 dimensions and the particle-hole symmetric insulator in 1+1 dimensions in terms of massive Dirac fermions. Integrating out the massive…
High-order topological insulators (HOTIs), as generalized from topological crystalline insulators (TCIs), are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical…
Higher-order topological superconductors and superfluids host lower-dimensional Majorana corner and hinge states since novel topology exhibitions on boundaries. While such topological nontrivial phases have been explored extensively, more…
Interfacing s-wave superconductors and quantum spin Hall edges produces time-reversal-invariant topological superconductivity of a type that can not arise in strictly 1D systems. With the aim of establishing sharp fingerprints of this novel…
We consider the effect of contact interaction in a prototypical quantum spin Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field with opposite directions for the two spin states restricts two-dimensional particle…
Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent complex quantum ground states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime:…
Two parallel helical edge channels hosting interacting electrons, when proximitized by local and nonlocal pairings, can host time-reversal-invariant pairs of topological zero modes at the system corners. Here we show that realistic…
We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar…
Quantum Hall states - the progenitors of the growing family of topological insulators -- are rich source of exotic quantum phases. The nature of these states is reflected in the gapless edge modes, which in turn can be classified as integer…
We consider the edge of a two-dimensional electron system that is in the quantum-Hall-effect regime at filling factor 1-1/m with m being an odd integer, where microscopic theory explaining the occurrence of the quantum Hall effect in the…
The chiral $p$-wave superconductor/superfluid in two dimensions (2D) is the simplest and most robust system for topological quantum computation . Candidates for such topological superconductors/superfluids in nature are very rare. A widely…
The rich phase diagram of quantum spin-ladder systems has attracted much attention in the theoretical literature. The progress in experimental realisations of this fascinating physics however has been much slower. While materials with a…
Conventional topological classification theory dictates that time-reversal symmetry confines the quantum spin Hall (QSH) effect to a $\mathbb{Z}_2$ classification, permitting only a single pair of gapless helical edge states. Here, we…
In a GaAs/AlGaAs two-dimensional electron system with two occupied subbands, the experimentally determined phase diagram in the density-magnetic field plane exhibits rich topological features. Ring-like structures are observed at even…
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological…
The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which is one of the most striking phenomena in condensed matter physics, involves the topologically protected dissipationless charge current flow along the edges of the…
We propose a new topological quantum state of matter---the two-dimensional (2D) Weyl half semimetal (WHS), which features 2D Weyl points at Fermi level belonging to a single spin channel, such that the low-energy electrons are described by…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…