相关论文: Partition Functions and Stability Criteria of Topo…

The outstanding transport properties expected at the edge of two-dimensional time-reversal invariant topological insulators have proven to be challenging to realize experimentally, and have so far only been demonstrated in very short…

We introduce a novel class of interaction-enabled topological crystalline insulators in two- and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal…

In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…

We study the partition function for the low-energy edge excitations of the incompressible electron fluid. On an annular geometry, these excitations have opposite chiralities on the two edges; thus, the partition function takes the standard…

We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…

The unique properties of spin-polarized surface or edge states in topological insulators (TIs) make these quantum coherent systems interesting from the point of view of both fundamental physics and their implementation in low power…

Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. While a range of different mechanisms to induce topological order have been introduced, a quest for…

Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\rm MoTe}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall…

Studying deterministic operators, we define an appropriate topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer…

While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…

We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these…

Quadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported…

Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle theta of zero or pi. It was recently shown that fractional quantized values of theta…

Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional…

Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and…

Spin-orbit coupled materials have attracted revived prominent research interest as of late, especially due their direct connection with topological notions. Arguably, a hallmark of this pursuit is formed by the concept of the topological…

We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…

An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can…

We study the properties of two dimensional topological spin hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal…

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…