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The discovery that the band structure of electronic insulators may be topologically non-trivial has unveiled distinct phases of electronic matter with novel properties. Recently, mechanical lattices have been found to have similarly rich…
A chiral superconductor has been proposed as one pathway to realize topological quantum computation utilizing the predicted Majorana normal fluid at its boundary (i.e., a point, edge, or surface). The search for experimental realizations…
We prove a topological criterion for the existence of zero-energy Majorana bound-state on a disclination, a rotation symmetry breaking point defect, in 4-fold symmetric topological crystalline superconductors (TCS). We first establish a…
The relation between bulk topological invariants and experimentally observable physical quantities is a fundamental property of topological insulators and superconductors. In the case of chiral symmetric systems in odd spatial dimensions…
The engineering of topological non-trivial states of matter, using cold atoms, has made great progress in the last decade. Driven by experimental successes, it has become of major interest in the cold atom community. In this work we…
Chiral superconductors are one of the predominant quantum electronic states of matter where topology, symmetry, and Fermiology intertwine. This is pushed to a new limit by further invoking the coupling between spin and charge degrees of…
The possibility of realizing topological insulators by spontaneous formation of electronic superstructure is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a…
Two-dimensional moir\'e Chern bands provide an exceptional platform for exploring a variety of many-body quantum phases at zero magnetic field within a lattice system. One particular intriguing possibility is that flat Chern bands can, in…
We present a topological description of quantum spin Hall effect (QSHE) in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be…
Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be continuously connected to the clean limit and are therefore genuinely disorder-driven. We demonstrate this in…
Hexagonally patterned two-dimensional $p$-type semiconductor systems are quantum simulators of graphene with strong and highly tunable spin-orbit interactions. We show that application of purely in-plane magnetic fields, in combination with…
A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetry based classification of condensed matter. Exotic spin transport phenomena such as the…
Higher-order topological insulators have attracted great research interest recently. Different from conventional topological insulators, higher-order topological insulators do not necessarily require spin-orbit coupling, which makes it…
In two-dimensional topological nodal superconductors, Majorana edge states have been conventionally believed to exhibit only spin-triplet pairing correlations. However, we reveal a substantial spin-singlet pairing component in Majorana edge…
Of the available classes of insulators which have been shown to contain topologically non-trivial properties one of the most important is class AII, which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$ This class…
The topological classification of fermion systems in mixed states is a long standing quest. For Gaussian states, reminiscent of non-interacting unitary fermions, some progress has been made. While the topological quantization of certain…
With the recent discovery of the quantum anomalous Hall insulator (QAHI), which exhibits the conductive quantum Hall edge states without external magnetic field, it becomes possible to create a novel topological superconductor (SC) by…
We theoretically find that the second-order topological insulator, i.e., corner states, can be engineered by coupling two copies of two-dimensional $\mathbb{Z}_2$ topological insulators with opposite spin-helicities. As concrete examples,…
We study superconductors with $n$-fold rotational invariance both in the presence and in the absence of spin-orbit interactions. More specifically, we classify the non-interacting Hamiltonians by defining a series of $Z$-numbers for the…
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic…