Topological materials have become the focus of intense research in recent years, since they
exhibit fundamentally new physical phenomena with potential applications for novel devices …

In this article, we give a comprehensive review of recent progress in research on symmetry-
protected topological superfluids and topological crystalline superconductors, and their …

We complete a classification of topological phases and their topological defects in crystalline
insulators and superconductors. We consider topological phases and defects described by …

We show that Dirac fermion systems in two dimensions generally exhibit a disorder-induced
nodal arc replacing the nodal point and tilted Dirac cone, provided that the two components …

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally
realize a recently proposed family of nearest-neighbor tight-binding models having …

We identify three-dimensional higher-order superconductors characterized by the
coexistence of one-dimensional Majorana hinge states and gapless surface states. We …

We review two important non-perturbative approaches for extracting the physics of low-
dimensional strongly correlated quantum systems. Firstly, we start by providing a …

We investigate the fate of topological states on fractal lattices. Focusing on a spinless chiral
p-wave paired superconductor, we find that this model supports two qualitatively distinct …

We investigate topological Cooper pairing, including gapless Weyl and fully gapped class
DIII superconductivity, in a three-dimensional doped Luttinger semimetal. The latter …

A scheme is proposed to construct integer and fractional topological quantum states of
fermions in two spatial dimensions. We devise models for such states by coupling wires of …