Topological insulators are crystalline solids with supposedly very special properties. If
stumbling upon such a crystal, which is possible because topological insulators are known …

The Weyl semimetal (WSM) is a newly proposed quantum state of matter. It has Weyl nodes
in bulk excitations and Fermi arc surface states. We study the effects of disorder and …

Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties
for the topological states. In this paper, we summarize and briefly review the work completed …

Topological insulators and superconductors support extended surface states protected
against the otherwise localizing effects of static disorder. Specifically, in the Wigner-Dyson …

This work presents a computational program based on the principles of non-commutative
geometry and showcases several applications to topological insulators. Noncommutative …

Odd index pairings of $ K_1 $-group elements with Fredholm modules are of relevance in
index theory, differential geometry and applications such as to topological insulators. For the …

We use constructive bounded Kasparov K-theory to investigate the numerical invariants
stemming from the internal Kasparov products K i (𝒜)× KK i (𝒜, ℬ)→ K 0 (ℬ)→ ℝ, i= 0, 1 …

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial
dimensions d≥ 1. When the Fermi level lies in a spectral gap or a mobility gap, the …

An index theorem for higher Chern characters of odd Fredholm modules over crossed
product algebras is proved, together with a local formula for the associated cyclic cocycle …

We investigate a symmetry-protected Z 2 topological electron glass, a glassy equivalent of
the Z 2 topological band insulator in crystalline systems, and uncover associated quantum …