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

Unlike their Hermitian counterparts, non-Hermitian (NH) systems may display an
exponential sensitivity to boundary conditions and an extensive number of edge-localized …

This paper is a survey of the ℤ 2-valued invariant of topological insulators used in
condensed matter physics. The ℤ-valued topological invariant, which was originally called …

Topological effects in integrated photonic waveguide structures [Invited] clickable element to
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The goal of this paper is to advance the development of wave-guiding subwavelength
crystals by developing designs whose properties are stable with respect to imperfections in …

Floquet topological insulators describe independent electrons on a lattice driven out of
equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In …

In this paper, we introduce a variation of the notion of topological phase reflecting metric
structure of the position space. This framework contains not only periodic and non-periodic …

The search for strong topological phases in generic aperiodic materials and meta-materials
is now vigorously pursued by the condensed matter physics community. In this work, we first …

We study one-dimensional insulators obeying a chiral symmetry in the single-particle
picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined …

In a basic framework of a complex Hilbert space equipped with a complex conjugation and
an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and …