Pursuing topological phases in natural and artificial materials is one of the central topics in
modern physical science and engineering. In classical magnetic systems, spin waves (or …

One-dimensional helical liquids can appear at boundaries of certain condensed matter
systems. Two prime examples are the edge of a quantum spin Hall insulator and the hinge …

Non-Hermitian band theory distinguishes between line gaps and point gaps. While point
gaps can give rise to intrinsic non-Hermitian band topology without Hermitian counterparts …

In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising
in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain …

Flat-band superconductivity has theoretically demonstrated the importance of band topology
to correlated phases. In two dimensions, the superfluid weight, which determines the critical …

Bound states at sharp corners have been widely viewed as the hallmark of two-dimensional
second-order topological insulators and superconductors. In this paper, we show that the …

The disorder effects on higher-order topological phases in periodic systems have attracted
much attention. However, in aperiodic systems, such as quasicrystalline systems, the …

We uncover an alternative two-particle Berry phase mechanism to realize exotic corner
modes in second-order topological insulators (TIs) and topological superconductors (TSCs) …

Amorphous topological states, which are independent of the specific spatial distribution of
microscopic constructions, have gained much attention. Recently, higher-order topological …

Among the many far-reaching consequences of the potential existence of a magnetic
monopole, it induces a topological zero mode in the Dirac equation, which was derived by …