A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

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 …

Topological insulators are a new phase of matter, with the striking property that conduction
of electrons occurs only on their surfaces,,. In two dimensions, electrons on the surface of a …

Topological photonics is a rapidly emerging field of research in which geometrical and
topological ideas are exploited to design and control the behavior of light. Drawing …

There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

Rapidly growing demands for fast information processing have launched a race for creating
compact and highly efficient optical devices that can reliably transmit signals without losses …

The application of topology, the mathematics of conserved properties under continuous
deformations, is creating a range of new opportunities throughout photonics. This field was …

The theory of electric polarization in crystals defines the dipole moment of an insulator in
terms of a Berry phase (geometric phase) associated with its electronic ground state,. This …

Topological features—global properties not discernible locally—emerge in systems ranging
from liquid crystals to magnets to fractional quantum Hall systems. A deeper understanding …

We show that the bulk-boundary correspondence for topological insulators can be modified
in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with …