The Hall effect, in which a current flows perpendicular to an electrical bias, has been
prominent in the history of condensed matter physics. Appearing variously in classical …

The topological properties of an object, associated with an integer called the topological
invariant, are global features that cannot change continuously but only through abrupt …

The anomalous Hall effect (AHE) is one of the most fundamental phenomena in physics. In
the highly conductive regime, ferromagnetic metals have been the focus of past research …

Over the past twenty-five years, mathematical concepts associated with geometric phases
have come to occupy a central place in our modern understanding of the physics of …

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic
excitations that are protected by topology and symmetry. As three-dimensional analogs of …

Quantum anomalous valley Hall effect (QAVHE), which combines both the features of QAHE
and AVHE, is both fundamentally intriguing and practically appealing, but is experimentally …

The photonic spin Hall effect (SHE) refers to the transverse spin separation of photons with
opposite spin angular momentum, after the beam passes through an optical interface or …

The origin of anomalous Hall effect (AHE) in magnetic materials is one of the most intriguing
aspects in condensed matter physics and has been a controversial topic for a long time …

Whenever a quantum system undergoes a cyclic evolution governed by a slow change of
parameters, it acquires a phase factor: the geometric phase. Its most common formulations …

Spin Hall effects are a collection of relativistic spin-orbit coupling phenomena in which
electrical currents can generate transverse spin currents and vice versa. Despite being …