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 …

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 …

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 …

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 …

Ever since its discovery the notion of Berry phase has permeated through all branches of
physics. Over the past three decades it was gradually realized that the Berry phase of the …

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 …

The anomalous Hall effect (AHE) occurs in solids with broken time-reversal symmetry,
typically in a ferromagnetic phase, as a consequence of spin-orbit coupling. Experimental …

The anomalous Hall effect is a fundamental transport process in solids arising from the spin-
orbit coupling. In a quantum anomalous Hall insulator, spontaneous magnetic moments and …

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 …

In 3D momentum space, a topological phase boundary separating the Chern insulating
layers from normal insulating layers may exist, where the gap must be closed, resulting in a …