The planar Hall effect (PHE) is one of the hot topics in field condensed matter physics. In recent years, PHE has received great attention especially topological materials such as insulators and semimetals, progress been made. Different from ordinary effect, transverse current, magnetic field, electric can appear same plane cannot be explained by Lorentz force, which largely depends on anisotro...

We study the semi-classical limit of the Schrödinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play ...

A topological quantum phase requires a finite momentum-space Berry curvature which, conventionally, can arise through breaking the inversion or the time-reversal symmetry so as to generate nontrivial, topologically invariant quantities associated with the underlying energy band structure (e.g., a finite Chern number). For conventional graphene or graphenelike two-dimensional (2D) systems with g...

The main result of Xiao et al. [ Phys. Rev. Lett. 95, 137204 (2005)] is shown to follow from Hamiltonian mechanics. In a recent paper on the semiclassical dynamics of a Bloch electron, Xiao, Shi and Niu [1] claim that, due to a Berry curvature term, Liouville’s theorem on the conservation of the phasespace volume element would be violated, a fact which would have been overlooked so far. Their m...

Kagome materials have emerged as a setting for emergent electronic phenomena that encompass different aspects of symmetry and topology. It is debated whether the XV$_6$Sn$_6$ kagome family (where X rare earth element), recently discovered bilayer metals, hosts topologically non-trivial ground state resulting from opening spin-orbit coupling gaps. These states would carry finite spin-Berry curva...