Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

  title={Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects},
  author={Ganesh Sundaram and Q. Niu},
  journal={Physical Review B},
We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first-order gradient correction and obtain all kinds of Berry phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking interband couplings. For… 
Coherent wave-packet evolution in coupled bands
We develop a formalism for treating coherent wave-packet dynamics of charge and spin carriers in degenerate and nearly degenerate bands. We consider the two-band case carefully in view of spintronics
Semiclassical wave packet dynamics in nonuniform electric fields
We study the semi-classical theory of wave packet dynamics in crystalline solids extended to include the effects of a non-uniform electric field. In particular, we derive a correction to the
Semiclassical dynamics of electron wave packet states with phase vortices.
S semiclassical higher-order wave packet solutions of the Schrödinger equation with phase vortices are considered and the magnetic-monopole Berry curvature appears in momentum space, which results in a spin-orbit-type interaction and a Berry/Magnus transverse force acting on the wave packet.
Electron dynamics in slowly modulated crystals: theorems of power and adiabatic drifting
Abstract We discuss electron dynamics in crystals which are modulated slowly in space and time. The equations of motion for the center-of-mass position and crystal momentum of a wave packet involve
Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons
Abstract Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we studied the
Berry phase and anomalous velocity of Weyl fermions and Maxwell photons
We consider two systems of wave equations whose wave packet solutions have trajectories that are altered by the “anomalous velocity” effect of a Berry curvature. The first is the matrix Weyl equation
Multiband effects in equations of motion of observables beyond the semiclassical approach
The equations of motion for the position and gauge invariant crystal momentum are considered for multiband wave packets of Bloch electrons. For a localized packet in a subset of bands well-separated
Quantum kinetic equation in phase-space textured multiband systems
Starting from the density-matrix equation of motion, we derive a semiclassical kinetic equation for a general two-band electronic Hamiltonian, systematically including quantum-mechanical corrections
Electric polarization in inhomogeneous crystals
We derive the charge density up to second order in spatial gradient in inhomogeneous crystals using the semiclassical coarse graining procedure based on the wave packet method. It can be recast as
Phase-space curvature in spin-orbit-coupled ultracold atomic systems
We consider a system with spin-orbit coupling and derive equations of motion which include the effects of Berry curvatures. We apply these equations to investigate the dynamics of particles with


Geometry of the Time-Dependent Variational Principle in Quantum Mechanics
The time-dependent variational principle (TDVP).- Lie algebras and symplectic structures.- Symplectic structure on group representation spaces.- Geometry of the TDVP.- Simple applications.- The