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

Abstract

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 inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

“…A reciprocal gauge field of geometric origin (Berry connection) appears naturally in such EOM. [7] Then we combine our formalism with the Boltzmann transport theory to describe such phenomena as spin and orbital transport. Its relevance to quantum charge/spin pumping [14,15] will be also briefly discussed.…”

“…[1,2] Recently a group of condensed-matter physicists [3,4] embodied the idea of detecting a monopole in the band structure. [5] In crystal momentum space, monopoles appear as a source or a sink of the reciprocal magnetic field [6,7] associated with the geometric phase of Bloch electrons. The geometric phase of a Bloch electron, i.e., its Berry phase, has also attracted much attention on the technological side, in particular, in the context of spintronics.…”

Multiphase semiclassical approximation of the one-dimensional harmonic crystal: I. The periodic case

“…This modelling has already been incontered in several papers; let us quote [20,23] where it is referred to as "the deformed crystal". Moreover, many studies have been made in the field of "incommensurate crystals", see [16,21,18], emphasizing the so-called modulated Kronig-Penney model.…”

“…2 whereṼ per (t, y) = cos y + π 2 sin(ky + Ω(k)t) . It is interesting to make a link with a feature pointed out in [23], namely the tendency for the lattice to drag the electron with its displacement motion, called "lattice tracking". First, observe that even if supplying the WKB system (7)- (9) with initial data such that a 0 ≡ 1 and ∂ x ϕ ≡ 0, we would have ψ ε (t, x) = ψ ε (t = 0, x) because of the time-dependence of z n,κ .…”

Intrinsic contribution to spin Hall and spin Nernst effects in a bilayer graphene

“…The corresponding extrinsic SHE is associated with mechanisms of spin-orbit scattering on impurities and other defects (skew scattering and/or side jump), while the intrinsic SHE is a consequence of a nontrivial trajectory of charge carriers in the momentum space due to the spin-orbit contribution of a perfect crystal lattice to the corresponding band structure. The intrinsic SHE may be described in terms of the Berry phase formalism 14,15 and therefore it is also referred to as the topological SHE.…”