Nonadiabatic wavepacket dynamics: k-space formulation

TL;DR

This paper introduces a k-space formulation for simulating wavepacket dynamics in crystals under electric fields, revealing insights into Bloch oscillations, Zener tunneling, and the role of quantum geometry.

Contribution

It presents a novel k-space approach to model wavepacket evolution in crystals, incorporating quantum metric and Berry connection effects.

Findings

Observation of Bloch oscillations and Zener tunneling in a 1D model

Identification of Berry connection as a key factor in spread oscillations

Analysis of wavepacket dynamics using quantum geometric concepts

Abstract

The time evolution of wavepackets in crystals in the presence of a homogeneous electric field is formulated in k-space in a numerically tractable form. The dynamics is governed by separate equations for the motion of the waveform in k-space and for the evolution of the underlying Bloch-like states. A one-dimensional tight-binding model is studied numerically, and both Bloch oscillations and Zener tunneling are observed. The long-lived Bloch oscillations of the wavepacket center under weak fields are accompanied by oscillations in its spatial spread. These are analyzed in terms of a k-space expression for the spread having contributions from both the quantum metric and the Berry connection of the Bloch states. We find that when sizeable spread oscillations do occur, they are mostly due to the latter term.