Nonadiabatic wavepacket dynamics:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math>-space formulation

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 wave form in $k$ space and for the evolution of the underlying Bloch-type 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 sizable spread oscillations do occur, they are mostly due to the latter term.

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