Universal semiclassical equations based on the quantum metric
- URL: http://arxiv.org/abs/2106.12383v1
- Date: Wed, 23 Jun 2021 13:24:29 GMT
- Title: Universal semiclassical equations based on the quantum metric
- Authors: C. Leblanc and G. Malpuech and D. D. Solnyshkov
- Abstract summary: We derive semiclassical equations of motion for an accelerated wavepacket in a two-band system.
We show that these equations can be formulated in terms of the static band geometry described by the quantum metric.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We derive semiclassical equations of motion for an accelerated wavepacket in
a two-band system. We show that these equations can be formulated in terms of
the static band geometry described by the quantum metric. We consider the
specific cases of the Rashba Hamiltonian with and without a Zeeman term. The
semiclassical trajectories are in full agreement with the ones found by solving
the Schr\"odinger equation. This formalism successfully describes the adiabatic
limit and the anomalous Hall effect traditionally attributed to Berry
curvature. It also describes the opposite limit of coherent band superposition
giving rise to a spatially oscillating Zitterbewegung motion. At $k=0$, such
wavepacket exhibits a circular trajectory in real space, with its radius given
by the square root of the quantum metric. This quantity appears as a universal
length scale, providing a geometrical origin of the Compton wavelength.
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