Valley-dependent time evolution of coherent electron states in tilted anisotropic Dirac materials

TL;DR

This paper investigates how the tilt of Dirac cones in anisotropic 2D materials influences the time evolution of coherent electron states under electric and magnetic fields, revealing valley-dependent quantum behaviors.

Contribution

It introduces a canonical transformation to analyze valley-dependent electron dynamics in tilted Dirac materials under electromagnetic fields.

Findings

Valley-dependent behavior of the Wigner function for Landau and coherent states.

Electric fields influence quantum uncertainties differently across valleys.

Negative Wigner function values indicate quantum noise and non-classical states.

Abstract

The effect of the Dirac cone tilt of anisotropic two-dimensional materials on the time evolution of coherent electron states in the presence of electric and magnetic fields is studied. We propose a canonical transformation that maps the anisotropic Dirac-Weyl Hamiltonian with tilted Dirac cones to an effective and isotropic Dirac Hamiltonian under these fields. In this way, the well-known Landau-level spectra and wave functions allow calculating the Wigner matrix representation of Landau and coherent states. We found a valley dependency in the behavior of the Wigner function for both Landau and coherent electron states. The time evolution shows that the interplay of the Dirac cone tilt and the electric field keeps the uncertainties of both position and momentum in one valley significantly lower than in the other valley. The increment of quantum noise correlates with the emergence of negative values in the Wigner function. These results may help us to understand the generation of coherent electron states under the interaction with electromagnetic fields. The reported valley-dependent signatures in the Wigner function of materials with tilted Dirac cones may be revealed by quantum tomography experiments, even in the absence of electric fields.