  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.
