Coherent states for graphene under the interaction of crossed electric and magnetic fields

Abstract: We construct the coherent states for charge carriers in a graphene layer immersed in crossed external electric and magnetic fields. For that purpose, we solve the Dirac-Weyl equation in a Landau-like gauge avoiding applying techniques of special relativity, and thus we identify the appropriate rising and lowering operators associated to the system. We explicitly construct the coherent states as eigenstates of a matrix annihilation operator with complex eigenvalues. In order to describe the effects of both fields on these states, we obtain the probability and current densities, the Heisenberg uncertainty relation and the mean energy as functions of the parameter $\beta=c\,\mathcal{E}/(v_{\rm F}B)$. In particular, these quantities are investigated for magnetic and electric fields near the condition of the Landau levels collapse ($\beta\rightarrow1$).