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 $\beta =c\mathcal{E}/(v_{\mathrm{F}}B)$. In particular, these quantities are investigated for magnetic and electric fields near the condition of the Landau levels collapse ($\beta \to 1$).

arXiv comment21 pages, 10 figures

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• Electron in bilayer graphene with magnetic fields leading to shape invariant potentials
• Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well
• An algorithm for exact analytical solutions for tilted anisotropic Dirac materials
• Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices
• Multiphoton coherent states for bilayer graphene
• Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions