Coherent states in magnetized anisotropic 2D Dirac materials

Abstract

In this work, we construct coherent states for electrons in anisotropic 2D Dirac materials immersed in a uniform magnetic field perpendicularly oriented to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the external magnetic field through a vector potential. By solving a Dirac-like equation with an anisotropic Fermi velocity, we identify two sets of scalar ladder operators that allow us to define generalized annihilation operators, which are generators of either the Heisenberg-Weyl or su(1,1) algebra. We construct both bidimensional and su(1,1) coherent states as eigenstates of such annihilation operators with complex eigenvalues. In order to illustrate the effects of the anisotropy on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ration between the Fermi velocities along the $x$- and $y$-axes, the shape of the probability density is modified on the $xy$-plane with respect to the isotropic case and according to the classical dynamics.

arXiv comment25 pages, 9 figures

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• Schrödinger-type 2D coherent states of magnetized uniaxially strained graphene
• Critical behavior for point monopole and dipole electric impurities in uniformily and uniaxially strained graphene
• Coherent states in the symmetric gauge for graphene under a constant perpendicular magnetic field
• Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
• Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices
• Multiphoton coherent states for bilayer graphene