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 orthogonal 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 magnetic field. By solving a Dirac-like equation with an anisotropic Fermi velocity, we define two sets of generalized ladder operators that are generators of either the Heisenberg–Weyl or su(1,1) algebra and construct coherent states as eigenstates of the generalized annihilation operators with complex eigenvalues. In order to illustrate the anisotropy effects on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ratio 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.