# Coherent states in magnetized anisotropic 2D Dirac materials

## TL;DR

This paper constructs and analyzes coherent states for electrons in anisotropic 2D Dirac materials under a magnetic field, revealing how anisotropy affects their probability densities and energy properties.

## Contribution

It introduces a method to define and study coherent states in anisotropic 2D Dirac materials, incorporating bidimensional effects and algebraic structures like Heisenberg-Weyl and su(1,1).

## Key findings

- Anisotropy modifies the shape of probability densities.
- Coherent states are eigenstates of generalized annihilation operators.
- Energy and probability distributions depend on the anisotropy ratio.

## 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.