# Barut-Girardello coherent states for anisotropic 2D-Dirac materials

## TL;DR

This paper constructs and analyzes Barut-Girardello coherent states for charge carriers in anisotropic 2D-Dirac materials under magnetic fields, revealing how anisotropy influences quantum state properties and probability densities.

## Contribution

It introduces a method to construct nonlinear coherent states for anisotropic 2D-Dirac materials and explores the effects of anisotropy on their quantum properties.

## Key findings

- Probability density varies with uniaxial strain direction.
- Anisotropy affects the mean energy and occupation number.
- Coherent states exhibit different uncertainty relations depending on strain.

## Abstract

We construct the Barut-Girardello coherent states for charge carriers in anisotropic 2D-Dirac materials immersed in a constant homogeneous magnetic field which is orthogonal to the sample surface. For that purpose, we solve the anisotropic Dirac equation and identify the appropriate arising and lowering operators. Working in a Landau-like gauge, we explicitly construct nonlinear coherent states as eigenstates of a generalized annihilation operator with complex eigenvalues which depends on an arbitrary function $f$ of the number operator. In order to describe the anisotropy effects on these states, we obtain the Heisenberg uncertainty relation, the probability density, mean energy value and occupation number distribution for three different functions $f$. For the case in which the anisotropy is caused by uniaxial strain, we obtain that when a stress is applied along the $x$-axis of the material surface, the probability density for the nonlinear coherent states is smaller compared to when the material is stressed along the orthogonal axis.