Barut-Girardello coherent states in graphene under uniform uniaxial strain

We construct the Barut-Girardello coherent states for charge carriers in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene sample. We consider the situation in which the membrane is deformed uniformly and uniaxially, avoiding the generation of pseudomagnetic fields. For that purpose, we solve the Dirac-Weyl equation with an anisotropic Fermi velocity 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 effects of strain on these states, we obtain the Heisenberg uncertainty relation, the probability density and mean energy value for three different functions $f$. In general, when the deformation is along the $x$-axis of the membrane, the probability density obtained for the nonlinear coherent states is smaller than when the deformation is along the orthogonal direction.