Schr\"{o}dinger-type 2D coherent states of magnetized uniaxially strained graphene

Abstract

We revisit the uniaxially strained graphene immersed in a uniform homogeneous magnetic field orthogonal to the layer in order to describe the time evolution of coherent states build from a semi-classical model. We consider the symmetric gauge vector potential to render the magnetic field, and we encode the tensile and compression deformations on an anisotropy parameter $\zeta$. After solving the Dirac-like equation with an anisotropic Fermi velocity, we define a set of matrix ladder operators and construct electron coherent states as eigenstates of a matrix annihilation operator with complex eigenvalues. Through the corresponding probability density, we are able to study the anisotropy effects on these states on the $xy$-plane as well as their time evolution. Our results show clearly that the quasi-period of electron coherent states is affected by the uniaxial strain.