Schrödinger-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 built 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 ζ. 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 and their time evolution. Our results clearly show that the quasi period of electron coherent states is affected by the uniaxial strain.

Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices

“…Also, the width of the WF and its location along the q y -axis are also affected by the value of k x , in contrast with the case of uniformly strained graphene, where the momentum in the orthogonal direction only affects the location, not the shape. These results constitute remarkable differences with respect to the previous works [32][33][34][35] for 2D Dirac materials with an anisotropic but homogeneous Fermi velocity under a external magnetic field. In general, our findings for dispersive pseudo-Landau-levels expand the CS formalism and offer a novel scenario for electronic transport studios.…”

“…In comparison with the results shown in [35], we can see that k x plays a role similar to that of tensile or compression deformations in auto-correlation function, modifying what time the fast oscillations appear, that also depends on the valley index.…”

“…First, its location along the q y -axis depends on the value of the momentum k x . This is related to that the center of the cyclotron in the Landau-like gauge is given by [35] X…”

“…This fact produces a strain-induced modulation of the optical transmittance [30] and of the Faraday (Kerr) effect in graphene [31]. Moreover, it is precisely by taking advantage of the strain-induced anisotropy that the concept of strain engineering has been also extended to the context of CSs in recent works [32][33][34][35][36], but all limited to the case of uniform strains.…”

Coherent states in the symmetric gauge for graphene under a constant perpendicular magnetic field

“…The results of B U q β,n and 2 B (R ) 2 β,n agree with Eq. ( 83) and those in [56], respectively. The latter also corresponds to the mean value of (R ) 2 for the eigenstates Ψ ± m,n , since the partial coherent states Π β,n are basically equal to the pseudo-spinor eigenstates Ψ ± m,n but centered on the point (x 0 , y 0 ).…”