Coherent states in magnetized anisotropic 2D Dirac materials

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. * ediaz@fis.cinvestav.mx † moliva@fis.cinvestav.mx ‡ yconcha@umich.mx § raya@ifm.umich.mx arXiv:1907.06551v1 [quant-ph]

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

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“…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.…”

Electron coherent states in strained graphene

“…It is worth to mention that this physical problem has been generalized and addressed by defining the external field in the symmetric gauge [6], in order to describe the bidimensional effects of anisotropy in strained graphene and 2D Dirac materials in general.…”

Critical behavior for point monopole and dipole electric impurities in uniformly and uniaxially strained graphene

“…We start from the two-dimensional (2D) Dirac Hamiltonian describing an electric monopole impurity in graphene immersed in a perpendicular magnetic field B uniformly distributed in space. Considering the tensor character of the Fermi velocity induced by strain, v [35][36][37][38], such an equation is written as…”

“…First, notice that neglecting the potential well potential, Eq. (24), in the K point, with j −1/2, renders the energy eigenvalues in the well-known form of LLs corrected by strain through the renormalization of the Fermi velocity v F → λv F [35][36][37][38], namely,…”