In this paper we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of all, we will identify the appropriate annihilation and creation operators. Then, we will derive the coherent states as eigenstates of the annihilation operator, with complex eigenvalues. Several physical quantities, as the Heisenberg uncertainty product, probability density and mean energy value, will be as well explored.
Recent experimental advances in the reconstruction of the Wigner function (WF) in electronic systems have led us to consider the possibility of employing this theoretical tool in the analysis of electron dynamics of uniaxially strained graphene. In this work, we study the effect of strain on the WF of electrons in graphene under the interaction of a uniform magnetic field. This mechanical deformation modifies drastically the shape of the Wigner and Husimi function of Landau and coherent states. The WF has a different behavior straining the material along the zigzag direction in comparison with the armchair one and favors the obtention of electron coherent states. The time evolution of the WF for electron coherent states shows fluctuations between classical and quantum behavior with a local maximum value moving in a closed path. The phase-space representation shows more clearly the effect of non-equidistant of relative Landau levels in the time evolution of electron coherent states than other approaches. Our findings may be useful in establishing protocols for the realization of electron coherent states in graphene as well as a bridge between condensed matter and quantum optics.
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. * ediaz@fis.cinvestav.mx † yconcha@umich.mx ‡
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]
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