Optical conductivity of curved graphene

Abstract

Abstract. We compute the optical conductivity for an out-of-plane deformation in graphene using an approach based on solutions of the Dirac equation in curved space. Different examples of periodic deformations along one direction translates into an enhancement of the optical conductivity peaks in the region of the far and mid infrared frequencies for periodicities ∼ 100 nm. The width and position of the peaks can be changed by dialling the parameters of the deformation profiles. The enhancement of the optical conductivity is due to intraband transitions and the translational invariance breaking in the geometrically deformed background. Furthemore, we derive an analytical solution of the Dirac equation in a curved space for a general deformation along one spatial direction. For this class of geometries, it is shown that curvature induces an extra phase in the electron wave function, which can also be explored to produce interference devices of the Aharonov-Bohm type.

Shifted Landau levels in curved graphene sheets

“…where a n denote the individual intensities of the energy eigenfunctions, which are determined by the amount of overlap with the initial wave function (25). Thus, we can measure the Landau levels E n by a Fourier transformation of the time evolution of the spinor:…”

Quantum Field Theory Approach to the Optical Conductivity of Strained and Deformed Graphene

“…However, in order to simplify the calculations we will take Y y (x, y) = Y y (x). The corresponding Dirac Hamiltonian reads [6]:…”

“…Graphene is a 2D material whose low energy electronic excitations can be described by a massless Dirac equation [1,2,3,4,5,6]. The Dirac equation can be motivated starting from the tight-binding model and assuming that graphene is a flat sheet.…”

“…Recall that, electrons are confined within a 2D surface which leaves in a 3D world. Further, as discussed in [6] the use of a Dirac equation in a 2D curved space can accommodate not only geometric deformations of the pristine material but can also be used to study strained graphene.…”

“…The interpretation of Landau levels spacing in terms of a pseudo magnetic field unveil intense fields of the order ∼300 T. For one dimensional periodic deformations like e.g. ripples, in [6] it was studied how optical properties are changed by deforming graphene. The main goal of all such studies is, of course, to learn how to tailor the properties of such a promising material as graphene.…”