Light absorption in distorted graphene

Solid State Communications, 2007

Graphene is the first example of truly two-dimensional crystals-it's just one layer of carbon atoms. It turns out to be a gapless semiconductor with unique electronic properties resulting from the fact that charge carriers in graphene demonstrate charge-conjugation symmetry between electrons and holes and possess an internal degree of freedom similar to "chirality" for ultrarelativistic elementary particles. It provides unexpected bridge between condensed matter physics and quantum electrodynamics (QED). In particular, the relativistic Zitterbewegung leads to the minimum conductivity of order of conductance quantum e 2 /h in the limit of zero doping; the concept of Klein paradox (tunneling of relativistic particles) provides an essential insight into electron propagation through potential barriers; vacuum polarization around charge impurities is essential for understanding of high electron mobility in graphene; index theorem explains anomalous quantum Hall effect.

2007

We consider the relationship between the tight-binding Hamiltonian of the twodimensional honeycomb lattice of carbon atoms with nearest neighbor hopping only and the 2 + 1 dimensional Hamiltonian of quantum electrodynamics which follows in the continuum limit. We pay particular attention to the symmetries of the free Dirac fermions including spatial inversion, time reversal, charge conjugation and chirality. We illustrate the power of such a mapping by considering the effect of the possible symmetry breaking which corresponds to the creation of a finite Dirac mass, on various optical properties. In particular, we consider the diagonal AC conductivity with emphasis on how the finite Dirac mass might manifest itself in experiment. The optical sum rules for the diagonal and Hall conductivities are discussed.

Physical Review B, 2013

We calculate the optical (ω T) conductivity in clean graphene in the ultimate low-energy regime, when retardation effects of the electromagnetic interaction become important and when the full Lorentz symmetry emerges. In contrast to what happens with the short range or with the Coulomb long-range instantaneous interactions, the optical conductivity is now no longer equal to its noninteracting value, but acquires universal corrections in powers of the fine structure constant. The coefficient of the first order correction is computed, and found to be of order one. We also present the result for the conductivity in the large-N limit, with N as the number of Dirac fermions species, to the order 1/N 2 .

Journal of Physics: Condensed Matter, 2014

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.

A single atomic layer of carbon, graphene, has the low-energy "relativistic-like" gapless quasiparticle excitations which in the continuum approximation are described by quantum electrodynamics in 2+1 dimensions. The Diraclike character of charge carriers in graphene leads to several unique electronic properties which are important for applications in electronic devices. We study the gap opening in graphene following the ideas put forward by P. I. Fomin for investigation of chiral symmetry breaking and particle mass generation in quantum field theory.

2014

The enormous list of publications on transport measurements in graphene starts with the seminal papers by the groups from Manchester and Columbia [1a]. Already these studies indicated a very robust transport behavior, which is characterized by a “V”-shaped conductivity with respect to charge density n and a minimal conductivity σmin ≈ 4e2∕h at the charge neutrality point n = 0. In the presence of a magnetic field, there are Shubnikov–de Haas oscillations for the longitudinal conductivity σxx and quantum Hall plateaux for the Hall conductivity σxy at a sufficiently strong magnetic field. These properties have been confirmed subsequently by various experimental groups in more detailed studies and measurements under various conditions and for different types of samples. Many of those results are collected and discussed in a number of extensive reviews [2–4]. Optical properties of graphene for light with frequency ω are (directly) related to the optical (or AC) conductivity σAC xx (ω). ...

Physical Review Letters, 2009

Journal of Computational and Theoretical Nanoscience, 2011

Charge carriers in graphene are chiral quasiparticles ("massless Dirac fermions"). Graphene provides therefore an amazing opportunity to study subtle quantum relativistic effects in condensed matter experiment. Here I review a theory of one of these unusual features of graphene, a "pseudodiffusive" transport in the limit of zero charge carrier concentration, which is related to existence of zero-modes of the Dirac operator and to the Zitterbewegung of unltrarelativistic particles. A conformal mapping technique is a powerful mathematical tool to study these phenomena, as demonstrated here, using the Aharonov-Bohm effect in graphene rings with Corbino geometry as an example.

Journal of Nanophotonics, 2018

Microscopic quantum theory of nonlinear stimulated scattering of 2D massless Dirac particles in doped graphene on Coulomb field of impurity ions at the presence of an external strong coherent electromagnetic radiation is developed. We consider high Fermi energies and low frequencies (actually terahertz radiation) to exclude the valence electrons excitations. The Liouville-von Neumann equation for the density matrix is solved analytically, taking into account the interaction of electrons with the scattering potential in the Born approximation. With the help of this solution, the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of 2D Dirac fermions is calculated. It is shown that one can achieve the efficient absorption coefficient by this mechanism.

Scientific Reports, 2013