Related papers: Generalized uncertainty principle in graphene
Dirac's classical theorem asserts that, for $n \ge 3$, any $n$-vertex graph with minimum degree at least $n/2$ is Hamiltonian. Furthermore, if we additionally assume that such graphs are regular, then, by the breakthrough work of Csaba,…
This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later…
We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac…
The spatially nonlocal response functions of graphene obtained on the basis of first principles of quantum field theory using the polarization tensor are considered in the areas of both the on-the-mass-shell and off-the-mass-shell waves. It…
We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated…
The physics of graphene is acting as a bridge between quantum field theory and condensed matter physics due to the special quality of the graphene quasiparticles behaving as massless two dimensional Dirac fermions. Moreover, the particular…
The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
We study the DC transport of finite graphene samples with random gap. Using Dirac fermions to describe the low-energy physics near the Dirac point, we employ a generalized Drude form for the conductivity. The latter is constant for a…
The Dirac equation in curved space is used to study the optical transmittance of deformed graphene along a given direction. Our theoretical analysis of the available experimental data for the light transmittance suggests that the periodic…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
We present quantum-mechanical density-matrix formalism for calculating the nonlinear optical response of magnetized graphene, valid for arbitrarily strong magnetic and optical fields. We show that magnetized graphene possesses by far the…
The intertwining technique has been widely used to study the Schr\"odinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the…
We evaluate the electronic transmission and conductance in bilayer graphene through a finite number of potential barriers. Further, we evaluate the dispersion relation in a bilayer graphene superlattice with a periodic potential applied to…
Graphene, a single sheet of graphite with honeycomb lattice structure, has massless carriers with tunable density and polarity. We investigate the ground state phase diagram of two graphene sheets (embedded in a dielectric) separated by…
Graphene is a recently discovered carbon based material with unique physical properties. This is a monolayer of graphite, and the two-dimensional electrons and holes in it are described by the effective Dirac equation with a vanishing…
We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle…
The present study explores the edge states in a finite-width graphene ribbon and a semi-infinite geometry subject to a perpendicular magnetic field and an in-plane electric field, applied perpendicular to a zigzag edge. To accomplish this,…
We investigate the relativistic quantum dynamics of amassless electron in graphene in a two-dimensional noncommutative (NC) plane under a constant background magnetic field. To address the issue of gauge invariance, we employ an effective…