Related papers: Complex Supersymmetry in Graphene
We show that, by going beyond the low-energy approximation for which the dispersion relations of graphene are linear, the corresponding emergent field theory is a specific generalization a Dirac field theory. The generalized Dirac…
In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…
We study the interaction of electrons in graphene with the quantized electromagnetic field in the presence of an applied uniform electric field using the Dirac model of graphene. Electronic states are represented by exact solutions of the…
Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional electron systems and, ultimately, create materials with tailored electronic properties. Previously, it proved difficult to…
The general covariance of the Dirac equation is exploited in order to explore the curvature effects appearing in the electronic properties of graphene. Two physical situations are then considered: the weak curvature regime, with…
Graphene on two dimensional (2D) noncommutative (NC) plane in the presence of a constant background magnetic field has been studied. To handel the gauge-invariance issue we start our analysis by a effective massles NC Dirac field theory…
We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are…
In this review article we discuss the recent progress in studying ballistic transport for charge carriers in graphene through highly inhomogenous magnetic field known as magnetic barrier in combination with gate voltage induced…
Here we present a theory of mirror-symmetric magic angle twisted trilayer graphene. The electronic properties are described by a Hubbard model with long range tunneling matrix elements. The electronic properties are obtained by solving the…
Using the Lewis-Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some…
We show that graphene, in its simplest form and settings, is a practical table-top realization of the analog of exotic quantum gravity scenarios, which are speculated to lead to certain generalized Heisenberg algebras. In particular, we…
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…
We study the dynamics of carriers in graphene subjected to an inhomogeneous magnetic field. For a magnetic field with an hyperbolic profile the corresponding Dirac equation can be analyzed within the formalism of supersymmetric quantum…
In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of…
We study the energy of quasi-particles in graphene within the Hartree-Fock approximation. The quasi-particles are confined via an inhomogeneous magnetic field and interact via the Coulomb potential. We show that the associated functional…
A general discussion of graphene in external electromagnetic field is provided. In general, the formulation is not Lorentz invariant because of Zeeman energy. But it can be restored approxiamtely in the case of strong magnetic field, the…
An electrostatic quantum dot cannot be formed in monolayer graphene, because of the Klein tunnelling. However, a dot can be formed with the help of a uniform magnetic field. As shown here, a spatial modulation of the Dirac gap leads to…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
The low-energy physics of graphene is described by relativistic Dirac fermions with spin and valley degrees of freedom. Mechanical strain can be used to create a pseudo magnetic field pointing to opposite directions in the two valleys. We…
The objective of this note is to provide an interpretation of the discrete version of Morse inequalities, following Witten's approach via supersymmetric quantum mechanics, adapted to finite graphs, as a particular instance of Morse-Witten…