Related papers: Complex Supersymmetry in Graphene
The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical…
Graphene is described at low-energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to…
The exceptional electronic properties of monoatomic thin graphene sheets triggered numerous original transport concepts, pushing quantum physics into the realm of device technology for electronics, optoelectronics and thermoelectrics. At…
We consider electronic transport accross one-dimensional heterostructures described by the Dirac equation. We discuss the cases where both the velocity and the mass are position dependent. We show how to generalize the Dirac Hamiltonian in…
We study the electronic and transport properties of a graphene-based superlattice theoretically by using an effective Dirac equation. The superlattice consists of a periodic potential applied on a single-layer graphene deposited on a…
We show how the two-dimensional Dirac oscillator model can describe some properties of electrons in graphene. This model explains the origin of the left-handed chirality observed for charge carriers in monolayer and bilayer graphene. The…
We study quantum phase transitions in graphene superlattices in external magnetic fields, where a framework is presented to classify multiflavor Dirac fermion critical points describing hopping tuned topological phase transitions of integer…
The electrons in graphene for energies close to the Dirac point have been found to form strongly interacting fluid. Taking this fact into account we have extended previous work on the transport properties of graphene by taking into account…
Graphene-based multilayer systems serve as versatile platforms for exploring the interplay between electron correlation and topology, thanks to distinctive low-energy bands marked by significant quantum metric and Berry curvature from…
The topological electronic structure of crystalline materials often gives rise to intriguing surface states, such as Dirac surface states in topological insulators, Fermi arc surface states in Dirac semimetals, and topological…
In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field,…
Electric and magnetic waveguides are considered in planar Dirac materials like graphene as well as their classical version for relativistic particles of zero mass and electric charge. In order to solve the Dirac-Weyl equation analytically,…
A connection is established between the continuum limit of the low-energy tight-binding description of graphene immersed in an in-plane magnetic field and the Chiral Magnetic Effect in Quantum Chromodynamics. A combination of mass gaps that…
We consider a system of Dirac fermions in graphene submitted to a constant perpendicular magnetic field and scattered by a barrier potential. We show that our system can be used to establish a link with quantum optics through the…
Recent studies show that periodic potentials can generate superlattice Dirac points at energies in graphene (is the Fermi velocity of graphene and G is the reciprocal superlattice vector). Here, we perform scanning tunneling microscopy and…
By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference…
We investigate planar quantum electrodynamics (QED) with two degenerate staggered fermions in an external magnetic field on the lattice. We argue that in external magnetic fields there is dynamical generation of mass for two-dimensional…
Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is…
We present the electronic properties of massless Dirac fermions characterized by geometry and topology on a graphene sheet in this chapter. Topological effects can be elegantly illuminated by the Atiyah-Singer index theorem. It leads to a…
We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of…