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Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport…
This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric…
In an ideal graphene sheet charge carriers behave as two-dimensional (2D) Dirac fermions governed by the quantum mechanics of massless relativistic particles. This has been confirmed by the discovery of a half-integer quantum Hall effect in…
Electrons moving in graphene behave as massless Dirac fermions, and they exhibit fascinating low-frequency electrical transport phenomena. Their dynamic response, however, is little known at frequencies above one terahertz (THz). Such…
Graphene, a monolayer of carbon atoms arranged in a hexagonal pattern, provides a unique two-dimensional (2D) system exhibiting exotic phenomena such as quantum Hall effects, massless Dirac quasiparticle excitations and universal absorption…
The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from the behavior of non-relativistic electrons seen in traditional atomic and impurity systems. Surprisingly, many key theoretical predictions for…
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…
Electrons in graphene behave like Dirac fermions, permitting phenomena from high energy physics to be studied in a solid state setting. A key question is whether or not these Fermions are critically influenced by Coulomb correlations. We…
Recent experiments have proven that the quasiparticles in graphene obey a Dirac equation. Here we show that microwaves are an excellent probe of their unusual dynamics. When the chemical potential is small the intraband response can exhibit…
The electrical conductivity of suspended graphene has recently been measured for the first time, and found to behave as \sigma ~ \sqrt{|n|} as expected for Dirac quasiparticles at large carrier density. The charge inhomogeneity is strongly…
Exact stationary solutions of the electron-photon Dirac equation are obtained to describe the strong interaction between massless Dirac fermions in graphene and circularly polarized photons. It follows from them that this interaction forms…
Electrostatic confinement of charge carriers in graphene is governed by Klein tunneling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at pn junction boundaries. Reflection and…
The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical…
The Dirac point and linear band structure in Graphene bestow it with remarkable electronic and optical properties, a subject of intense ongoing research. Explanations of high electronic mobility in graphene, often invoke the masslessness of…
A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the…
We study quasiparticle dynamics in graphene exposed to a linearly-polarized electromagnetic wave of very large intensity. Low-energy transport in such system can be described by an effective time-independent Hamiltonian, characterized by…
A number of interesting properties of graphene and graphite are postulated to derive from the peculiar bandstructure of graphene. This bandstructure consists of conical electron and hole pockets that meet at a single point in momentum (k)…
In this paper, we study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. Since the…
Following a nonperturbative formulation of strong-field QED developed in our earlier works, and using the Dirac model of the graphene, we construct a reduced QED_{3,2} to describe one species of the Dirac fermions in the graphene…
Our previous results on the nonperturbative calculations of the mean current and of the energy-momentum tensor in QED with the T-constant electric field are generalized to arbitrary dimensions. The renormalized mean values are found; the…