Exactly solvable cases in QED with t-electric potential steps

We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical transport are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long- range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, p-n junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.

Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T\(_c\) superconductors to the topological insulators and beyond, various electronic systems exhibit properties which can be well described by the Dirac equation. Such physics is no longer the exclusive domain of quantum field theories and other esoteric mathematical musings; instead, real physics of real systems is governed by such equations, and important materials science and practical implications hinge on our understanding of Dirac particles in two and three dimensions. While the physics that gives rise to the massless Dirac Fermions in each of the above mentioned materials is different, the low energy properties are governed by the same Dirac kinematics. The aim of this article is to review a selected cross-section of this vast field by highlighting the generalities, and contrasting the specifics, of several physical systems.