Properties of Graphene: A Theoretical Perspective

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 the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic

Constraining Pseudorandom Functions Privately

In a constrained pseudorandom function (PRF), the master secret key can be used to derive constrained keys, where each constrained key k is constrained with respect to some Boolean circuit C. A constrained key k can be used to evaluate the PRF on all inputs x for which C(x) = 1. In almost all existing constrained PRF constructions, the constrained key k reveals its constraint C. In this paper we introduce the concept of private constrained PRFs, which are constrained PRFs with the additional property that a constrained key does not reveal its constraint. Our main notion of privacy captures the intuition that an adversary, given a constrained key k for one of two circuits C_0 and C_1, is unable to tell which circuit is associated with the key k. We show that constrained PRFs have natural applications to searchable symmetric encryption, cryptographic watermarking, and much more. To construct private constrained PRFs we first demonstrate that our strongest notions of privacy and functionality can be achieved using indistinguishability obfuscation. Then, for our main constructions, we build private constrained PRFs for bit-fixing constraints and for puncturing constraints from concrete algebraic assumptions