11 research outputs found
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