Entanglement Entropy as a Probe of the Proximity Effect in Holographic Superconductors

We study the entanglement entropy as a probe of the proximity effect of a superconducting system by using the gauge/gravity duality in a fully back-reacted gravity system. While the entanglement entropy in the superconducting phase is less than the entanglement entropy in the normal phase, we find that near the contact interface of the superconducting to normal phase the entanglement entropy has a different behavior due to the leakage of Cooper pairs to the normal phase. We verify this behavior by calculating the conductivity near the boundary interface.Comment: 10 pages, 7 figures, extended version to be published in JHE

Strong Cosmic Censorship in Charged de Sitter spacetime with Scalar Field Non-minimally Coupled to Curvature

We examine the stability and the strong cosmic censorship in the Reissner-Nordstrom-de Sitter (RN-dS) black hole by investigating the evolution of a scalar field non-minimally coupled to the curvature. We find that when the coupling parameter is negative, the RN-dS black hole experiences instability. The instability disappears when the coupling parameter becomes non-negative. With the increase of the coupling parameter, the violation of the strong cosmic censorship occurs at a larger critical charge ratio. But such an increase of the critical charge is suppressed by the increase of the cosmological constant. Different from the minimal coupling situation, it is possible to accommodate $\beta\ge1$ in the near extremal black hole when the scalar field is non-minimally coupled to curvature. The increase of the cosmological constant can allow $\beta\ge1$ to be satisfied for even smaller value of the coupling parameter. The existence of $\beta\ge1$ implies that the resulting curvature can continuously cross the Cauchy horizon.Comment: 14 pages, 4 figures, 5 table

Formation of Fermi surfaces and the appearance of liquid phases in holographic theories with hyperscaling violation

We consider a holographic fermionic system in which the fermions are interacting with a U(1) gauge field in the presence of a dilaton field in a gravity bulk of a charged black hole with hyperscaling violation. Using both analytical and numerical methods, we investigate the properties of the infrared and ultaviolet Green's functions of the holographic fermionic system. Studying the spectral functions of the system, we find that as the hyperscaling violation exponent is varied, the fermionic system possesses Fermi, non-Fermi, marginal-Fermi and log-oscillating liquid phases. Various liquid phases of the fermionic system with hyperscaling violation are also generated with the variation of the fermionic mass. We also explore the properties of the flat band and the Fermi surface of the non-relativistic fermionic fixed point dual to the hyperscaling violation gravity.Comment: 19 pages, 8 figures; v2: minor clarifications, section VI added, references added; accepted for publication in JHE

Algebraic Cayley Graphs over Finite Fields

A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of Chung

Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201

Fermionic phase transition induced by the effective impurity in holography

We investigate the holographic fermionic phase transition induced by the effective impurity in holography, which is introduced by massless scalar fields in Einstein-Maxwell-massless scalar gravity. We obtain a phase diagram in $(\alpha, T)$ plane separating the Fermi liquid phase and the non-Fermi liquid phase.Comment: 17 pages, 9 figure