Antonio M. García-García

A general class of holographic superconductors.

We introduce a simple generalization of the basic holographic superconductor model in which the spontaneous breaking of a global U(1) symmetry occurs via the Stückelberg mechanism. This more general setting allows tuning features such as the order of the transition. The physical vacuum of the condensed phase and the order of the transition are determined by a detailed analysis of the free energy of the system. For first order transitions, we identify a metastable phase above the critical temperature. In this case, the conductivity shows additional poles, thus suggesting that the condensate has internal structure.

Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model

We study spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, a variant of the k-body embedded random ensembles studied for several decades in the context of nuclear physics and quantum chaos. We show analytically that the fourth- and sixth-order energy cumulants vanish in the limit of a large number of particles N→∞, which is consistent with a Gaussian spectral density. However, for finite N, the tail of the average spectral density is well approximated by a semicircle law. The specific heat coefficient, determined numerically from the low-temperature behavior of the partition function, is consistent with the value obtained by previous analytical calculations. For energy scales of the order of the mean level spacing we show that level statistics are well described by random matrix theory. Due to the underlying Clifford algebra of the model, the universality class of the spectral correlations depends on N. For larger energy separations we identify an energy scale that grows with N, reminiscent of the Thouless energy in mesoscopic physics, where deviations from random matrix theory are observed. Our results are a further confirmation that the Sachdev-Ye-Kitaev model is quantum chaotic for all time scales. According to recent claims in the literature, this is an expected feature in field theories with a gravity dual.

Holographic approach to phase transitions

We provide a description of phase transitions at finite temperature in strongly coupled field theories using holography. For this purpose, we introduce a general class of gravity duals to superconducting theories that exhibit various types of phase transitions (first or second order with both mean and non-mean field behavior) as parameters in their Lagrangian are changed. Moreover the size and strength of the conductivity coherence peak can also be controlled. Our results suggest that certain parameters in the gravitational dual control the interactions responsible for binding the condensate and the magnitude of its fluctuations close to the transition.

Observation of shell effects in superconducting nanoparticles of Sn

In a zero-dimensional superconductor, quantum size effects (QSE) not only set the limit to superconductivity, but are also at the heart of new phenomena such as shell effects, which have been predicted to result in large enhancements of the superconducting energy gap. Here, we experimentally demonstrate these QSE through measurements on single, isolated Pb and Sn nanoparticles. In both systems superconductivity is ultimately quenched at sizes governed by the dominance of the quantum fluctuations of the order parameter. However, before the destruction of superconductivity, in Sn nanoparticles we observe giant oscillations in the superconducting energy gap with particle size leading to enhancements as large as 60%. These oscillations are the first experimental proof of coherent shell effects in nanoscale superconductors. Contrarily, we observe no such oscillations in the gap for Pb nanoparticles, which is ascribed to the suppression of shell effects for shorter coherence lengths. Our study paves the way to exploit QSE in boosting superconductivity in low-dimensional systems.

Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N

We show analytically that the spectral density of the

A thermal quench induces spatial inhomogeneities in a holographic superconductor

q

Bardeen-Cooper-Schrieffer Theory of Finite-Size Superconducting Metallic Grains

-body Sachdeev-Ye-Kitaev (SYK) model agrees with that of Q-Hermite polynomials with Q a non-trivial function of

Chiral phase transition in lattice QCD as a metal-insulator transition

q \ge 2

BCS superconductivity in metallic nanograins: Finite-size corrections, low-energy excitations, and robustness of shell effects.

and the number of Majorana fermions

Normal modes and time evolution of a holographic superconductor after a quantum quench

N \gg 1