Holographic Description of Finite Size Effects in Strongly Coupled Superconductors

Abstract

Despite its fundamental and practical interest, the understanding of mesoscopic effects in strongly coupled superconductors is still limited. Here we address this problem by studying holographic superconductivity in a disk and a strip of typical size $\ell$. For $\ell <{\ell }_c$, where ${\ell }_c$ depends on the chemical potential and temperature, we have found that the order parameter vanishes. The superconductor-metal transition at $\ell ={\ell }_c$ is controlled by mean-field critical exponents which suggests that quantum and thermal fluctuations induced by finite size effects are suppressed in holographic superconductors. Intriguingly, the effective interactions that bind the order parameter increases as $\ell$ decreases. Most of these results are consistent with experimental observations in Pb nanograins at low temperature and qualitatively different from the ones expected in a weakly coupled superconductor.

4 pages, 3 figures

References in corpus (6)

• Building an AdS/CFT superconductor
• Holographic Dual of BCFT
• Observation of shell effects in superconducting nanoparticles of Sn
• Towards a holographic marginal Fermi liquid
• A Holographic Josephson Junction
• A Striped Holographic Superconductor

Cited by in corpus (6)

• Numerical Methods for Finding Stationary Gravitational Solutions
• Central Charges for BCFTs and Holography
• Lattice potentials and fermions in holographic non Fermi-liquids: hybridizing local quantum criticality
• Winding up a finite size holographic superconducting ring beyond Kibble-Zurek mechanism
• Zeroth Order Phase Transition in a Holographic Superconductor with Single Impurity
• The Emergence of Superconducting Systems in Anti-de Sitter Space