Building an AdS/BCFT Josephson junction within Horndeski gravity

TL;DR

The paper develops an AdS$_4$/BCFT$_3$ holographic model of Josephson junctions in Horndeski gravity using a single scalar field, with Neumann boundary dynamics on the BCFT boundary. By solving the probe-limit equations for a complex charged scalar and gauge field, it derives how the Horndeski parameters $\alpha$ and $\gamma$ modulate the phase difference $\Gamma$ and hence the Josephson current $J=J_{max}\sin(\Gamma)$ across constriction and SNS-like normal junctions. It provides explicit expressions for the condensate $\langle\mathcal{O}\rangle$ and the maximal current $J_{max}$, showing exponential suppression with gap width $\Sigma$ and a coherence length $\zeta=\sqrt{(\alpha+\gamma\Lambda)/(6\alpha\gamma)}$. The work highlights the physical relevance of boundary tensions and Horndeski couplings in shaping holographic superconducting transport, offering a framework to model tunable Josephson devices in AdS/BCFT.

Abstract

This work explores the constriction and normal Josephson junctions of superconductors within Horndeski's gravitational theory framework. Through a single scalar field of this theory, we provide a dual holographic description via the AdS/BCFT correspondence. We identify a critical temperature below which a charged condensate forms through a second-order phase transition in constriction and normal junctions. Our findings reveal that the condensate comprises pairs of quasiparticles. The junctions between superconductors are characterized by weak links that lead to supercurrent flow, with their magnitude determined by the phase difference between the superconductors, which is modulated by the Horndeski parameters. This supercurrent is governed by the Josephson current-phase relation, highlighting the intricate interplay between gravitational theory and superconducting phenomena.

Figures (9)

• Figure 1: AdS/CFT correspondence in the presence of boundary hypersurface $\Omega$.
• Figure 2: The figure presents the bulk manifold into the two domains $\Omega_{\pm}$. In the AdS/BCFT correspondence scheme $\mathcal{M}_{\pm}$ are asymptotically AdS spaces so that $\Omega_{\pm}=\mathcal{M}_{\pm}\cup\partial\Omega_{\pm}$ where $\partial\Omega_{\pm}$ are manifolds that satisfy $\partial\Omega_{\pm}=\mathcal{M}_{\pm}=\mathcal{P}_{\pm}$ ( left side). In the right side, we have the gluing of two Anti-de Sitter (AdS) geometries Kawamoto:2023wzjKanda:2023zse that form the normal junction. In this case, one couples two brane field theories (BFTs) via gravitational interactions in the dual holographic perspective that corresponds to the case $\mathcal{M}_{\pm}=\mathcal{P}_{\pm}$ (where in these regions the scalar field represents the brane).
• Figure 3: The figure presents the junction of two profiles with the two domains $\partial\Omega_{\pm}$ for the values $\theta=\theta'-2\pi/3$, $\Sigma=1/4$, $\Lambda=-1$, $\alpha=8/3$ with $\gamma=0$ ( solid), $\gamma=-0.1$ ( dashed), $\gamma=-0.2$ ( dot dashed), and $\gamma=-0.3$ ( thick).
• Figure 4: The holographic dual of a disk.
• Figure 5: The figure shows the behavior of the equation (\ref{['currentjsp']}). In the left side for the values $\theta=\theta'-2\pi/3$, $\Lambda=-1$, $\alpha=8/3$, $\Sigma=1/4$ with $\gamma=-0.1$ ( solid), $\gamma=-0.2$ ( dashed), $\gamma=-0.3$ ( dot dashed), and $\gamma=-0.4$ ( thick). In the right side for the values $\gamma=0.1$ ( solid), $\gamma=0.2$ ( dashed), $\gamma=0.3$ ( dot dashed), and $\gamma=0.4$ ( thick).