Twisted kink crystal in holographic superconductor

TL;DR

This paper explores complex inhomogeneous condensate structures, including twisted kink crystals, in a holographic superconductor model, revealing their properties, stability, and connections to known fermionic models.

Contribution

It introduces and analyzes twisted kink crystal condensates in holographic superconductors, linking them to solutions from the Gross-Neveu and Nambu-Jona-Lasinio models.

Findings

Identification of various inhomogeneous condensates including twisted kink crystals.

Non-monotonic phase difference behavior with respect to current.

Thermodynamic stability confirmed through free energy analysis.

Abstract

Holographic superconductor model represents various inhomogeneous solutions with homogeneous sources. In this paper, we study inhomogeneous structures in the presence of the homogeneous current and the chemical potential. We find single complex kink condensates, multiple complex kinks condensates and twisted kink crystal condensates in which both the amplitude and the phase of the order parameter modulate in space. Analyzing the gauge-invariant phase difference in the single complex kink condensates, we find the non-monotonic behaviour with respect to the current. We confirm that the multiple complex kinks condensates and the twisted kink crystal condensates are well described by the analytic solutions obtained from the Gross-Neveu model or the Nambu-Jona-Lasinio model. We also analyze the thermodynamic stability of the complex kink(s) condensates by computing the free energy. Our results imply that holographic superconductor model provides the boundary physics which is effectively represented by the Ginzburg-Landau theory with higher corrections.