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.
Highlights
Over the past two decades, strongly coupled systems have been investigated in the framework of the gauge/ gravity correspondence [1,2,3]
We find that holographic superconductor model represents the boundary physics beyond the conventional GL theory only containing c0, c1, and c3, FIG. 6
We study the inhomogeneous solutions which appear in the (3 þ 1)-dimensional holographic superconductor model
Summary
Over the past two decades, strongly coupled systems have been investigated in the framework of the gauge/ gravity correspondence [1,2,3]. We have shown that inhomogeneous solutions, which are not included in the standard GL model, appear in the holographic superconductors and the qualitative consistency with inhomogeneous solutions in the BCS model has been checked It implies that the holographic superconductors describe the superconducting phenomena beyond the GL theory with second order derivatives, the mass term, and the quartic potential term. Once the (metastable) inhomogeneous solutions in the presence of the current are found and shown to be consistent with the previously known solutions (such as complex kink(s) solutions or twisted kink crystal solutions) it will be more evident that the holographic superconductors describe the superconducting phenomena.
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