Introduction to holographic superconductor models

Abstract

In the last years it has been shown that some properties of strongly coupled superconductors can be potentially described by classical general relativity living in one higher dimension, which is known as holographic superconductors. This paper gives a quick and introductory overview of some holographic superconductor models with s-wave, p-wave and d-wave orders in the literature from point of view of bottom-up, and summarizes some basic properties of these holographic models in various regimes. The competition and coexistence of these superconductivity orders are also studied in these superconductor models.

Holographic antiferromagnetic quantum criticality andAdS2scaling limit

“…One may already notice strong similarities between the GL expansion, F, and the Lagrangian of the holographic model, L. This similarity offers the suggestion that the polarization fields of the holographic model, M ð1Þμν and M ð2Þ μν , play the same role as the quadruple fields used in the GL expansion, although their spacial and matrix dimensions are different. Note that the analogous similarity also exists between the GL theory of superconductivity and the holographic superconductor model [21]. Thus, following this observation, we arrive at the remarkable conclusion that the holographic model describes an exotic magnetic state where the antiferromagnetic and quadruple ordering coexist.…”

“…In recent years, this duality has been extensively applied in condensed matter systems. Some remarkable progress has been made in this direction, including holographic superfluids (superconductors) [19,20] (for a recent review, see [21]), (non-) Fermi liquids [22][23][24] and so on. The models in the AdS/ CFT frame for ferromagnetism/paramagnetism and antiferromagnetism/paramagnetism phase transitions have also been proposed in [25,26].…”

“…Without loss of generality, we can set βðr h Þ ¼ 1 due to the linearity of the equation of β. When T N ¼ 0, the initial conditions (21) imply that…”

Refractive index in generalized superconductors with Born–Infeld electrodynamics

“…Along this line, there have been a lot of works studying various gravity models with the property of the so-called holographic superconductor, for reviews, see Refs. [9][10][11][12] and references therein.…”

Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics

“…Recently, there appeared a new direction in applying this correspondence to shed some lights in condensed matter physics, with the hope that the strongly coupled systems can be computationally tractable and conceptually more transparent (for a review, see [4][5][6] and references therein). The simplest example of the duality between the superconductor and gravity theory was first formulated in [7].…”