Holographic Superconductors (0810.1563v1)

Abstract: It has been shown that a gravitational dual to a superconductor can be obtained by coupling anti-de Sitter gravity to a Maxwell field and charged scalar. We review our earlier analysis of this theory and extend it in two directions. First, we consider all values for the charge of the scalar field. Away from the large charge limit, backreaction on the spacetime metric is important. While the qualitative behaviour of the dual superconductor is found to be similar for all charges, in the limit of arbitrarily small charge a new type of black hole instability is found. We go on to add a perpendicular magnetic field B and obtain the London equation and magnetic penetration depth. We show that these holographic superconductors are Type II, i.e., starting in a normal phase at large B and low temperatures, they develop superconducting droplets as B is reduced.

• The paper establishes a gravitational dual to superconductivity using AdS/CFT, demonstrating a robust phase transition at a critical temperature.
• It employs numerical methods to reveal conductivity gaps, diamagnetic currents, and superconducting droplet formation under varying magnetic fields.
• The study uncovers dual condensation mechanisms and backreaction effects, offering a novel approach to modeling strongly correlated systems.

Overview of Holographic Superconductors

The paper explores the formulation and analysis of holographic superconductors by utilizing the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. A gravitational dual to a superconductor is constructed by coupling a Maxwell field and a charged scalar to AdS gravity. This research addresses two primary expansions: firstly, by examining varying charge values for the scalar field, and secondly, by introducing a perpendicular magnetic field to obtain characteristics such as the London equation and magnetic penetration depth. The paper indicates that these holographic superconductors behave as Type II, forming superconducting droplets as the magnetic field intensity decreases.

Phase Transition and Conductivity

The paper establishes a comprehensive numerical analysis of the phase transition under different charges and temperatures, yielding critical insights into critical temperatures and order parameter behavior. Results indicate a robust transition at a critical temperature $T_c$ below which the charged operator condenses. Examination of the electric and thermal conductivities, along with the thermoelectric response, highlights translational invariance effects and reveals typical superconducting properties such as gap formation and infinite DC conductivity in the superconducting phase.

Implications of Backreaction and Condensate Charge

One significant aspect of the paper is the impact of backreaction when considering charges beyond the probe limit. The critical temperature $T_c$ is shown to decrease for finite charges compared to the large charge regime. Interestingly, even neutral operators can condense under certain conditions—suggesting dual mechanisms controlling the instability leading to superconductivity. Such dual mechanisms offer a novel angle compared to traditional quantum field theoretical treatments and BCS theory.

Interaction with Magnetic Fields

The introduction of magnetic fields demonstrates the system's classification as a Type II superconductor. The presence of a perpendicular magnetic field is shown to generate diamagnetic currents and predict superconducting droplets, with superconductivity persisting up to a critical field strength, $B_{c2}$, beyond which the normal state is regained. This behavior implies potential applications of the model in systems where strong magnetic response is intrinsic, possibly approximating thin-film superconductors.

Theoretical Implications and Structural Insights

From a theoretical standpoint, the paper emphasizes the natural emergence of superconductivity within the holographic framework, contrasting with traditional Landau-Ginzburg theory which relies on phenomenological parameters for instability induction. The use of AdS/CFT to model emergent phenomena such as superconductivity opens avenues for entirely new approaches to understanding quantum critical points and provides a bridge to explore strongly coupled field theories.

The research also serves as a stepping stone for embedding superconducting models into string theory, thereby obtaining fully microscopically understood phenomena, which could revolutionize how we approach condensed matter physics problems with strong interactions. This adoption of the AdS/CFT correspondence furnishes detailed predictions, illustrating the model's substantial promise in approximating certain classes of strongly correlated electronic systems, where conventional methods falter.

Future Directions

The paper lays groundwork for further exploration of superconductivity in strongly correlated and quantum critical systems via holography. Potential future research could investigate specific embedding within string theory contexts and extensions to incorporate dynamic photon interactions for a detailed description of electromagnetic effects in holographic superconductors. Moreover, exploring p-wave and d-wave superconductivity phenomena using similar methodologies could unravel new types of pairing mechanisms essential for quantum materials.

In summary, this work on holographic superconductors represents a significant step towards a better understanding of superconductivity in strongly interacting regimes, challenging traditional approaches, and showing the versatility of the AdS/CFT framework in bridging gaps across different domains in theoretical physics.