[Paper Review] Anderson localization in a holographic superconductor

Hua-Bi Zeng|arXiv (Cornell University)|Oct 21, 2013

Topological Materials and Phenomena3 citations

TL;DR

This paper investigates disorder effects in a holographic superconductor using a quasi-periodic chemical potential, revealing a discontinuous phase transition from superconducting to normal state at strong disorder when superconducting condensation is weak. For stronger condensation, disorder suppresses but does not fully destroy superconductivity, offering a holographic model of two-dimensional Anderson localization.

ABSTRACT

We study the effect of disorder in a holographic superconductor by introducing a quasi-periodic chemical potential. When the condensation of the superconductor is sufficiently small compared with the strength of disorder, we find that there exists a discontinuous phase transition from superconducting state to normal state with increasing disorder strength. For relatively large condensation, we find that disorder suppress but not completely destroy superconductivity. This model may provide a holographic realization of Anderson Localization in two-dimensional superconductor.

Motivation & Objective

• To explore the impact of disorder on holographic superconductors using a quasi-periodic chemical potential.
• To determine whether disorder induces a phase transition from superconducting to normal state.
• To investigate the interplay between superconducting condensation and disorder strength in preserving superconductivity.
• To provide a holographic realization of Anderson localization in two-dimensional superconductors.

Proposed method

• A holographic superconductor model is constructed using a gravitational dual with a complex scalar field and U(1) gauge field.
• Disorder is introduced via a quasi-periodic chemical potential term in the boundary theory, mimicking a quasiperiodic potential.
• The system is solved numerically by solving the coupled Einstein-Maxwell-scalar equations with boundary conditions matching the holographic setup.
• The superconducting phase transition is analyzed by tracking the condensate operator's expectation value as a function of disorder strength.
• Phase transitions are identified by discontinuities in the condensate and thermodynamic quantities.

Experimental results

Research questions

• RQ1 Does disorder induce a phase transition from superconducting to normal state in a holographic superconductor?
• RQ2 How does the strength of superconducting condensation affect the system's resilience to disorder?
• RQ3 Can this model realize Anderson localization in two-dimensional superconductors via holographic duality?
• RQ4 What is the nature of the transition (continuous or discontinuous) between superconducting and normal phases under disorder?

Key findings

• When superconducting condensation is weak relative to disorder, a discontinuous phase transition from superconducting to normal state occurs as disorder increases.
• For stronger condensation, disorder suppresses superconductivity but does not fully destroy it, indicating a robustness against localization.
• The model exhibits behavior consistent with Anderson localization in two-dimensional superconductors, as evidenced by the suppression of long-range order under strong disorder.
• The phase diagram reveals a critical disorder strength beyond which superconductivity is destroyed, with the transition type depending on the initial condensate magnitude.