Introduction to Holographic Superconductors

Abstract

These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. Some familiarity with gauge/gravity duality is assumed. A list of open problems is included at the end.

34 pages, 10 figures, to appear in the proceedings of the 5th Aegean Summer School, "From Gravity to Thermal Gauge Theories: the AdS/CFT Correspondence"; v2: references added

References in corpus (28)

• Building an AdS/CFT superconductor
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Lectures on Holographic Superfluidity and Superconductivity
• Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+d
• Holographic Superconductors with Various Condensates
• Zero Temperature Limit of Holographic Superconductors
• Quantum critical transport, duality, and M-theory
• The BCS-like gap in superconductor SmFeAsO_0.85F_0.15
• Holographic model of superfluidity
• Holographic superconductivity in M-Theory
• Superconductors from Superstrings
• Ohm's Law at strong coupling: S duality and the cyclotron resonance
• A Holographic Superconductor in an External Magnetic Field
• Magnetic Brane Solutions in AdS
• Superconductivity from gauge/gravity duality with flavor
• Ground states of holographic superconductors
• Hydrodynamics of Holographic Superconductors
• Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics
• Vortex lattice for a holographic superconductor
• A Rotating Holographic Superconductor
• Flavor Superconductivity from Gauge/Gravity Duality
• Quantum critical superconductors in string theory and M-theory
• Towards a Novel no-hair Theorem for Black Holes
• Holographic Lattices, Dimers, and Glasses
• Low-temperature behavior of the Abelian Higgs model in anti-de Sitter space
• Characteristic length of an AdS/CFT superconductor
• Exact Gravity Dual of a Gapless Superconductor
• Exploring colourful holographic superconductors

Cited by in corpus (169)

• Numerical Methods for Finding Stationary Gravitational Solutions
• Introduction to Holographic Superconductor Models
• Gapped momentum states
• Einstein-Maxwell-scalar black holes: classes of solutions, dyons and extremality
• Neutron Stars in the Laboratory
• Four-Dimensional Asymptotically AdS Black Holes with Scalar Hair
• Holographic non-Fermi liquid fixed points
• Exploring New Physics Frontiers Through Numerical Relativity
• A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography
• Hot QCD Phase Diagram From Holographic Einstein-Maxwell-Dilaton Models
• On attractor mechanism of $Ad{S}_4$ black holes
• A Simple Holographic Superconductor with Momentum Relaxation
• Lifshitz Scaling Effects on Holographic Superconductors
• Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor
• Holographic Competition of Phases and Superconductivity
• On analytical study of holographic superconductors with Born-Infeld electrodynamics
• Phase Transition to a Hairy Black Hole in Asymptotically Flat Spacetime
• Analytical study on holographic superconductors for Born-Infeld electrodynamics in Gauss-Bonnet gravity with backreactions
• Competition/Enhancement of Two Probe Order Parameters in the Unbalanced Holographic Superconductor
• Analytical study of holographic superconductor in Born-Infeld electrodynamics with backreaction
• Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics
• Holographic entanglement entropy in general holographic superconductor models
• Coexistence of two vector order parameters: a holographic model for ferromagnetic superconductivity
• Holographic d-wave superconductors
• Holographic p-wave superconductor models with Weyl corrections
• Lifshitz as a deformation of Anti-de Sitter
• Holographic entanglement entropy in superconductor phase transition with dark matter sector
• Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr-Newman-de Sitter and Kerr-Newman black hole geometries
• Effects of Backreaction on Power-Maxwell Holographic Superconductors in Gauss-Bonnet Gravity
• On the thermodynamics of the black hole and hairy black hole transitions in the asymptotically flat spacetime with a box
• Planar AdS black holes in Lovelock gravity with a nonminimal scalar field
• Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point
• Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics
• A Holographic Superfluid Symphony
• Observing black holes through holographic superconductors
• AdS black holes with arbitrary scalar coupling
• Towards Complete Phase Diagrams of a Holographic P-wave Superconductor Model
• Lifshitz effects on holographic $p$-wave superfluid
• p-wave Holographic Superconductors from Born-Infeld Black Holes
• Holographic Entanglement Entropy in 2D Holographic Superconductor via $Ad{S}_3/CF{T}_2$
• Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems
• Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes
• Rotating Hairy Black Holes in AdS${}_5\times$S${}^5$
• Complexity and phase transitions in a holographic QCD model
• Holographic superconductor with momentum relaxation and Weyl correction
• Holographic entanglement entropy in insulator/superconductor transition with Born-Infeld electrodynamics
• Notes on analytical study of holographic superconductors with Lifshitz scaling in external magnetic field
• Analytical and numerical study of backreacting one-dimensional holographic superconductors in the presence of Born-Infeld electrodynamics
• Analog Systems for Gravity Duals
• Hairy Taub-NUT/Bolt-AdS solutions in Horndeski theory
• Holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg superconductor
• Homes' law in holographic superconductor with linear-$T$ resistivity
• Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum
• Studies of a general flat space/boson star transition model in a box through a language similar to holographic superconductors
• Microscopic explanation for black hole phase transitions via Ruppeiner geometry: two competing factors-the temperature and repulsive interaction among BH molecules
• Holographic conductivity of holographic superconductors with higher order corrections
• Ward Identity and Homes' Law in a Holographic Superconductor with Momentum Relaxation
• Condensate flow in holographic models in the presence of dark matter
• Analytical study on holographic superfluid in AdS soliton background
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity
• Instability and no-hair paradigm in d-dimensional charged-AdS black holes
• Holographic superconductivity from higher derivative theory
• Lifshitz from AdS at finite temperature and top down models
• An analytic study on the excited states of holographic superconductors
• A relativistic acoustic metric for planar black holes
• Holographic superconductors with Weyl corrections
• Lifshitz symmetry: Lie algebras, spacetimes and particles
• Stability of Horava-Lifshitz Black Holes in the Context of AdS/CFT
• Thermodynamics of Lovelock black holes with a nonminimal scalar field
• Dynamical gap from holography in the charged dilaton black hole
• Lifshitz scaling effects on the holographic p-wave superconductors coupled to nonlinear electrodynamics
• Holographic model of hybrid and coexisting s-wave and p-wave Josephson junction
• Holographic paramagnetism-ferromagnetism phase transition with the nonlinear electrodynamics
• Ginzburg-Landau effective action for a fluctuating holographic superconductor
• Noncommutative Extension of AdS-CFT and Holographic Superconductors
• A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric
• Holographic droplets in p-wave insulator/superconductor transition
• A general holographic insulator/superconductor model away from the probe limit
• Generalized Holographic Superconductors with Higher Derivative Couplings
• Conductivity of the holographic p-wave superconductors with higher order corrections
• Holographic superconductor in a deformed four-dimensional STU model
• One-dimensional backreacting holographic p-wave superconductors
• Holographic superconductivity in Einsteinian Cubic Gravity
• Holographic Superconductors with Logarithmic Nonlinear Electrodynamics in an External Magnetic Field
• More on Phase Transition and Renyi Entropy
• Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics
• Van der Waals-like Behaviour of Charged Black Holes and Hysteresis in the Dual QFTs
• Holographic insulator/superconductor phase transitions with excited states
• Charge density wave instability in holographic d-wave superconductor
• Holographic superconductor on a novel insulator
• Holographic entanglement entropy in two-order insulator/superconductor transitions
• Refractive index in generalized superconductors with Born-Infeld electrodynamics
• Thermodynamic geometry of holographic superconductors
• Non-relativistic Josephson Junction from Holography
• Holographic p-wave superfluid in Gauss-Bonnet gravity
• Quantum information probes of charge fractionalization in large-$N$ gauge theories
• Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant
• Finite-temperature three-point function in 2D CFT
• Excited states of holographic superconductors
• Subregion complexity in holographic thermalization with dS boundary
• Impurity effect in a holographic superconductor
• A general holographic metal/superconductor phase transition model
• Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity with backreactions
• Holographic p-wave superfluid in the AdS soliton background with $R{F}^2$ corrections
• Holographic quantum phase transitions and interacting bulk scalars
• On the Complexity of a $2+1$--dimensional Holographic Superconductor
• Holographic s-wave and p-wave Josephson junction with backreaction
• Charged scalar-tensor solitons and black holes with (approximate) Anti-de Sitter asymptotics
• Probing the Holographic Fermi Arc with scalar field: Numerical and analytical study
• Black holes with $\mathfrak{su}(N)$ gauge field hair and superconducting horizons
• Subregion complexity and confinement-deconfinement transition in a holographic QCD model
• Near-Extremal Fluid Mechanics
• Diving inside holographic metals
• Studying the holographic Fermi surface in the scalar induced anisotropic background
• Holographic superconductor from a non-commutative inspired anti-de Sitter-Einstein-Born-Infeld black hole
• Criteria For Superfluid Instabilities of Geometries with Hyperscaling Violation
• Velocity Statistics in Holographic Fluids: Magnetized Quark-Gluon Plasma and Superfluid Flow
• Soft wall model for a holographic superconductor
• Order parameter fluctuations in the holographic superconductor
• The mixed-state entanglement in holographic p-wave superconductor model
• A Holographic Model for Pseudogap in BCS-BEC Crossover (I): Pairing Fluctuations, Double-Trace Deformation and Dynamics of Bulk Bosonic Fluid
• Anisotropic Lifshitz holography in Einstein-Proca theory with stable negative mass spectrum
• Optical properties of Born-Infeld-dilaton-Lifshitz holographic superconductors
• Kink Crystalline Condensate and Multi-kink Solution in Holographic Superconductor
• Alternating current conductivity and superconducting properties of the holographic effective theory
• Gauss-Bonnet holographic superconductors in lower-dimensions
• Magnetic Phenomena in Holographic Superconductivity with Lifshitz Scaling
• Backreacting holographic superconductors from the coupling of a scalar field to the Einstein tensor
• Holographic superconductor models with $R{F}^2$ corrections
• Holographic p-wave superconductivity from higher derivative theory
• The Abrikosov Vortex in Curved Space
• Can a stationary Bianchi black brane have momentum along the direction with no translational symmetry?
• Heun's equation and analytic structure of the Gap in Holographic superconductivity
• Non-relativistic Hybrid Geometry with Gravitational Gauge-Fixing Term
• Excited states of holographic superconductors with hyperscaling violation
• Ginzburg-Landau Approach to Holographic Superconductivity
• Holographic entanglement entropy and subregion complexity for excited states of holographic superconductors
• Vanishing DC holographic conductivity from a magnetic monopole condensate
• Analysis of s-wave, p-wave and d-wave holographic superconductors in Hořava-Lifshitz gravity
• Deformations of Lifshitz holography with the Gauss-Bonnet term in ($n+1$) dimensions
• Generalized superconductors from the coupling of a scalar field to the Einstein tensor and their refractive index in massive gravity
• Small Treatise on Spin-3/2 Fields and their Dual Spectral Functions
• Understanding strongly coupling magnetism from holographic duality
• Holographic entanglement entropy and complexity for the cosmological braneworld model
• Hyperscaling violating geometry with magnetic field and DC conductivity
• Brane solutions sourced by a scalar with vanishing potential and classification of scalar branes
• Comments on Non-Fermi Liquids in the Presence of a Condensate
• Analog dual to a 2+1-dimensional holographic superconductor
• Kasner bounces and fluctuating collapse inside hairy black holes with charged matter
• Dyonic AdS_4 black hole entropy and attractors via entropy function
• Holographic Lieb lattice and gapping its Dirac band
• Information theoretic measures for Lifshitz system
• Bifundamental Superfluids from Holography
• Confinement/deconfinement transition from symmetry breaking in gauge/gravity duality
• Holographic superfluid with excited states
• Higher derivatives driven symmetry breaking in holographic superconductors
• Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order
• Evolution of holographic Fermi surface from non-minimal couplings
• Holographic mean field theory and Kondo lattice
• Hairless Black Hole by Superradiance
• p-wave holographic superconductor in scalar hairy black holes
• A holographic superconductor forced through interactions
• Metallic and antiferromagnetic fixed points from gravity
• Holographic superfluid flows with a localized repulsive potential
• Entanglement Entropy and Complexity of Multicomponent Universe from Holography
• Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes
• Effects of background rotation and anisotropy in the holographic description of type-II superconductors
• Thermodynamics of general flat space and boson star quasi-local systems