The Physics of Pair Density Waves

Abstract

We review the physics of pair density wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as charge density wave, and discuss related vestigial states that emerge as a consequence of partial meting of the PDW order. We review and critically discuss the mounting experimental evidence for such PDW order in the cuprate superconductors, the status of the theoretical microscopic description of such order, and the current debate on whether the PDW is a "mother order" or another competing order in the cuprates. In addition, we give an overview of the weak coupling version of PDW order, Fulde-Ferrell-Larkin-Ovchinnikov states, in the context of cold atom systems, unconventional superconductors, and non-centrosymmetric and Weyl materials.

arXiv comment43 pages, 16 figures, 236 references. Mildly edited final version to appear in Annual Reviews of Condensed Matter Physics (with improved figures)

References in corpus (178)

• Many-Body Physics with Ultracold Gases
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Theory of ultracold Fermi gases
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Observation of resonance condensation of fermionic atom pairs
• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Theory of Intertwined Orders in High Temperature Superconductors
• Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state
• Fermionic Superfluidity with Imbalanced Spin Populations and the Quantum Phase Transition to the Normal State
• A Four-Unit-Cell Periodic Pattern of Quasiparticle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+d
• Evidence for Superfluidity in a Resonantly Interacting Fermi Gas
• Superconductivty without inversion symmetry: MnSi versus CePt_3Si
• A `checkerboard' electronic crystal state in lightly hole-doped Ca_{2-x}Na_{x}CuO_{2}Cl_{2}
• Inhomogeneous Superconductivity in Condensed Matter and QCD
• An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates
• Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State in CeCoIn5
• Spin-Imbalance in a One-Dimensional Fermi Gas
• Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review
• Antiferromagnetic Order Induced by an Applied Magnetic Field in a High-Temperature Superconductor
• Fulde-Ferrell-Larkin-Ovchinnikov State in Heavy Fermion Superconductors
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Observation of Phase Separation in a Strongly-Interacting Imbalanced Fermi Gas
• Interior Gap Superfluidity
• Crystalline Color Superconductivity
• Resonantly-paired fermionic superfluids
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material)
• Two-Dimensional Superconducting Fluctuations in Stripe-Ordered La(1.875)Ba(0.125)CuO(4)
• BEC-BCS crossover in "magnetized" Feshbach-resonantly paired superfluids
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Detection of a Cooper-Pair Density Wave in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$
• Measurement of positive and negative scattering lengths in a Fermi gas of atoms
• Dynamical layer decoupling in a stripe-ordered, high T_c superconductor
• Diamagnetism and Cooper pairing above $T_c$ in cuprates
• Phase separation in asymmetrical fermion superfluids
• Stripe order in superconducting La(2-x)Ba(x)CuO(4) for 0.095 <= x <= 0.155
• Asymmetric Two-component Fermion Systems in Strong Coupling
• Stripe order, depinning, and fluctuations in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$ and La${}_{1.875}$Ba${}_{0.075}$Sr${}_{0.050}$CuO${}_4$
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• Calorimetric Evidence for a Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State in the Layered Organic Superconductor κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$
• Attractive Fermi gases with unequal spin populations in highly elongated traps
• The Ground State of the Pseudogap in Cuprate Superconductors
• Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates
• Dislocations and vortices in pair density wave superconductors
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• Phase diagram of a strongly interacting polarized Fermi gas in one dimension
• Fermi liquid instabilities in the spin channel
• Superconductivity and Ferromagnetism in Oxide Interface Structures: Possibility of Finite Momentum Pairing
• Imbalanced Feshbach-resonant Fermi gases
• Charge density wave fluctuations in La2-xSrxCuO4 and their competition with superconductivity
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• The Crystallography of Color Superconductivity
• Anomalous metals -- failed superconductors
• Finite temperature phase diagram of a polarised Fermi condensate
• BEC-BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids
• Superconductivity of doped Weyl semimetals: finite-momentum pairing and electronic analogues of the 3He-A phase
• Evidence for unusual superconducting correlations coexisting with stripe order in La(1.875)Ba(0.125)CuO(4)
• Epsilon expansion for a Fermi gas at infinite scattering length
• Renormalization group fixed points, universal phase diagram, and 1/N expansion for quantum liquids with interactions near the unitarity limit
• Pair Density Wave in the Pseudogap State of High Temperature Superconductors
• Quantum liquid crystals in imbalanced Fermi gas: fluctuations and fractional vortices in Larkin-Ovchinnikov states
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Theory of 2D superconductor with broken inversion symmetry
• Periodic alternating $0,\pi$-junction structures as realization of $\varphi$-Josephson junctions
• Evidence of Andreev bound states as a hallmark of the FFLO phase in $\kappa$-(BEDT-TTF)${}_2$Cu(NCS)${}_2$
• Magnetic-field Induced Pair Density Wave State in the Cuprate Vortex Halo
• Inhomogeneous LOFF phase revisited for surface superconductivity
• Superfluid stability in BEC-BCS crossover
• Superconductivity in Weyl metals
• Amperean Pairing Instability in the U(1) Spin Liquid State with Fermi Surface and Application to $\kappa -(BEDT-TTF{)}_{2}C{u}_2(CN{)}_3$
• Inhomogeneous superconducting state in quasi-one-dimensional systems
• Quasi-one-dimensional polarized Fermi superfluids
• Dispersive charge density wave excitations and temperature dependent commensuration in Bi2Sr2CaCu2O8+δ
• The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review
• Stripe order from the perspective of the Hubbard model
• Phase diagram of a cold polarized Fermi gas
• Magnetic field - temperature phase diagram of quasi-two-dimensional organic superconductor lambda-(BETS)_2 GaCl_4 studied via thermal conductivity
• Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• ARPES studies of cuprate Fermiology: superconductivity, pseudogap, and quasiparticle dynamics
• Fluctuations and phase transitions in Larkin-Ovchinnikov liquid crystal states of population-imbalanced resonant Fermi gas
• Anomalous In-Plane Anisotropy of the Onset of Superconductivity in (TMTSF)2ClO4
• Topological nodal Cooper pairing in doped Weyl metals
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Induced P-wave Superfluidity in Asymmetric Fermi Gases
• Large-N expansion for unitary superfluid Fermi gases
• Direct spectroscopic evidence for phase competition between the pseudogap and superconductivity in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Cold asymmetrical fermion superfluids
• Pair Density Wave correlations in the Kondo-Heisenberg Model
• Rotated stripe order and its competition with superconductivity in La${}_{1.88}$Sr${}_{0.12}$CuO${}_4$
• Energy gaps in the failed high-Tc superconductor La1.875Ba0.125CuO4
• Pairing in a two-component ultracold Fermi gas: phases with broken space symmetries
• Fluctuation Dominated Josephson Tunneling with a Scanning Tunneling Microscope
• Magnetic-Torque Evidence for the Fulde-Ferrell-Larkin-Ovchinnikov State for In-Plane Magnetic Fields in the Organic Superconductor k-(BEDT-TTF)2Cu(NCS)2
• Commensurate $4a_0$ period Charge Density Modulations throughout the $B{i}_{2}S{r}_{2}CaC{u}_2{O}_{8+x}$ Pseudogap Regime
• Pair density wave, charge density wave and vortex in high Tc cuprates
• Protected nodal electron pocket from multiple-Q ordering in underdoped high temperature superconductors
• Order parameter and vortices in the superconducting Q-phase of CeCoIn5
• Theory of quasi-one dimensional imbalanced Fermi gases
• On the use of STM superconducting tips at very low temperatures
• Probing optically silent superfluid stripes in cuprates
• Thermodynamic evidence for the Fulde-Ferrell-Larkin-Ovchinnikov state in the KFe2As2 superconductor
• Nature of Stripes in the Generalized t-J Model Applied to The Cuprate Superconductors
• Superconducting phase diagram and FFLO signature in $\lambda$-(BETS)${}_2$GaCl${}_4$ from rf penetration depth measurements
• Superconductivity in the doped $t$-$J$ model: results for four-leg cylinders
• Larkin-Ovchinnikov state in resonant Fermi gas
• Phase Fluctuations and Kosterlitz-Thouless Transition in Two-Dimensional Fulde-Ferrell-Larkin-Ovchinnikov Superconductors
• Microscopic study of the Fulde-Ferrell-Larkin-Ovchinnikov state in an all-organic superconductor
• Intertwined Order in a Frustrated 4-leg $t-J$ Cylinder
• Pair-Density-Wave Superconducting Order in Two-Leg Ladders
• Spin Gap in a Doped Kondo Chain
• Spectral signatures of modulated d-wave superconducting phases
• Scanning Josephson spectroscopy on the atomic scale
• Intertwined order and holography: the case of the parity breaking pair density wave
• Pair Density Waves in Superconducting Vortex Halos
• Pair-Density-Wave Superconducting States and Electronic Liquid Crystal Phases
• An Experimental and Semi-Empirical Method to Determine the Pauli-Limiting Field in Quasi 2D Superconductors as applied to $\kappa$-(BEDT-TTF)${}_2$Cu(NCS)${}_2$: Strong Evidence of a FFLO State
• Direct observation of charge order in underdoped and optimally doped Bi${}_2$(Sr,La)${}_2$CuO${}_{6+\delta }$ by resonant inelastic x-ray scattering
• Evolution from a nodeless gap to d(x2-y2) form in underdoped La(2-x)SrxCuO4
• Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials
• A Striped Holographic Superconductor
• Non-standard pairing in asymmetric trapped Fermi gases
• 1D to 3D Crossover of a Spin-Imbalanced Fermi Gas
• Finite momentum Cooper pairing in 3D topological insulator Josephson junctions
• Second-harmonic current-phase relation in Josephson junctions with ferromagnetic barriers
• Incommensurate Geometry of the Elastic Magnetic Peaks in Superconducting La1.88Sr0.12CuO4
• Transition to the Fulde-Ferrel-Larkin-Ovchinnikov phases in three dimensions : a quasiclassical investigation at low temperature with Fourier expansion
• Calorimetric Measurements of Magnetic-Field-Induced Inhomogeneous Superconductivity Above The Paramagnetic Limit
• Superconductivity with Finite-Momentum Pairing in Zero Magnetic Field
• The magnetic phase diagram of underdoped YBa2Cu3Oy inferred from torque magnetization and thermal conductivity
• Nonuniform states in noncentrosymmetric superconductors
• Towards a two-dimensional superconducting state of La${}_{2-x}$Sr${}_x$CuO${}_2$ in a moderate external magnetic field
• The equation of state of ultracold Bose and Fermi gases: a few examples
• Stability of RVB hole stripes in high-temperature superconductors
• BCS superfluidity in ultracold gases with unequal atomic populations
• Unusual interplay between superconductivity and field-induced charge order in YBa2Cu3Oy
• Pairing Theory of Striped Superconductivity
• Determination of the optical properties of La{2-x}Ba{x}CuO{4} for several dopings, including the anomalous x=1/8 phase
• Evolution of the Fermi surface in phase fluctuating d-wave superconductors
• Nodal quasi-particles and coexisting orders in striped superconductors
• Anti-phase Modulation of Electron- and Hole-like States in Vortex Core of Bi2Sr2CaCu2Ox Probed by Scanning Tunneling Spectroscopy
• Checkerboard order in vortex cores from pair-density-wave superconductivity
• Holographic Pair and Charge Density Waves
• Quantum oscillations in a biaxial pair density wave state
• Uniaxial linear resistivity of superconducting La(1.905)Ba(0.095)CuO(4) induced by an external magnetic field
• Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors
• Staggered liquid phases of the 1D Kondo-Heisenberg lattice model
• Bipartite electronic superstructures in the vortex core of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain
• Topological density-wave states in a particle-hole symmetric Weyl metal
• Pair Density Wave in the Doped $t$-$J$ Model with Ring Exchange on a Triangular Lattice
• Probing the superconducting condensate on a nanometer scale
• Quantum liquid-crystal order in resonant atomic gases
• Quantum Oscillations in a $\pi$-Striped Superconductor
• Goldstone modes in Larkin-Ovchinnikov-Fulde-Ferrell superconductors
• Tuning from failed superconductor to failed insulator with magnetic field
• Effective model for a supercurrent in a pair-density wave
• Phase transitions in superconductor liquid crystals
• Topological Pair-Density-Wave Superconducting States
• Optical Conductivity From Pair Density Waves
• Intertwined Orders in Holography: Pair and Charge Density Waves
• High-Resolution Scanning Tunneling Spectroscopy of Vortex Cores in Inhomogeneous Electronic States of Bi2Sr2CaCu2Ox
• Quasi One Dimensional Pair Density Wave Superconducting State
• Comment on "Superfluid stability in the BEC-BCS crossover"
• Evolution of superconducting correlations within magnetic-field-decoupled CuO(2) layers of La(1.905)Ba(0.095)CuO(4)
• Suppression of superfluid stiffness near Lifshitz-point instability to finite momentum superconductivity
• Quantum oscillations of the specific heat in d-wave superconductors with loop current order
• Evidence for magnetic-field-induced decoupling of superconducting bilayers in La${}_{2-x}$Ca${}_{1+x}$Cu${}_2$O${}_6$
• Recent Developments in the SO(5) Theory of High $T_c$ Superconductivity
• Scanning tunneling spectroscopy characterization of the pseudogap and the x = 1/8 anomaly in La2-xSrxCuO4 thin films
• Spatial modulations of mid-gap states in (001)La${}_{1.88}$Sr${}_{0.12}$CuO${}_4$ films: Indications for anti-phase ordering of the d-wave order parameter
• Shapiro steps in Josephson junctions with alternating critical current density
• Proposal to measure the pair field correlator of a fluctuating pair density wave
• Detection of Striped Superconductors Using Magnetic Field Modulated Josephson Effect
• Response to Comment on "Pairing and Phase Separation in a Polarized Fermi Gas"
• Interplay between pair density waves and random field disorders in the pseudogap regime of cuprate superconductors
• Signatures of pair-density wave order in phase-sensitive measurements of La${}_{2-x}$Ba${}_x$CuO${}_4$-Nb Josephson junctions and SQUIDs

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• Supercurrent-Induced Weyl Superconductivity
• Optically active Higgs and Leggett modes in multiband pair-density-wave superconductors with Lifshitz invariant
• Charge Order and Fluctuations in Bi${}_2$Sr${}_{2-x}$La${}_x$CuO${}_{6+\delta }$ Revealed by ${}^{63,65}$Cu-Nuclear Magnetic Resonance
• Gapless Higgs Mode in the Fulde-Ferrell-Larkin-Ovchinnikov State of a Superconductor
• Translation Invariant Bipolarons and Charge Density Waves in High-Temperature Superconductors
• Continuous Wigner-Mott transition at $\nu =1/5$
• Dimensional crossover on multileg attractive-$U$ Hubbard ladders
• Oxygen on-site Coulomb energy in Pr${}_{1.3-x}$La${}_{0.7}$Ce${}_x$CuO${}_4$ and Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ and its relation with Heisenberg exchange
• Paramagnetic contribution in superconductors with different-mass Cooper pairs
• Microscopic theory of pair density waves in spin-orbit coupled Kondo lattice
• Intertwined Magnetism and Superconductivity in Isolated Correlated Flat Bands
• Interplay of Zeeman field, Rashba spin-orbit interaction, and superconductivity: Transition temperature and quasiparticle excitation
• Holographic striped superconductor
• Discovery of smectic charge and pair-density-wave orders in topological monolayer 1T${}^{\prime }$-MoTe${}_2$
• Bypassing the lattice BCS-BEC crossover in strongly correlated superconductors: resilient coherence from multiorbital physics
• Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
• Numerical study of bi-layer two-orbital model for La${}_3$Ni${}_2$O${}_7$ on a plaquette ladder
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Minimal model of charge and pairing density waves in X-ray scattering experiments
• Nematic single-component superconductivity and loop-current order from pair-density wave instability
• Switchable chiral 2x2 pair density wave in pure CsV3Sb5
• Efficiency of the superconducting diode effect of pair-density-wave states in two-dimensional $d$-wave altermagnets
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
• Pairing tendencies in the doped Kitaev-Heisenberg model
• Reciprocal and nonreciprocal paraconductivity in bilayer multiphase superconductors
• Strong pair-density-wave fluctuations in an exactly solvable doped Mott insulator
• Superconducting gap modulations: are they from pair density waves or pair-breaking scattering?
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• Thermal Transport in Superconductors with coexisting Spin Density Wave Order
• Electronic structure of topological defects in the pair density wave superconductor
• Dimensional crossover of superfluid ${}^3$He in a magnetic field
• The Symmetry Principle in Condensed Matter Physics (I)
• Charge-Density-Wave State in Extremely Overdoped Cuprates Driven by Phonons
• Finite-momentum and field-induced pairings in orbital-singlet spin-triplet superconductors
• An unusual first order phase transition in a 2D superconductor
• Detecting Topological Phase Transition in Superconductor-Semiconductor Hybrids by Electronic Raman Spectroscopy
• Effective binding potential from Casimir interactions: the case of the Bose gas
• Phase-sensitive evidence for pair density waves in a kagome superconductor
• Visualization of defect-induced interband proximity effect at the nanoscale
• Gradual emergence of superconductivity in underdoped LSCO
• $O(N)$ smectic $\sigma$-model
• Pseudogap phase and fractionalization: Predictions for Josephson junction setup
• Finite-momentum pairing and superlattice superconductivity in valley-imbalanced rhombohedral graphene
• The feedback driven atomic scale Josephson microscope
• Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response
• In-plane magnetic field-induced orbital FFLO superconductivity in twisted WSe${}_2$ homobilayers
• Kondo $s$-$d$ exchange in the CuO${}_2$ plane as the long sought interaction determining $T_c$ in cuprates
• La${}_{2-x}$Ba${}_x$CuO${}_4$ as a superconducting Rosetta Stone
• Intertwined order of generalized global symmetries
• Contrasting $c$-axis and in-plane uniaxial stress effects on superconductivity and stripe order in La${}_{1.885}$Ba${}_{0.115}$CuO${}_4$
• Emergent Pair Density Wave Order Across a Lifshitz Transition
• Proximity-induced charge density wave in a metallic system
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study
• Raman Response of the Charge Density Wave in Cuprate Superconductors
• Competing pair density wave orders in the square lattice $t$-$J$ model
• $\eta$-pairing on bipartite and non-bipartite lattices
• Derivation and physical interpretation of the general solutions to the wave equations for electromagnetic potentials
• Atomic-Scale Visualization of the Cuprate Pair Density Wave State
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators
• Exploring Strongly Interacting Gapless States: Cuprates, Pair Density Waves, and Fluctuating Superconductivity
• Modulation of superconducting properties by the charge density wave at the surface of 2H-NbSe2
• Unconventional superconductivity mediated by exciton density wave fluctuations
• The two critical temperatures conundrum in La${}_{1.83}$Sr${}_{0.17}$CuO${}_4$
• Eight-fold classification of superconducting orders
• Density-wave tendency from a topological nodal-line perspective
• Enhanced pairing mechanism in Cuprate-type crystals
• Evidence of intertwined pair density and charge density wave orders in UTe2
• Superconducting States and Intertwined Orders in Metallic Altermagnets
• Superfluid dome in the spatially modulated two-dimensional XY model
• Strongly correlated model of acousticlike plasmons persisting across the phase diagram of cuprate superconductors
• Strong Fulde-Ferrell Larkin-Ovchinnikov pairing fluctuations in polarized Fermi systems
• Grassmann tensor networks
• Anomalous Superfluid Density in Pair-Density-Wave Superconductors
• Topological pair density waves in kagome superconductors
• Observation of the crossover from quantum fluxoid to half-quantum fluxoid in a chiral superconducting device
• Pseudogap in electron-doped cuprates: thermal precursor to magnetism
• Alternate cleavage structure and electronic inhomogeneity in Ca-doped YBa${}_2$Cu${}_3$O${}_{7-\delta }$
• Tunable intertwining via collective excitations
• Engineering underdoped CuO${}_2$ nanoribbons in nm-thick $a$-axis YBa${}_2$Cu${}_3$O${}_{7-\delta }$ films
• Fermion quartets on the square lattice
• Pair density wave solution for a self-consistent model
• Observation of Subharmonic Charge-Density-Wave Correlations in La-Based Cuprates
• Gap fluctuations, Cooper pairs with finite center-of-mass momentum, and suppression of superconductivity in inhomogeneous systems with dopant superpuddles agglomerates
• Novel dynamical excitations and roton-based measurement of Cooper-pair momentum in a two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov superfluid on optical lattices
• Spin-triplet pair density wave superconductors
• Renormalization formalism for superconducting phase transition with inner-Cooper-pair dynamics
• Theory of Hofstadter Superconductors
• Exact analysis of the interplay of charge order and unconventional pairings in the 2D Hatsugai-Kohmoto model
• Pair-mixing induced Time-reversal-breaking superconductivity
• Visualizing Pair-breaking Scattering Interference in Bulk FeSe