Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves

Abstract

We analyze the leading vestigial instability due to the melting of a bidirectional pair-density-wave state in two dimensions. In a previous work by one of the authors, it was found that the interplay between pair-density-wave fluctuations with ordering momenta along the $x$ and $y$ directions can provide a strong attractive interaction for charge-$4e$ superconductivity in the $d$-wave channel. In this work, we go beyond the artificial large-$M$ mean-field theory previously adopted and compute the phase diagram by incorporating phase fluctuations of the pair-density-wave order parameters. By investigating the relevance of various topological defects, we show that the interaction in the $d$-wave channel, together with the strong anisotropy of phase fluctuations around the pair-density-wave ordering momenta, favors a vestigial charge-$4e$ superconducting order at intermediate temperatures. By contrast, a competing charge-density-wave vestigial order does not develop, due to the suppression of its stiffness.

Added references in Sections I and IV

References in corpus (59)

• Theory of Intertwined Orders in High Temperature Superconductors
• Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal
• The Physics of Pair Density Waves
• A superconductor to superfluid phase transition in liquid metallic hydrogen
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• Dislocations and vortices in pair density wave superconductors
• Charge-density-wave order with momentum $(2Q,0)$ and $(0,2Q)$ within the spin-fermion model: continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates
• Quantum liquid crystals in imbalanced Fermi gas: fluctuations and fractional vortices in Larkin-Ovchinnikov states
• Discovery of a Cooper-Pair Density Wave State in a Transition-Metal Dichalcogenide
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Fluctuations and phase transitions in Larkin-Ovchinnikov liquid crystal states of population-imbalanced resonant Fermi gas
• Detection of a Pair Density Wave State in UTe${}_2$
• Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagome superconductors
• Signatures of Chiral Superconductivity in Rhombohedral Graphene
• Pair density wave, charge density wave and vortex in high Tc cuprates
• Chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5
• Phase transitions in a three dimensional $U(1)\times U(1)$ lattice London superconductor: Metallic superfluid and charge-4e superconducting states
• Chiral excitonic order from twofold van Hove singularities in kagome metals
• Magnetic-field sensitive charge density wave orders in the superconducting phase of UTe2
• Interplay between pair-density-wave and charge-density-wave orders in underdoped cuprates
• Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems
• Smectic Pair Density Wave Order in EuRbFe4As4
• Charge-$4e$ superconductivity from multi-component nematic pairing: Application to twisted bilayer graphene
• Strong Coupling Limit of the Holstein-Hubbard Model
• Charge-4e and charge-6e flux quantization and higher charge superconductivity in kagome superconductor ring devices
• Conventional and charge six superfluids from melting hexagonal Fulde-Ferrell-Larkin-Ovchinnikov phases in two dimensions
• Charge-$4e$ superconductivity from nematic superconductors in 2D and 3D
• Interplay between Pair Density Wave and a Nested Fermi Surface
• Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks
• Pair-Density-Wave in the Strong Coupling Limit of the Holstein-Hubbard model
• Pair density wave order from electron repulsion
• Pair density wave in doped three-band Hubbard model on two-leg square cylinders
• Charge-4e supercurrent in a two-dimensional InAs-Al superconductor-semiconductor heterostructure
• Striped electronic phases in an incommensurately modulated van der Waals superlattice
• Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides
• Microscopic mechanism for fluctuating pair density wave
• Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model
• Phase coherence of pairs of Cooper pairs as quasi-long-range order of half-vortex pairs in a two-dimensional bilayer system
• Visualizing the melting of the charge density wave in UTe2 by generation of pairs of topological defects with opposite winding
• Triplet Pair-Density Wave Superconductivity on the $\pi$-flux Square Lattice
• Pair density wave and reentrant superconducting tendencies originating from valley polarization
• Sublattice modulated superconductivity in the Kagome Hubbard model
• Solvable model for a charge-$4e$ superconductor
• Cascade of vestigial orders in two-component superconductors: nematic, ferromagnetic, s-wave charge-4e, and d-wave charge-4e states
• Directly visualizing nematic superconductivity driven by the pair density wave in NbSe${}_2$
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• Vestigial singlet pairing in a fluctuating magnetic triplet superconductor: Applications to graphene moiré systems
• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
• Pair-density-wave and $s\pm \mathrm{i}d$ superconductivity in a strongly coupled, lightly doped Kondo insulator
• Theory of charge-6e condensed phase in Kagome lattice superconductors
• Charge-4$e$ Superconductivity in a Hubbard model
• Pair-density-wave superconductivity: a microscopic model on 2D honeycomb lattice
• Cooper quartets in interacting hybrid superconducting systems
• Intertwined Orders and the Physics of High Temperature Superconductors
• Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order
• Local condensation of charge-$4e$ superconductivity at a nematic domain wall
• Phase coherence of charge-$6e$ superconductors via a frustrated Kagome XY antiferromagnet
• Symmetry induced pairing in dark excitonic condensate at finite temperature
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study