Pair-Density-Wave Superconducting Order in Two-Leg Ladders

Abstract

We show using bosonization methods that extended Hubbard-Heisenberg models on two types of two leg ladders (without flux and with flux $\pi$ per plaquette) have commensurate pair-density wave (PDW) phases. In the case of the conventional (flux-less) ladder the PDW arises when certain filling fractions for which commensurability conditions are met. For the flux $\pi$ ladder the PDW phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and power-law superconducting correlations. In this phase the uniform superconducting order parameter, the $2k_F$ charge-density-wave (CDW) order parameter and the spin-density- wave Néel order parameter exhibit short range (exponentially decaying) correlations. We discuss in detail the case in which the bonding band of the ladder is half filled for which the PDW phase appears even at weak coupling. The PDW phase is shown to be dual to a uniform superconducting (SC) phase with quasi long range order. By making use of bosonization and the renormalization group we determine the phase diagram of the spin-gapped regime and study the quantum phase transition. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. We generalize the analysis to the case of other commensurate fillings of the bonding band, where we find higher order commensurate PDW states for which we determine the form of the effective bosonized field theory and discuss the phase diagram. We compare our results with recent findings in the Kondo-Heisenberg chain. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders.

21 pages, 4 figures (one with two subfigures), revised text, 5 new references; total of 49 references

References in corpus (14)

• Two-Dimensional Superconducting Fluctuations in Stripe-Ordered La(1.875)Ba(0.125)CuO(4)
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Dynamical layer decoupling in a stripe-ordered, high T_c superconductor
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• The Ground State of the Pseudogap in Cuprate Superconductors
• Evidence for unusual superconducting correlations coexisting with stripe order in La(1.875)Ba(0.125)CuO(4)
• Theory of the striped superconductor
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Pair Density Wave correlations in the Kondo-Heisenberg Model
• Diamagnetism of doped two-leg ladders and probing the nature of their commensurate phases
• Stability of RVB hole stripes in high-temperature superconductors
• Charge-Density-Wave and Superconductor Competition in Stripe Phases of High Temperature Superconductors
• Bosonization and density-matrix renormalization group studies of Fulde-Ferrell-Larkin-Ovchinnikov phase and irrational magnetization plateaus in coupled chains
• 1D-FFLO state in the absence of time-reversal symmetry breaking

Cited by in corpus (59)

• Theory of Intertwined Orders in High Temperature Superconductors
• The Hubbard Model
• The Physics of Pair Density Waves
• Topological orbital ladders
• Chiral Ladders and the Edges of Chern Insulators
• Ultracold fermions in a cavity-induced artificial magnetic field
• Ground States of a Bose-Hubbard Ladder in an Artificial Magnetic Field: Field-Theoretical Approach
• Intertwined Order in a Frustrated 4-leg $t-J$ Cylinder
• Pair-Density-Wave Superconducting States and Electronic Liquid Crystal Phases
• Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering
• Interplay between Pair Density Wave and a Nested Fermi Surface
• Pair-Density-Wave in the Strong Coupling Limit of the Holstein-Hubbard model
• Cavity-induced chiral states of fermionic quantum gases
• Pair density wave in doped three-band Hubbard model on two-leg square cylinders
• Quantum Entanglement and Thermal Reduced Density Matrices in Fermion and Spin Systems on Ladders
• Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders
• Analytical approach to a bosonic ladder subject to a magnetic field
• Umklapp scattering as the origin of $T$-linear resistivity in the normal state of high-$T_c$ cuprate superconductors
• Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides
• Pair Density Wave in the Doped $t$-$J$ Model with Ring Exchange on a Triangular Lattice
• Evidence of pair-density wave in doping Kitaev spin liquid on the honeycomb lattice
• Microscopic mechanism for fluctuating pair density wave
• Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder
• Topological Pair-Density-Wave Superconducting States
• Triplet Pair-Density Wave Superconductivity on the $\pi$-flux Square Lattice
• Quasi One Dimensional Pair Density Wave Superconducting State
• Unconventional Quantum Electrodynamics with Hofstadter-Ladder Waveguide
• Possible superconductivity with Bogoliubov Fermi surface in lightly doped Kagome U(1) spin liquid
• Singlet, Triplet and Pair Density Wave Superconductivity in the Doped Triangular-Lattice Moiré System
• Flux-Stabilized Majorana Zero Modes in Coupled One-Dimensional Fermi Wires
• Finite wave vector pairing in doped two-leg ladders
• Dissipative time evolution of a chiral state after a quantum quench
• Higgs Modes in the Pair Density Wave Superconducting State
• Exact solution for finite center-of-mass momentum Cooper pairing
• Topology and the one-dimensional Kondo-Heisenberg model
• Ground-state and spectral properties of an asymmetric Hubbard ladder
• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
• Pair-density-wave superconductivity: a microscopic model on 2D honeycomb lattice
• Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain
• Pair density wave, unconventional superconductivity, and non-Fermi liquid quantum critical phase in frustrated Kondo lattice
• Cavity-induced Fulde-Ferrell-Larkin-Ovchinnikov superfluids of ultracold Fermi gases
• Intertwined Orders and the Physics of High Temperature Superconductors
• Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order
• Pair density wave characterized by a hidden string order parameter
• Spin-orbit coupling and proximity effects in metallic carbon nanotubes
• Correlations and confinement of excitations in an asymmetric Hubbard ladder
• Optically active Higgs and Leggett modes in multiband pair-density-wave superconductors with Lifshitz invariant
• Orbital phases of fermions in an asymmetric optical ladder
• Transport Properties of Stripe-Ordered High Tc Cuprates
• Ladder-like optical conductivity in the spin-fermion model
• Confinement-Induced Enhancement of Superconductivity in a Spin-$\frac{1}{2}$ Fermion Chain Coupled to a ${\mathbb{Z}}_2$ Lattice Gauge Field
• Electronic structure of topological defects in the pair density wave superconductor
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Unconventional superfluidity in quasi-one-dimensional systems
• Weak localization and magnetoresistance in a two-leg ladder model
• Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study
• Emergent Pair Density Wave Order Across a Lifshitz Transition
• Spin-triplet pair density wave superconductors