Pair Density Waves in Superconducting Vortex Halos

Abstract

We analyze the interplay between a d-wave uniform superconducting and a pair-density-wave (PDW) order parameter in the neighborhood of a vortex. We develop a phenomenological nonlinear sigma-model, solve the saddle point equation for the order parameter configuration, and compute the resulting local density of states in the vortex halo. The intertwining of the two superconducting orders leads to a charge density modulation with the same periodicity as the PDW, which is twice the period of the charge-density-wave that arises as a second-harmonic of the PDW itself. We discuss key features of the charge density modulation that can be directly compared with recent results from scanning tunneling microscopy and speculate on the role PDW order may play in the global phase diagram of the hole-doped cuprates.

arXiv comment14 pages, 10 figures; minor corrections in the numerical results

References in corpus (73)

• How to detect fluctuating order in the high-temperature superconductors
• Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O(6+x)
• Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3Oy
• Theory of Intertwined Orders in High Temperature Superconductors
• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Magnetic-field-induced charge-stripe order in the high temperature superconductor YBa2Cu3Oy
• Imaging the Effects of Individual Zinc Impurity Atoms on Superconductivity in Bi2Sr2CaCu2O8+delta
• Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states
• Ubiquitous Interplay between Charge Ordering and High-Temperature Superconductivity in Cuprates
• Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor
• Antiferromagnetic Order Induced by an Applied Magnetic Field in a High-Temperature Superconductor
• Electronic liquid crystal state in the high-temperature superconductor YBCO(6.45)
• Electron pockets in the Fermi surface of hole-doped high-Tc superconductors
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Spatially modulated "Mottness" in La2-xBaxCuO4
• Preemptive nematic order, pseudogap, and orbital order in the iron pnictides
• Three-Dimensional Charge Density Wave Order in YBa2Cu3O6.67 at High Magnetic Fields
• 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)
• Resonant X-ray Scattering Study of Charge Density Wave Correlations in YBa${}_2$Cu${}_3$O${}_{6+x}$
• 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${}_{8+x}$
• Connection between charge-density-wave order and charge transport in the cuprate superconductors
• Dynamical layer decoupling in a stripe-ordered, high T_c superconductor
• Diamagnetism and Cooper pairing above $T_c$ in cuprates
• Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
• Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates
• A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor
• Dislocations and vortices in pair density wave superconductors
• Emergence of charge order from the vortex state of a high temperature superconductor
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• X-ray diffraction observation of charge density wave order at zero magnetic field in ortho-II YBa${}_2$Cu${}_3$O${}_{6.54}$
• Thermodynamic phase diagram of static charge order in underdoped YBCO
• 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
• Quasiparticle mass enhancement approaching optimal doping in a high-Tc superconductor
• Bond order in two-dimensional metals with antiferromagnetic exchange interactions
• Landau Theory of Stripe Phases in Cuprates and Nickelates
• Evidence for unusual superconducting correlations coexisting with stripe order in La(1.875)Ba(0.125)CuO(4)
• Broken translational and rotational symmetry via charge stripe order in underdoped YBCO
• Theory of the striped superconductor
• Distinguishing Patterns of Charge Order: Stripes or Checkerboards
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Ideal charge density wave order in the high-field state of superconducting YBCO
• Quantum Oscillations in Hole-Doped Cuprates
• 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
• Topological states and braiding statistics using quantum circuits
• Probing optically silent superfluid stripes in cuprates
• Interpretation of scanning tunneling quasiparticle interference and impurity states in cuprates
• Nematicity in stripe ordered cuprates probed via resonant x-ray scattering
• Interplay between pair-density-wave and charge-density-wave orders in underdoped cuprates
• Competing Order in the Mixed State of High Temperature Superconductors
• Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)
• Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors
• Spectral signatures of modulated d-wave superconducting phases
• Vortex Lattice Melting and Hc2 in underdoped YBa2Cu3Oy
• Superconductivity with Finite-Momentum Pairing in Zero Magnetic Field
• Switching of magnetic domains reveals evidence for spatially inhomogeneous superconductivity
• The magnetic phase diagram of underdoped YBa2Cu3Oy inferred from torque magnetization and thermal conductivity
• Towards a two-dimensional superconducting state of La${}_{2-x}$Sr${}_x$CuO${}_2$ in a moderate external magnetic field
• Checkerboard order in vortex cores from pair-density-wave superconductivity
• Neutron scattering study of spin ordering and stripe pinning in superconducting La${}_{1.93}$Sr${}_{0.07}$CuO${}_4$
• Quantum Oscillations in a $\pi$-Striped Superconductor
• Breakdown of the universal Josephson relation in spin ordered cuprate superconductors
• Fluctuation diamagnetism in high temperature superconductors
• Higgs Modes in the Pair Density Wave Superconducting State
• Quantum oscillations of the specific heat in d-wave superconductors with loop current order
• The Mixed State of a $\pi$-Striped Superconductor
• Evidence for magnetic-field-induced decoupling of superconducting bilayers in La${}_{2-x}$Ca${}_{1+x}$Cu${}_2$O${}_6$
• Scattering from incipient stripe order in the high-temperature superconductor Bi2Sr2CaCu2O8+d
• Magnetic-field Induced Interconversion of Cooper Pairs and Density Wave States within Cuprate Composite Order

Cited by in corpus (53)

• The Physics of Pair Density Waves
• Magnetic-field Induced Pair Density Wave State in the Cuprate Vortex Halo
• Visualizing the Energy-gap Modulations of the Cuprate Pair Density Wave State
• Pair density wave, charge density wave and vortex in high Tc cuprates
• Unusual interplay between superconductivity and field-induced charge order in YBa2Cu3Oy
• Fractionalized pair density wave in the pseudo-gap phase of cuprate superconductors
• Interplay between Pair Density Wave and a Nested Fermi Surface
• Pair density wave order from electron repulsion
• Modeling the pseudogap metallic state in cuprates: quantum disordered pair density wave
• 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
• A DMRG study: Pair-density wave in spin-valley locked systems
• Fragile superconductivity in the presence of weakly disordered charge density waves
• Pair density wave and loop current promoted by van Hove singularities in moiré systems
• Millikelvin scanning tunneling microscope at 20/22 T with a graphite enabled stick-slip approach and an energy resolution below 8$\mu$eV: Application to conductance quantization at 20 T in single atom point contacts of Al and Au
• Incorporation of charge- and pair-density-wave states into the one-band model of d-wave superconductivity
• Maxwell-Higgs vortices with internal structure
• Two-dimensional superconducting fluctuations associated with charge density wave stripes in La${}_{1.87}$Sr${}_{0.13}$Cu${}_{0.99}$Fe${}_{0.01}$O${}_4$
• Spatially Inhomogeneous Competition between Superconductivity and the Charge Density Wave in YBa${}_2$Cu${}_3$O${}_{6.67}$
• Suppression of superfluid stiffness near Lifshitz-point instability to finite momentum superconductivity
• Unconventional quantum vortex matter state hosts quantum oscillations in the underdoped high-temperature cuprate superconductors
• Odd-frequency pair density wave correlations in underdoped cuprates
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Planar ringlike vortices
• The phase diagram of the underdoped cuprates at high magnetic field
• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
• Mass hierarchy in collective modes of pair-density-wave superconductors
• Fractionalizing a local pair density wave: a good "recipe" for opening a pseudo-gap
• Fluctuations and Higgs mechanism in Under-Doped Cuprates: a Review
• Frustrated superconductivity and sextetting order
• Strange metal from incoherent bosons
• Spatially modulated susceptibility in thin film La${}_{2-x}$Ba${}_x$CuO${}_4$
• Proposal to measure the pair field correlator of a fluctuating pair density wave
• Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory
• Incipient loop current order in the under-doped cuprate superconductors
• Intertwined Orders and the Physics of High Temperature Superconductors
• Intertwined Orders and Electronic Structure in Superconducting Vortex Halos
• Engineering Phase Competition Between Stripe Order and Superconductivity in La${}_{1.88}$Sr${}_{0.12}$CuO${}_4$
• Fulde-Ferrell-Larkin-Ovchinnikov state in strongly correlated d-wave superconductors
• Quantum oscillations from a pair-density wave
• Optically active Higgs and Leggett modes in multiband pair-density-wave superconductors with Lifshitz invariant
• Vortex structure in a $d$-wave superconductor obtained by a confinement transition from the pseudogap metal
• SU(2) Chern-Simons Theory Coupled to Competing Scalars
• Electronic structure of topological defects in the pair density wave superconductor
• Landau-Ginzburg theory of charge density wave formation accompanying lattice and electronic long-range ordering
• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• Charge modulation in the background of depleted superconductivity inside vortices
• Atomic-Scale Visualization of the Cuprate Pair Density Wave State
• Universal limiting transition temperature for the high $T_{\mathrm{c}}$ superconductors
• Anomalous Superfluid Density in Pair-Density-Wave Superconductors
• Pair density wave solution for a self-consistent model
• Observation of Subharmonic Charge-Density-Wave Correlations in La-Based Cuprates