Elastic Theory of pinned flux lattices

Abstract

The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon =4-d)$, the functional renormalization group. We find universal logarithmic growth of displacements for $2<d<4$: $\overline{⟨u(x)-u(0){⟩}^2}\sim A_d\log |x|$ and persistence of algebraic quasi-long range translational order. When the two methods can be compared they agree within $10\%$ on the value of $A_d$. We compute the function describing the crossover between the ``random manifold'' regime and the logarithmic regime. This crossover should be observable in present decoration experiments.

12 pages, Revtex 3.0

Cited by in corpus (258)

• The Flux-Line Lattice in Superconductors
• Elastic theory of flux lattices in presence of weak disorder
• Creep and depinning in disordered media
• Phase diagrams of flux lattices with disorder
• Moving glass phase of driven lattices
• Inverse melting of the vortex lattice
• Moving glass theory of driven lattices with disorder
• Irreversibility, Mechanical Entanglement and Thermal Melting in Superconducting Vortex Crystals with Point Impurities
• Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates
• Instabilities and disorder-driven first-order transition of the vortex lattice
• Dynamic instabilities and memory effects in vortex matter
• Nonequilibrium Steady States of Driven Periodic Media
• The Ginzburg-Landau Theory of Type II superconductors in magnetic field
• Pinning and Sliding of Driven Elastic Systems: from Domain Walls to Charge Density Waves
• Topological Defects in the Random-Field XY Model and Randomly Pinned Vortex Lattices
• Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors
• Stability of Elastic Glass Phases in Random Field XY Magnets and Vortex Lattices in Type II Superconductors
• Smectic Liquid Crystals in Random Environments
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Topological Order in the Vortex Glass Phase of High-Temperature Superconductors
• Anomalous Peak Effect in CeRu2 and NbSe2 : Fracturing of a Flux Line Lattice?
• Bosonic Mott Insulator with Meissner Currents
• Disorder in quantum many-body systems
• Pinning-induced transition to disordered vortex phase in layered superconductors
• The spherical 2+p spin glass model: an analytically solvable model with a glass-to-glass transition
• Large times off-equilibrium dynamics of a particle in a random potential
• The Phase Diagram of Disordered Vortices from London Langevin Simulations
• Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles
• Pinned Wigner Crystals
• Vortex dynamics in two-dimensional systems at high driving forces
• Quasi-long-range order in nematics confined in random porous media
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• Two-stage magnetic-field-tuned superconductor-insulator transition in underdoped La${}_{2-x}$Sr${}_x$CuO${}_4$
• A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
• Dynamical response of a weakly pinned two-dimensional Wigner crystal
• Dynamical response of a pinned two-dimensional Wigner crystal
• Effects of point defects on the phase diagram of vortex states in high-Tc superconductors in B//c axis
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Creep via dynamical functional renormalization group
• Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase
• The Tribology of Sliding Elastic Media
• Replica Symmetry Breaking Instability in the 2D XY model in a random field
• Absence of Two-Dimensional Bragg Glasses
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model
• Melting of 'porous' vortex matter
• Vortices Freeze like Window Glass: the Vortex Molasses Scenario
• Nematic--to--Smectic-A Transition in Aerogel
• Driven Dynamics of Periodic Elastic Media in Disorder
• Quasi-long range order in glass states of impure liquid crystals, magnets, and superconductors
• Direct observation of the flux-line vortex glass phase in a type II superconductor
• Depinning and creep motion in glass states of flux lines
• Ground-State Roughness of the Disordered Substrate and Flux Line in d=2
• Phase Behavior of Type-II Superconductors with Quenched Point Pinning Disorder: A Phenomenological Proposal
• Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-εdimensions
• Stability of the Bragg glass phase in a layered geometry
• Peak Effect, Fishtail Effect and Plateau Effect : The Reentrant Amorphization of Vortex Matter in 2H-NbSe_2
• Disorder Driven Melting of the Vortex Line Lattice
• Ordered, disordered and coexistent stable vortex lattices in NbSe_2 single crystals
• Fate of the Peak Effect in a Type-II Superconductor: Multicriticality in the Bragg-Glass Transition
• Electrostatic Attraction of Coupled Wigner Crystals: Finite Temperature Effects
• Dynamic and Static Properties of the Randomly Pinned Planar Flux Array
• Transport properties of BSCCO crystals with and without surface barriers
• Topological Order in the Phase Diagram for High-Temperature Superconductors with Point Defects
• Peak Effect in Superconductors: Melting of Larkin Domains
• Theory of magnetic skyrmion glass
• Dynamic Melting and Decoupling of the Vortex Lattice in Layered Superconductors
• Disordered Type-II Superconductors: A Universal Phase Diagram for Low-T${}_c$ Systems
• Disorder-induced Phase Transition of Vortex Matter in MgB2
• Glassy Roughness of a Crystalline Surface Upon a Disordered Substrate
• A study of supercooling of the disordered vortex phase via minor hysteresis loops in 2H-NbSe_2
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Random Field XY Model in Three Dimensions
• Glass phase of two-dimensional triangular elastic lattices with disorder
• Fragility of the Free-Energy Landscape of a Directed Polymer in Random Media
• Multiparticle ring exchange in the Wigner glass and its possible relevance to strongly interacting two-dimensional electron systems in the presence of disorder
• Exponential number of equilibria and depinning threshold for a directed polymer in a random potential
• Velocity-force characteristics of a driven interface in a disordered medium
• Vortices in coupled planes with columnar disorder and bosonic ladders
• Elastic systems with correlated disorder: Response to tilt and application to surface growth
• Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models
• Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
• Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
• Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts
• Experimental evidence for a Bragg glass density wave phase in a transition-metal dichalcogenide
• Langevin simulations of the out-of-equilibrium dynamics of the vortex glass in high-temperature superconductors
• Effect of oxygen-doping on Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+\delta }$ vortex matter: Crossover from electromagnetic to Josephson interlayer coupling
• Effect of electron irradiation on vortex dynamics in YBa_2Cu_3O_{7-x} single crystals
• Effect of oxygen-doping on Bi-2223 vortex matter: Crossover from electromagnetic to Josephson interlayer coupling
• Statics and dynamics of elastic manifolds in media with long-range correlated disorder
• Dynamics of superconducting vortices driven by oscillatory forces in the plastic flow regime
• Stable and Metastable vortex states and the first order transition across the peak effect region in weakly pinned 2H-NbSe_2
• Smectic Liquid Crystals in an Anisotropic Random Environment
• Long-range correlated random field and random anisotropy O(N) models: A functional renormalization group study
• Quasi-Long-Range Order in Random-Anisotropy Heisenberg Models
• Amorphization of Vortex Matter and Reentrant Peak Effect in YBa${}_2$Cu${}_3$O${}_{7-\delta }$
• Phase Transitions of the Flux Line Lattice in High-Temperature Superconductors with Weak Columnar and Point Disorder
• Real-space vortex glass imaging and the vortex phase diagram of SnMo6S8
• Random-Manifold to Random-Periodic Depinning of an Elastic Interface
• Aging and memory phenomena in magnetic and transport properties of vortex matter: a brief review
• Structure of Flux Line Lattices with Weak Disorder at Large Length Scales
• Universal distribution of threshold forces at the depinning transition
• Vortex dynamics and pinning properties analysis of MgB2 bulk samples by ac susceptibility measurements
• Relaxation and Glassy Dynamics in Disordered Type-II Superconductors
• Hessian spectrum at the global minimum of high-dimensional random landscapes
• Dynamics of Particle Deposition on a Disordered Substrate: I. Near- Equilibrium Behavior
• Two new topologically ordered glass phases of smectics confined in anisotropic random media
• Zero field Wigner crystal
• Dynamic Creation and Annihilation of Metastable Vortex Phase as a Source of Excess Noise
• Chaos and plasticity in superconductor vortices: a low-dimensional dynamics
• Fragile superconductivity in the presence of weakly disordered charge density waves
• Hysteretic behavior of the vortex lattice at the onset of the second peak for HgBa${}_2$CuO${}_{4+\delta }$ superconductor
• Vortex glass transition in a random pinning model
• "Soft" Anharmonic Vortex Glass in Ferromagnetic Superconductors
• No Ending Point in The Bragg-to-Vortex Glass Phase Transition Line at Low Temperatures
• Nonuniversal Correlations and Crossover Effects in the Bragg-Glass Phase of Impure Superconductors
• Non-Hermitian Luttinger Liquids and Vortex Physics
• A variational study of the random-field XY model
• Yield Stress and Compliance in Active Cell Monolayers
• Non-Universal Quasi-Long Range Order in the Glassy Phase of Impure Superconductors
• Flux jumps, Second Magnetization Peak anomaly and the Peak Effect phenomenon in single crystals of $YN{i}_2{B}_{2}C$ and $LuN{i}_2{B}_{2}C$
• Probability Distributions of Line Lattices in Random Media from the 1D Bose Gas
• Disordered hyperuniformity in superconducting vortex lattices
• Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces
• Domain regime in two-dimensional disordered vortex matter
• Muons as Local Probes of Three-body Correlations in the Mixed State of Type-II Superconductors
• Spin and pair density wave glasses
• Ordered magnetism in the intrinsically decorated $j{}_{\mathrm{eff}}$ = $\frac{1}{2}$ $\alpha$-CoV${}_3$O${}_8$
• Off equilibrium magnetic properties in a model for vortices in superconductors
• Bragg glass signatures in Pd${}_x$ErTe${}_3$ with X-ray diffraction Temperature Clustering (X-TEC)
• Parquet Graph Resummation Method for Vortex Liquids
• Vortex creep and critical current densities in superconducting (Ba,K)Fe${}_2$As${}_2$ single crystals
• A Discotic Disguised as a Smectic: A Hybrid Columnar Bragg Glass
• Simulation of the Zero Temperature Behavior of a 3-Dimensional Elastic Medium
• Vortex-lattice melting and paramagnetic depairing in the nematic superconductor FeSe
• Relaxation dynamics of vortex lines in disordered type-II superconductors following magnetic field and temperature quenches
• Anomalous Relaxation in the XY Gauge Glass
• Disorder Driven Critical Behavior of Periodic Elastic Media in a Crystal Potential
• Critical currents at the Bragg glass to vortex glass transition
• Vortex spectroscopy in the vortex glass: A real-space numerical approach
• Topological order generated by random field in a 2D exchange model
• Interstitials, Vacancies and Dislocations in Flux-Line Lattices: A Theory of Vortex Crystals, Supersolids and Liquids
• Absence of a True Vortex-Glass Phase above the Bragg Glass Transition Line in Bi-2212
• Grain boundaries in vortex matter
• Pinning and Depinning of the Bragg Glass in a Point Disordered Model Superconductor
• Random Field and Random Anisotropy Effects in Defect-Free Three-Dimensional XY Models
• Critical Currents and Order-Disorder Phase Transition in the Vortex States of YBa2Cu4O8 with Chemically Introduced Disorder
• Chiral pair fluctuations for the inhomogeneous chiral transition
• Amorphous Vortex Glass Phase in Strongly Disordered Superconductors
• Dynamical Inequality in Growth Models
• Characterization of the (Cu,C)Ba${}_2$Ca${}_3$Cu${}_4$O${}_{11+\delta }$ single crystals grown under high pressure
• Crystal surfaces with correlated disorder: Phase transitions between roughening and superroughening
• Thermal depinning and transverse-field tilting transitions in a planar vortex array pinned by a columnar defect
• Exactly solvable spin-glass models with ferromagnetic couplings: the spherical multi-$p$-spin model in a self-induced field
• Intrinsic Percolative Superconductivity in Heavily Overdoped High Temperature Superconductors
• An elastic lattice in a random potential
• Numerical Simulations of the Random Phase Sine Gordon Model
• Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate
• Gliding dislocations in a driven vortex lattice
• Pinning of Flux Lines by Planar Defects
• Planar defects and the fate of the Bragg glass phase of type-II superconductors
• Velocity-force characteristics of an interface driven through a periodic potential
• Disordered periodic systems at the upper critical dimension
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
• Diluted Josephson-junction arrays in a magnetic field: phase coherence and vortex glass thresholds
• Structure Factor of the 3D Random Field XY Model
• Diffuse Scattering from Correlated Electron Systems
• X-ray spectrum of a pinned charge density wave
• Field Theory of Disordered Elastic Interfaces at 3-Loop Order: Critical Exponents and Scaling Functions
• Unconventional Low-Energy Excitations of Cuprate Superconductors
• Interaction effects in non-Hermitian models of vortex physics
• Universality of glass scaling in a YBa${}_2$Cu${}_3$O${}_{7-\delta }$ thin film
• Vortex phase diagram and temperature-dependent second-peak effect in overdoped Bi${}_2$Sr${}_2$CuO${}_{6+\delta }$ crystals
• Numerical studies of the phase diagram of layered type II superconductors in a magnetic field
• Evolution in the split-peak structure across the Peak Effect region in single crystals of $2H$-NbSe${}_2$
• Phase Diagram Of A Hard-sphere System In A Quenched Random Potential: A Numerical Study
• The phase diagram of high-Tc's: Influence of anisotropy and disorder
• Dimensional Crossover of Vortex Dynamics Induced by Gd Substitution on Bi2212 Single Crystals
• Ordered vs Disordered States of the Random-Field Model in Three Dimensions
• X-ray diffraction of a disordered charge density wave
• 3D XY scaling theory of the superconducting phase transition
• Dual role of an ac driving force and the underlying two distinct order-disorder transitions in the vortex phase diagram of Ca3Ir4Sn13
• Characterization of relaxation processes in interacting vortex matter through a time-dependent correlation length
• Magnetocaloric Studies of the Peak Effect in Nb
• Vortex creep at very low temperatures in single crystals of the extreme type-II superconductor Rh${}_9$In${}_4$S${}_4$
• Random field and random anisotropy O(N) spin systems with a free surface
• Random Field XY Model in Three Dimensions: The Role of Vortices
• First-order disorder-driven transition and inverse melting of the vortex lattice
• Entanglement transition of elastic lines in a strongly disordered environment
• The role of rare events in the pinning problem
• Excess of topological defects induced by confinement in vortex nanocrystals
• Non-equilibrium quasi-long-range order of driven random field O(N) model
• Suppression of the Melting Line in a Weakly Disordered Flux-line System
• Non-Gaussian effects and multifractality in the Bragg glass
• Random-strain-induced correlations in materials with intertwined nematic and magnetic orders
• Order and Creep in Flux Lattices and CDWs Pinned by Planar Defects
• Numerical Investigation of the Dynamics of a Thin Film Type II Superconductor with and without Disorder
• Dimensional reduction and its breakdown in the driven random field O(N) model
• Depinning and plasticity of driven disordered lattices
• Phase Diagram of Vortices in High-Tc Superconductors from Lattice Defect Model with Pinning
• Effect of Dilute Random Field on Continuous-Symmetry Order Parameter
• Flux line relaxation kinetics following current quenches in disordered type-II superconductors
• Smectic order, pinning, and phase transition in a smectic liquid crystal cell with a random substrate
• Unified Phase Diagram for the Three-Dimensional XY Model of a Point Disordered Type-II Superconductor
• Nonequilibrium steady states of driven magnetic flux lines in disordered type-II superconductors
• Flux-lattice melting in two-dimensional disordered superconductors
• Is there a Glass Transition in Planar Vortex Systems?
• Bragg- and Moving-glasses: a theory of disordered vortex lattices
• Nonequilibrium Kosterlitz-Thouless transition in a three-dimensional driven disordered system
• Planar pinning induced, lowering of vortex dimensionality and low field melting in a single crystal of Ba0.6K0.4Fe2As2
• Power countings versus physical scalings in disordered elastic systems - Case study of the one-dimensional interface
• Instability and Fluctuations of Flux Lines with Point Impurities in a Parallel Current
• Disorder induced transition into a one-dimensional Wigner glass
• A Model for Topological p-wave Superconducting Wires with Disorder and Interactions
• Interacting Arrays of Steps and Lines in Random Media
• Pinning and elastic properties of vortex matter in highly strained Nb${}_{75}$Zr${}_{25}$: Analogy with viscous flow of disordered solids
• Numerical study of the disorder-driven roughening transition in an elastic manifold in a periodic potential
• Melting of Flux Lines in an Alternating Parallel Current
• No quasi-long-range order in strongly disordered vortex glasses: a rigorous proof
• Magnetic relaxation in the "Bragg-glass" phase in BSCCO
• The Large N Random Phase sine-Gordon Model
• New evidence for super-roughening in crystalline surfaces with disordered substrate
• On the Abrikosov transition in disordered superconducting films
• Collective roughening of elastic lines with hard core interaction in a disordered environment
• Structure of an Elastic Lattice Pinned by Hopping Defects
• Fragile-to-strong glass transition in two-dimensional vortex liquids
• A New Phenomenology for the Disordered Mixed Phase
• Glass phases of flux lattices in layered superconductors
• Statistical, Collective and Critical Phenomena of Classical 1D Disordered Wigner Lattices
• Effect of dilute, strongly pinning impurities on charge density waves
• Reply to "Comment on "Effects of Point Defects on the Phase Diagram of Vortex States in High-Tc Superconductors in the B//c Axis""
• On mean field theory for ac-driven elastic interfaces exposed to disorder
• Anisotropy in spatial order-disorder transformations and the vortex lattice symmetry transition in $YN{i}_2{B}_{2}C$ and $LuN{i}_2{B}_{2}C$
• Perturbation theory for ac-driven interfaces in random media
• Typical versus average helicity modulus in the three-dimensional gauge glass: Understanding the vortex glass phase
• Smectics $A$ and $C$, and the Transition between them, in Uniaxial Disordered Environments
• Exact longitudinal plasmon dispersion relations for one and two dimensional Wigner crystals
• Three Magnetization Peaks in HgBa${}_2$Ca${}_2$Cu${}_3$O${}_8$ Single Crystals
• Sliding Objects with Random Friction
• Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors
• Coulombian Disorder in Periodic Systems
• Smectic vortex glass
• Phase Diagram of Vortices in High-T_c Superconductors with a Melting Line in the deep H_{c2} Region
• Near-Equilibrium Dynamics of Crystalline Interfaces with Long-Range Interactions in 1+1 Dimensional Systems
• The Smectic $A$-$C$ Phase Transition in Biaxial Disordered Environments
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Energy minima and ordering in ferromagnets with quenched randomness
• Longitudinal and transverse dissipation in a simple model for the vortex lattice with screening
• Roughening of a growing surface on a crystal with correlated disorder: influence of nonlinearity
• An Exactly Solvable Model of Randomly Pinned Charge Density Waves in Two Dimensions
• Numerical Simulations of Random Phase Sine-Gordon Model and Renormalization Group Predictions
• Impact of long-range interactions on the disordered vortex lattice
• Interplay of Quantum and Thermal Fluctuations in Two-Dimensional Randomly Pinned Charge Density Waves
• Strange metal and Fermi arcs from disordering spin stripes
• Low-temperature behavior of the $O(N)$ models below two dimensions
• Finite temperature crossovers in periodic disordered systems
• Elastic Chain in a Random Potential: Simulation of the Displacement Function $<(u(x)-u(0){)}^2>$ and Relaxation
• Monte Carlo Simulation of the Crossover from Bose Glass to Bragg Glass Phase in Layered BSCCO with Columnar Defects
• Commensurate - Incommensurate vortex phase in a nanopatterned superconductor