Theory of Superconductivity

1957/12/01 by J. Bardeen, Leon N. Cooper, L. N. Cooper +1 · 13,094 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic physics #BCS theory #Condensed matter physics #Coulomb #Electron #Excited state #Ground state #Pairing #Phonon #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Superconductivity #Surface and Thin Film Phenomena

paper · pdf · doi:10.1103/physrev.108.1175

published in Physical Review 108(5), 1175-1204 (American Institute of Physics)

openalex publication_date 1957/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

A theory of superconductivity is presented, based on the fact that the interaction between electrons resulting from virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy, \ensuremathℏ\ensuremathω. It is favorable to form a superconducting phase when this attractive interaction dominates the repulsive screened Coulomb interaction. The normal phase is described by the Bloch individual-particle model. The ground state of a superconductor, formed from a linear combination of normal state configurations in which electrons are virtually excited in pairs of opposite spin and momentum, is lower in energy than the normal state by amount proportional to an average (\ensuremathℏ\ensuremathω)², consistent with the isotope effect. A mutually orthogonal set of excited states in one-to-one correspondence with those of the normal phase is obtained by specifying occupation of certain Bloch states and by using the rest to form a linear combination of virtual pair configurations. The theory yields a second-order phase transition and a Meissner effect in the form suggested by Pippard. Calculated values of specific heats and penetration depths and their temperature variation are in good agreement with experiment. There is an energy gap for individual-particle excitations which decreases from about 3.5kT_c at T=0\ifmmode^∘\else\textdegree\fiK to zero at T_c. Tables of matrix elements of single-particle operators between the excited-state superconducting wave functions, useful for perturbation expansions and calculations of transition probabilities, are given.

Citations

• Der gegenwärtige Stand der Theorie der Supraleitung
• Superconductivity of Isotopes of Mercury
• Ein neuer Effekt bei Eintritt der Supraleitf�higkeit
• Isotope Effect in the Superconductivity of Mercury

Cited by

• Calculation of the Superconducting State Parameters with Retarded Electron-Phonon Interaction
• The Electron-Phonon Interaction in Normal Metals
• Quasinormal modes of black holes: From astrophysics to string theory
• Superconducting phases off-electron compounds
• Neutron Stars—Cooling and Transport
• Quantum algorithms for scientific computing
• Ring currents
• Phenomenological theory of unconventional superconductivity
• Possible phase transition in plasma mirror modes
• Magnetic Penetration Depth in a Superconductor
• A splitting integrator for the BCS equations of superconductivity
• Multicomponent Superfluids and Superconductors in Dense Nuclear and Quark Matter
• Large Language Models for Superconductor Discovery
• Self-consistent solution of Eliashberg equations for metal hydride superconductors
• Atomic scattering from Bose-Einstein condensates
• Proximity Effects in Ferromagnet/Superconductor Heterostructures
• Superconductivity with excitons and polaritons
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Lipschitz continuity and monotone decreasingness of the solution to the BCS gap equation for superconductivity
• Nonlinearities in Microwave Superconductivity
• A walk in the statistical mechanical formulation of neural networks
• The effect of nonlocal confining kernels on magnetic chiral condensates
• Higgs Mechanism in the Standard Model and a Possibility of its Direct Physical Realization
• Universality of rotons in liquids, generalized superfluidity criterion and helons in helium II
• Optical coherence: A convenient fiction
• Quantum-Critical Spin-Density Waves in Iron-Selenide High-Tc Superconductors
• Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices
• Magnetic-interaction-induced superconductivity in metals
• Black-Hole Solutions to Einstein's Equations in the Presence of Matter and Modifications of Gravitation in Extra Dimensions
• Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. I. Algebraic Formulation
• Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. II. Diagrammatic Formulation
• Superconductivity up to 243 K in the yttrium-hydrogen system under high pressure
• A Perspective on Conventional High-Temperature Superconductors at High Pressure: Methods and Materials
• Some contributions to many-body quantum mathematics
• Quasi-Particles and Gauge Invariance in the Theory of Superconductivity
• Theoretical progress and material studies of heavy fermion superconductors
• Existence of Long-Range Order in One and Two Dimensions
• The description of superconductivity in terms of dielectric response function
• Dynamical Mass Generations and Collective Excitations in the (Supersymmetric-)Nambu-Jona-Lasinio Model and a Gauge Theory with Left-Right-Asymmetric Majorana Mass Terms
• Hypothesis on the nature and origin of cold dark matter
• Типы и синдромы (фрагменты из «Авторитарной личности»)
• BCS-BEC crossover in quantum confined superconductors
• Gedanken Worlds without Higgs: QCD-Induced Electroweak Symmetry Breaking
• Cooper pairing with finite angular momentum: BCS versus Bose limits
• Prospecting for the superfluid transition in electron-hole coupled quantum wells using Coulomb drag
• Study of Bose-Einstein Condensation Process and Superconductivity
• Broad vs. narrow Fano-Feshbach resonances in the BCS-BEC crossover with trapped Fermi atoms
• A Simple Derivation of Josephson Formulae in Superconductivity
• Is electromagnetic gauge invariance spontaneously violated in superconductors?
• Analytical relationship for the cranking inertia
• Conductance enhancement in quantum-point-contact semiconductor-superconductor devices
• BEC, BCS and BCS-Bose Crossover Theories in Superconductors and Superfluids
• Revisiting the concept of chemical potential in classical and quantum gases: A perspective from Equilibrium Statistical Mechanics
• Should it really be that hard to model the chirality induced spin selectivity effect?
• Soliton-like solution in quantum electrodynamics
• S-Wave Superconductivity in Anisotropic Holographic Insulators
• To Phenomenological Theory of Superconductivity. Superconductivity - not fading electrical current in dissipative medium
• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
• Pressure dependence of structural, elastic, electronic, thermodynamic, and optical properties of van der Waals-type NaSn2P2 pnictide superconductor: insights from DFT study
• The physics of quantum 2.0: challenges in understanding quantum matter
• A mathematical derivation of zero-temperature 2D superconductivity from microscopic Bardeen-Cooper-Schrieffer model
• Bardeen-Cooper-Schrieffer Theory of Superconductivity in the Case of Overlapping Bands
• What causes the variation in superconducting properties of UTe₂?
• Introduction to High-Resolution Inelastic X-Ray Scattering
• Phonons in nontransition metals
• Eponyms in Science: how long can they get?
• Generalized Uncertainty Principle and Quantum Gravity Phenomenology
• Nanofabrication of high transition temperature superconductive electronics with focused helium ion irradiation
• Properties of boson-exchange superconductors
• The superfluid as a source of all interactions
• Beyond on-site Hubbard interaction in charge dynamics of cuprate superconductors
• Anomalous high-temperature superconductivity in YH₆
• Extended Fokker Planck model: properties and solutions
• Free energy and criticality in the nucleon pair breaking process
• Particle Correlations in Bose-Einstein Condensates
• Fractional generalization of the Ginzburg–Landau equation: an unconventional approach to critical phenomena in complex media
• 1S0 Pairing Gaps, Chemical Potentials and Entrainment Matrix in Superfluid Neutron-Star Cores for the Brussels–Montreal Functionals
• Linear response of a superfluid Fermi gas inside its pair-breaking continuum
• Numerical Simulation of the Coupling between Split-Ring Resonators and Antiferromagnetic Magnons
• The order parameter of high temperature superconductors, as measured by Andreev Saint-James reflection, Raman and neutron scattering
• Hot Hydride Superconductivity above 550 K
• Compositeness, Bargmann-Wigner solutions within a U(1)-interaction quantum-field-theory expansion, and charge
• Superconducting quantum interference device instruments and applications
• Observation of Yu-Shiba-Rusinov states in superconducting graphene
• Sum rules and energy scales in the high-temperature superconductorYBa2Cu3O6+x
• Broken Inversion Symmetry in Van Der Waals Topological Ferromagnetic Metal Iron Germanium Telluride
• Linear Scaling Quantum Transport Methodologies
• Superconducting transition temperatures of the elements related to elastic constants
• Functional renormalization for the BCS-BEC crossover
• The fundamental obscurity in quantum mechanics. Could the problem be considered universal?
• The education of Walter Kohn and the creation of density functional theory
• A Rigorous Demonstration of Superconductivity in a Repulsive Hubbard Model
• Richardson-Gaudin states of non-zero seniority II: Single-reference treatment of strong correlation
• Exotic and conventional superconductivity in a Dirac supersymmetric scheme
• Superconducting phase in the BCS model with imaginary magnetic field. II. Multi-scale infrared analysis
• Phase transition in black holes
• A new model and its physics
• Competition Between Induced Symmetry Breaking, Cooper Pairing and Chiral Condensate at Finite Density
• The BCS Gap Equation on a Banach Space Consisting of Functions both of the Temperature and of the Wave Vector
• A new representation for the Landau-de Gennes energy of nematic liquid crystals
• Superconducting phase in the BCS model with imaginary magnetic field. III. Non-vanishing free dispersion relations
• Theory of Correlated Pairs of Electrons Oscillating in Resonant Quantum States to Reach the Critical Temperature in a Metal
• Superconductivity in SrB3C3 clathrate
• Berry connection from many-body wave functions and superconductivity: Circuit quantization for superconducting qubits and absence of a dissipative quantum phase transition in Josephson junctions
• Possible Graviton Transitions and Gaser Action in High-Tc Superconductors
• Validity of many-body approximation methods for a solvable model
• Generator coordinate method applied to nuclei in the transition region
• Superconductivity versus magnetism in the palladium 'ides': Pd_1-c(H/D/T)_c
• Spin-Generator Coordinate Method for Electronic Structure
• The Uniform Electron Gas at Warm Dense Matter Conditions
• Theoretical investigation of high-temperature superconductivity
• Higher-Order Fermion Interactions in Effective Field Theories for Phase Transitions
• Pairing interaction and two-nucleon transfer reactions
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Probable observation of the nuclear Cooper pair mean square radius in superfluid nuclei
• Phonon mode splitting and phonon anomaly in multiband electron systems
• Cross-over from BCS superconductivity to Bose condensation and High-Tc Superconductors
• Superconducting phase in the BCS model with imaginary magnetic field
• Minimal Model for an Unbalanced Holographic Superconductor
• Motion of particles on a Four-Dimensional Asymptotically AdS Black Hole with Scalar Hair
• Decoherence, Control, and Symmetry in Quantum Computers
• Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic broken-symmetry random-phase approximation
• Intertwined Orders and the Physics of High Temperature Superconductors
• Thermodynamics and the virial expansion for trapped fluids in arbitrary external potentials
• Electromagnetic Proximity Effect: Superconducting Magnonics and Beyond
• A new first-principles calculation of field-dependent RF surface impedance of BCS superconductor and application to SRF cavities
• d-Mott Phases in One and Two Dimensions
• Superconductivity at very strong coupling
• Transport Studies of Lattice Bosons: Paradigms for Fluctuating Superconductivity
• A study of potential non-relativistic QED pairs in the Keldysh-Schwinger formalism
• BCS and BEC Finally Unified: A Brief Review
• Aspects of quantum gravity
• Two-dimensional Hubbard-Holstein bipolaron
• Low-temperature elastic moduli and dilational and shear internal frictions of superconducting ceramicGdBa2Cu3O7−δ
• The Functional Schrödinger Picture Approach to Many-Particle Systems
• Spontaneous breaking of Lorentz invariance
• Berry connection from many-body wave functions and superconductivity: Calculations by the particle number conserving Bogoliubov-de Gennes equations
• Conserving and gapless approximations for the composite bosons in terms of the constituent fermions
• Bose-Einstein condensation for general dispersion relations
• Photoacoustic wave propagating from normal into superconductive phases in Pb single crystals
• On Superfluid Phases of Cold Deconfined QCD Matter at Moderate Baryon Density
• Analytical approach to phase transitions in rotating and non-rotating 2D holographic superconductors
• Quantum Turbulence
• London penetration depth measurements using tunnel diode resonators
• Highly accurate ab-initio thermochemistry via real-space quantum Monte Carlo: Benzene
• Design of an experiment to study the motion of nano-liquid helium droplets
• Unconventional superfluidity in Bose-Fermi Mixtures
• Unconventional Superconductivity and Magnetism in Lanthanide and Actinide Intermetallic Compounds
• On the energy-momentum spectrum of a homogeneous Fermi gas
• Disentanglement-induced superconductivity
• Quantum confinement theory of ultra-thin films: electronic, thermal and superconducting properties
• Recent advances in the internal functionalization of carbon nanotubes: synthesis, optical, and magnetic resonance studies
• On Ultrafast Spin Dynamics: Spin Dependent Fast Response of Hot Electrons, of Band--Structure
• Superfluidity and vortices: A Ginzburg-Landau model
• Something about the Mechanism of Induction Phenomena: The forgotten work of Berta de Haas-Lorentz on diamagnetism in superconductors
• A possible mechanism of the lifetime effects of electron pairs at the SrTiO₃/LaTiO₃ interface
• Time Variation of the Ginzburg-Landau Order Parameter
• Charge transfer excitations and superconductivity in “ionic” metals
• Fermionic functional renormalization-group for first-order phase transitions: a mean-field model
• Stressed pairing in conventional color superconductors is unavoidable
• Rigidity of crystalline color superconducting quark matter
• Bulk viscosity in 2SC quark matter
• Disorder Operators and their Descendants
• Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field
• 2D multipartite valence bond states in quantum anti-ferromagnets
• Classical and quantum mechanics of the damped harmonic oscillator
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Electronic crystals: an experimental overview
• Detection of Quantum Critical Points by a Probe Qubit
• Dimensionality-induced entanglement in macroscopic dimer systems
• Dynamical mean-field equations for strongly interacting fermionic atoms in arbitrary potential traps
• Structure of quantum correlations in momentum space and off-diagonal long-range order inηpairing and BCS states
• Polarization-dependent resonant inelastic X-ray scattering study at the Cu L and O K -edges of YBa 2 Cu 3 O 7-x
• Dynamical chiral symmetry breaking and superconductivity in the supersymmetric Nambu–Jona-Lasinio model at finite temperature and density
• Negative-parity states and β decays in odd Ho and Dy nuclei withA=151,153
• Parity effect in a small superconducting grain: A rigorous result
• Out-of-plane impurities induce deviations from the monotonicd-wave superconducting gap of cuprate superconductors
• Role of confined phonons in thin-film superconductivity
• Coexistence of BCS- and BEC-Like Pair Structures in Halo Nuclei
• Critical temperature for kaon condensation in color-flavor-locked quark matter
• Renormalization group analysis of a Gürsey-model-inspired field theory. II
• Quasiparticle response of superconducting aluminum to electromagnetic radiation
• Absence of an isotope effect in the magnetic resonance in high-Tcsuperconductors
• Experimental realization of BCS-BEC crossover physics with a Fermi gas of atoms
• Induced entanglement enhanced by quantum criticality
• Similarity renormalization of the electron‐phonon coupling
• Spatial Structure of the Cooper Pair
• Scattering resonances in a degenerate Fermi gas
• Isotopic shift in angle-resolved photoemission spectra of Bi2Sr2CaCu2O8 due to quadratic electron–phonon coupling
• Discovery of an excited pair state in superfluid 3He
• Dynamical mean-field theory and numerical renormalization group study of superconductivity in the attractive Hubbard model
• Resonance Superfluidity in a Quantum Degenerate Fermi Gas
• Cold numbers: Superconducting supercomputers and presumptive anomaly
• Thermal conductivity of single-crystallineMgB2
• Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition
• Extraction of the electron self-energy from angle-resolved photoemission data: Application toBi2Sr2CaCu2O8+x
• Kondo effect and Josephson current through a quantum dot between two superconductors
• Suppression of the “Quasiclassical” Proximity Gap in Correlated-Metal–Superconductor Structures
• Solution of the Dyson equation for nucleons in the superfluid phase
• From the Bose-Einstein to fermion condensation
• Determination of the Superfluid Gap in Atomic Fermi Gases by Quasiparticle Spectroscopy
• Experimental evidence for Fröhlich superconductivity in high magnetic fields
• Momentum distribution curves in the superconducting state
• Single superconducting energy scale in electron-doped cuprate superconductor Pr₂-xCexCuO₄
• Magnetic flux periodicity of h/e in superconducting loops
• Resonance superfluidity: Renormalization of resonance scattering theory
• Breakdown of Fermi-liquid theory in a copper-oxide superconductor
• Microscopic Electron Models with Exact SO(5) Symmetry
• BCS-BEC crossover of neutron pairs in symmetric and asymmetric nuclear matter
• Generalized statistics and high-Tc superconductivity
• Effect of Magnetisation of Bulk Superconductors on Permanent Magnets for Reversible Braking Applications
• Nuclear level densities and γ-ray strength functions inSc<mml:mprescripts/><mml:none/>44,45
• A superconductor with 4-fermion attraction weakly perturbed by magnetic impurities
• Particle-number conservation in static-path approximation for thermal superfluid systems
• Evolution from BCS superconductivity to Bose-Einstein condensation: Current correlation function in the broken-symmetry phase
• BCS and attractive Hubbard model comparative study
• Approximate particle number projection for rotating nuclei
• The nature of the chemical bond in metals, alloys, and intermetallic compounds according to Linus Pauling
• Magnetization of Small Lead Particles
• Methods of quasiclassical Green’s functions in the theory of transport phenomena in superconducting mesoscopic structures
• SO(5)theory of antiferromagnetism and superconductivity
• Doping and energy dependent microwave conductivity of kinetic energy driven superconductors with extended impurities
• BCS theory ofq-deformed nucleon pairs:qBCS
• Minimally self-consistent T-matrix approximation to describe the low-temperature properties of the Hubbard model in the atomic limit
• Conceptual Developments of 20th Century Field Theories
• Spectrum and screening cloud in the central spin model
• A new basis set for the description of electrons in superconductors
• Magnetotransport near a quantum critical point in a simple metal
• Exact Electron-Pairing Ground States of Tight-Binding Models with Local Attractive Interactions
• Entanglement of electron spins in superconductors
• Exactly solvable discrete BCS-type Hamiltonians and the six-vertex model
• On the exactly solvable pairing models for bosons
• Strongly nonlinear magnetization above T c in Bi 2 Sr 2 CaCu 2 O 8 + δ
• Spectrum and completeness of the three-state superintegrable chiral Potts model
• Superconducting fluctuations in small grains – The Universal Hamiltonian and the reduced BCS model
• Effects of color superconductivity on the nucleation of quark matter in neutron stars
• Triplet pairing of neutrons in β-stable neutron star matter
• Phonon Dispersion and Electron-Phonon Coupling inMgB2andAlB2
• Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices
• Exact results on superconductivity due to interband coupling
• Isotope effect in superconducting gallium
• Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity
• Belief in thermodynamics has provoked false thermodynamics of superconductors
• Dynamical and invariant supersymmetry in the fermion pairing problem
• MECHANISM OF HIGH-Tc SUPERCONDUCTIVITY BASED MAINLY ON TUNNELING MEASUREMENTS IN CUPRATES
• Pairing and molecule formation along the BEC-BCS crossover for finite range potentials
• The BCS Functional for General Pair Interactions
• Fulde-Ferrell-Larkin-Ovchinnikov state in the one-dimensional attractive Hubbard model and its fingerprint in spatial noise correlations
• Kohn anomaly and interplay of electron-electron and electron-phonon interactions in epitaxial graphene
• Non-Hermitian Hamiltonians of Lie algebraic type
• Exactly-solvable models derived from a generalized Gaudin algebra
• Two gaps make a high-temperature superconductor?
• Double-gap superconducting proximity effect in armchair carbon nanotubes
• Arrays of Cooper pair boxes coupled to a superconducting reservoir: superradiance and revival
• Ground-State Entanglement of the BCS Model
• COOPER PAIRS AS BOSONS
• Microscopic study of inhomogeneous superconductors
• BCS approximation to the effective vector vertex of superfluid fermions
• Macroscopic Entanglement and Phase Transitions
• On the magnetic-field dependence of the longitudinal ultrasonic attenuation in a type-II superconductor
• Parity Dependence of Nuclear Level Densities
• Crystallography of three-flavor quark matter
• Kohn-Luttinger effect in gauge theories
• Weak-coupling treatment of electronic (anti-)ferroelectricity in the extended Falicov-Kimball model
• BCS and generalized BCS superconductivity in relativistic quantum field theory: Formulation
• Weak-Coupling Theory for Multiband Superconductivity Induced by Jahn–Teller Phonons
• Generalized Hartree-Fock theory and the Hubbard model
• Applications of the Octet Baryon Quark-Meson Coupling Model to Hybrid Stars
• Stochastic -theory in the strong coupling limit
• Energy Spectrum Symmetry of Heisenberg Model in Fock Space
• Cooper pairing with finite angular momentum via a central attraction: From the BCS to the Bose limits
• Isotope effect in the presence of magnetic and nonmagnetic impurities
• Level densities and thermodynamical quantities of heatedMo<mml:mprescripts/><mml:none/>93−98isotopes
• Nucleation of superconductivity and vortex matter in superconductor–ferromagnet hybrids
• Interplay of pairing and multipole interactions in a simple model
• Strong-coupling expansion for the pairing Hamiltonian for small superconducting metallic grains
• Tuning a Josephson junction through a quantum critical point
• Compensation of magnetic impurity effect in superconductors by radiation damage
• Electrostatic potential in a superconductor
• Numerical portrait of a relativistic BCS gapped superfluid
• Nature of the superconductor–insulator transition in disordered superconductors
• Control of the geometric phase and pseudospin dynamics on coupled Bose-Einstein condensates
• Superfluid density of high-Tc cuprate systems: implication on condensation mechanisms, heterogeneity and phase diagram
• Evidence for ubiquitous strong electron–phonon coupling in high-temperature superconductors
• Quasiparticle scattering in superconductors
• Dirac and Weyl Fermions in 3D Hopf-linked Honeycomb Lattices: Hopfene
• Superconductivity in Boron
• Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder
• Holographic conductivity of zero temperature superconductors
• The Riemann zeros and the cyclic renormalization group
• Properties of ferromagnetic superconductors
• Hall effect in heavy fermion metals
• A MODEL WITH INTERACTING COMPOSITES
• Condensate fraction of a Fermi gas in the BCS-BEC crossover
• Hyper-entanglement in a relativistic two-body system
• Electrodynamics of Perfect Conductors
• The oxygen isotope effect on critical temperature in superconducting copper oxides
• Bose-Einstein Condensation of Molecules
• Improved Nb SIS devices for heterodyne mixers between 700 GHz and 1.3 THz with NbTiN transmission lines using a normal metal energy relaxation layer
• Mixing of dx2−y2 and dxy superconducting states for different filling and temperature
• Dynamical symmetry breaking in spaces with a constant negative curvature
• Unconventional Superconductivity and Electron Correlations in the Cobalt OxyhydrateNa0.35CoO2·yH2Ofrom Nuclear Quadrupole Resonance
• BCS-BEC crossover in a relativistic boson-fermion model beyond mean field approximation
• Amplitude Fluctuations Driven by the Density of Electron Pairs within Nanosize Granular Structures inside Strongly Disordered Superconductors: Evidence for a Shell-Like Effect
• Breached pairing superfluidity at finite temperature and density
• Paired fermionic superfluids with s- and p-wave interactions
• d-wave superconductivity from electron-phonon interactions
• Emergent Models for Gravity: an Overview of Microscopic Models
• Electromagnetic Meissner Effect in Spin-One Color Superconductors
• Introduction to Many-Body Physics
• Enhancement of superconducting transition temperature by the additional second neighbor hopping in the model
• Quantum oscillations from Fermi arcs
• Effective contact pairing forces from realistic calculations in infinite homogeneous nuclear matter
• Superconductivity in single crystals of LaFePO
• Two-component few-fermion mixtures in a one-dimensional trap: Numerical versus analytical approach
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• Properties of superconductivity on a density wave background with small ungapped Fermi surface parts
• Bosonization and even Grassmann variables
• Wave-packet dynamics of Bogoliubov quasiparticles: Quantum metric effects
• Superconducting quark matter in SU (2) colour group
• Meissner effect in a charged Bose gas with short-range repulsion
• Generating functional approach for spontaneous coherence in semiconductor electron-hole-photon systems
• Mesoscopic phase separation in anisotropic superconductors
• Superconductivity in the elements, alloys and simple compounds
• Helium Group Gases
• Superconductivity: From Physics to Technology
• Magnetic Catalysis: A Review
• Statistical pairing fluctuation and phase transition in 94Mo
• The solution to the BCS gap equation and the second-order phase transition in superconductivity
• Angle-resolved photoemission studies of the cuprate superconductors
• Electronic structure of quantum materials studied by angle-resolved photoemission spectroscopy
• Ground-State Energy of a Finite System of Charged Particles
• Long-range proximity effect in La2/3Ca1/3MnO3/(100)YBa2Cu3O7−δferromagnet/superconductor bilayers: Evidence for induced triplet superconductivity in the ferromagnet
• Coupling of a high-energy excitation to superconducting quasiparticles in a cuprate from coherent charge fluctuation spectroscopy
• Number theory, periodic orbits, and superconductivity in nanocubes
• Accelerating the search for superconductors using machine learning
• The Anderson-Mott transition
• Tunable Electron-Electron Interactions inLaAlO3/SrTiO3Nanostructures
• Gravitomagnetism and magnetic permeability in superconductors
• Quantum entanglement and order parameter in a paired finite Fermi system
• Band-edge superconductivity
• Antiferromagnetism and singlet formation in underdoped high-Tccuprates: Implications for superconducting pairing
• Effects of thermal shape fluctuations and pairing fluctuations on the giant dipole resonance in warm nuclei
• The Challenge of Unconventional Superconductivity
• Heat transfer coefficient saturation in superconducting Nb tunnel junctions contacted to a NbTiN circuit and an Au energy relaxation layer
• Evidence of a magnetic Bose glass in(CH3)2CHNH3Cu(Cl0.95Br0.05)3from neutron diffraction
• Introduction to holographic superconductor models
• Bosonic particle-correlated states: A nonperturbative treatment beyond mean field
• Nonstrange hybrid compact stars with color superconducting matter
• Variation after particle-number projection for the Hartree-Fock-Bogoliubov method with the Skyrme energy density functional
• Breaking of nucleon Cooper pairs at finite temperature inMo<mml:mprescripts/><mml:none/>93−98
• Phase diagram and entanglement of the Ising model with Dzyaloshinskii-Moriya interaction
• New perspective on the scalar meson puzzle, from spontaneous chiral symmetry breaking beyond BCS
• Optical properties of the iron arsenic superconductorBaFe1.85Co0.15As2
• Discovery of the acoustic Faraday effect in superfluid 3He-B
• Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates
• Vortices in chiral, spin-triplet superconductors and superfluids
• Normal and anomalous solitons in the theory of dynamical Cooper pairing
• High-temperature superconductivity in hydrides: experimental evidence and details
• Anomalous behavior in high-pressure carbonaceous sulfur hydride
• Magnetic-field oscillations of the critical temperature in ultraclean, two-dimensional Type-I superconductor
• Bogoliubov transformations and fermion condensates in lattice field theories
• Analytical study on holographic superconductors for Born-Infeld electrodynamics in Gauss-Bonnet gravity with backreactions
• Conductivity of Paired Composite Fermions
• Bosonic Mott Insulator with Meissner Currents
• Bosons in high-temperature superconductors: an experimental survey
• Thermal equilibrium of two quantum Brownian particles
• First results of a cryogenic optical photon-counting imaging spectrometer using a DROID array
• Direct search for a ferromagnetic phase in a heavily overdoped nonsuperconducting copper oxide
• Signature of a Pairing Transition in the Heat Capacity of Finite Nuclei
• QUANTUM MONTE CARLO METHODS FOR NUCLEI AT FINITE TEMPERATURE
• ELECTRON–ELECTRON INTERACTION EFFECTS ON TRANSPORT THROUGH MESOSCOPIC SUPERCONDUCTING HYBRID JUNCTIONS
• Direct Observation of Nonlocal Effects in a Superconductor
• The BCS–Bose crossover theory
• Super-weakly coupled superconductivity in ultrathin superconductor–normal-metal bilayers
• Magnetic field evolution in superconducting neutron stars
• Thermodynamic Properties in Triangular-Lattice Superconductors
• Low-Energy Electrodynamics of Superconducting Diamond
• Weak Superconducting Pairing and a Single Isotropic Energy Gap in Stoichiometric LiFeAs
• The high-pressure superconductivity in SiH4: The strong-coupling approach
• Cooper pair transfer in nuclei
• Gap solitons in superfluid boson-fermion mixtures
• Einstein and Debye temperatures, electron-phonon coupling constant and a probable mechanism for ambient-pressure room-temperature superconductivity in intercalated graphite
• Understanding low-temperature bulk transport in samarium hexaboride without relying on in-gap bulk states
• Fixed-NSuperconductivity: The Crossover from the Bulk to the Few-Electron Limit
• Ba2phenanthrene is the main component in the Ba-doped phenanthrene superconductor
• Ghost condensation on the lattice
• Mean field calculation of thermal properties of simple nucleon matter on a lattice
• Slightly Imbalanced System of a Few Attractive Fermions in a One-Dimensional Harmonic Trap
• Beyond the Unified Model
• Condensate Formation in Collisionless Plasma
• The characterization of high-pressure superconducting state in compound: The strong-coupling description
• A lower bound for the BCS functional with boundary conditions at infinity
• Semiclassical Theory of Bardeen-Cooper-Schrieffer Pairing-Gap Fluctuations
• Finding symmetry breaking order parameters with Euclidean neural networks
• Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson–Fermion model
• Magnetic-field resilience of 3D transmons with thin-film Al/AlO_x/Al Josephson junctions approaching 1 T
• Quantum simulations with cold trapped ions
• Gaussian operator bases for correlated fermions
• Unconventional High-Energy-State Contribution to the Cooper Pairing in the Underdoped Copper-Oxide SuperconductorHgBa2Ca2Cu3O8+δ
• Spin-flip lifetimes in superconducting atom chips: Bardeen-Cooper-Schrieffer versus Eliashberg theory
• Single flux transistor: The controllable interplay of coherent quantum phase slip and flux quantization
• ASSESSING THE EFFECT OF COULOMB REPULSION ASYMMETRY ON ELECTRON PAIRING
• Electrothermal model of kinetic inductance detectors
• Quantum cluster theories
• Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential
• Evidence for bosonic mode coupling in electron dynamics of LiFeAs superconductor*
• Rescaling of applied oscillating voltages in small Josephson junctions
• The link between integrability, level crossings and exact solution in quantum models
• Alveolar Dynamics and Beyond – The Importance of Surfactant Protein C and Cholesterol in Lung Homeostasis and Fibrosis
• Superconducting Properties of 3D Low-Density Translation-Invariant Bipolaron Gas
• Multiple phase transitions in Pauli-limited iron-based superconductors
• The origins of macroscopic quantum coherence in high temperature superconductivity
• Correlation energy of the pairing Hamiltonian
• Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
• Characterization of zero-point vibration in one-component crystals
• Absorption and emission of a collective excitation by a fermionic quasiparticle in a Fermi superfluid
• Andreev reflections and the quantum physics of black holes
• Electrodynamics of correlated electron materials
• Gaudin models solver based on the correspondence between Bethe ansatz and ordinary differential equations
• Multilayered cuprate superconductor Ba2Ca5Cu6O12(O1−x,Fx)2 studied by temperature-dependent scanning tunneling microscopy and spectroscopy
• Pairing transition of nuclei at finite temperature
• Emergent spacetime and the origin of gravity
• Theory of superconductivity in strongly correlated electron systems
• QCD at high density/temperature
• Generalized Blonder-Tinkham-Klapwijk theory and conductance spectra with particle-hole mixing interface potential
• Interacting quark-diquark model of baryons
• Mean-field thermodynamic quantum time-space crystal: Spontaneous breaking of time-translation symmetry in a macroscopic fermion system
• Type-II superconductivity in W 5 Si 3 -type Nb 5 Sn 2 Al
• Mass yields of fission fragments of Pt to Ra isotopes
• The making of the Standard Model
• Study of the skin effect in superconducting materials
• Structure of the phonon vacuum state
• Bifurcations of Coupled Electron-Phonon Modes in an Antiferromagnet Subjected to a Magnetic Field
• Odd-triplet superconductivity in single-level quantum dots
• Interplay of superconductivity and bosonic coupling in the peak-dip-hump structure of Bi2Sr2CaCu2O8+δ
• Quantum turbulence in Bose–Einstein condensates: Present status and new challenges ahead
• Interplay between charge density wave and superconductivity in multiband systems with interband Coulomb interaction
• Optimal free descriptions of many-body theories
• α-cluster structure and density waves in oblate nuclei
• Comparing the full time-dependent Bogoliubov-de-Gennes equations to their linear approximation: a numerical investigation
• Ultracold Bose mixtures with spin-dependent fermion-mediated interactions
• From LaH10 to room–temperature superconductors
• Disappearance of superconductivity due to vanishing coupling in the overdoped Bi₂Sr₂CaCu₂O_8+δ
• Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids
• Superconductors and gravity
• Double-valued strong-coupling corrections to Bardeen–Cooper–Schrieffer ratios
• Harnessing ultraconfined graphene plasmons to probe the electrodynamics of superconductors
• An analytic study on the excited states of holographic superconductors
• Building (1+1) holographic superconductors in the presence of non-linear Electrodynamics
• Sum rule for the partial decay rates of bottom hadrons based on the dynamical supersymmetry of the s quark and the ud diquark
• Exactly solvable pairing model for superconductors withpx+ipy-wave symmetry
• Recent Progress of Point Contact Spectroscopy as a Probe of Correlated Electron States
• Emergence of superconductivity from fully incoherent normal state in an iron-based superconductor (Ba0.6K0.4)Fe2As2
• Balanced double-loop mesoscopic interferometer based on Josephson proximity nanojunctions
• Pairing properties from random distributions of single-particle energy levels
• BCS ansatz for superconductivity in the light of the Bogoliubov approach and the Richardson–Gaudin exact wave function
• New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation
• On the mathematical theory of superfluidity
• Dispersive effects in neutron matter superfluidity
• Influence of phonon renormalization in Eliashberg theory for superconductivity in two- and three-dimensional systems
• Emergence of superconductivity in heavy-electron materials
• New possibilities for QCD at finite density
• Observation of phonon peaks and electron-phonon bound states in graphene
• Review of thermal transport and electronic properties of borophene
• Decoherence of Einstein-Podolsky-Rosen pairs in a noisy Andreev entangler
• Large-scale prediction of the parity distribution in the nuclear level density and application to astrophysical reaction rates
• Thermal Signatures of Pairing Correlations in Nuclei and Nanoparticles
• Origin of21+excitation energy dependence on valence nucleon numbers
• Chemical physics of superconductivity in layered yttrium carbide halides from first principles
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Polariton Condensation and Lasing
• The Discovery of a Class of High-Temperature Superconductors
• Two-gap superconductivity in heavilyn-doped graphene:Ab initioMigdal-Eliashberg theory
• Coherent energy exchange between carriers and phonons in Peierls-distorted bismuth unveiled by broadband XUV pulses
• Probing the Unconventional Superconducting State of LiFeAs by Quasiparticle Interference
• Multi-body Correlations in SU(3) Fermi Gases
• Sub-micrometer epitaxial Josephson junctions for quantum circuits
• Exciton-polariton properties of hexagonal BN-based microcavity and their potential applications in BEC and superconductivity
• Superconductivity in Defective Pyrite-Type Iridium ChalcogenidesIrxCh2(Ch=Seand Te)
• Heavy quarks within the electroweak multiplet
• Possible “Magnéli” Phases and Self-Alloying in the Superconducting Sulfur Hydride
• Determination of gap solution and critical temperature in doped graphene superconductivity
• Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys
• The role of the chemical potential in the BCS theory
• Tunneling spectra of submicron Bi2Sr2CaCu2O8+ δ intrinsic Josephson junctions: evolution from superconducting gap to pseudogap
• Gentle perturbations of the free Bose gas. I
• Unified description of neutron superfluidity in the neutron-star crust with analogy to anisotropic multiband BCS superconductors
• En route to high Tc superconductivity via Rb substitution of guest metal atoms in SrB3C3 clathrate
• TheO(N) nonlinear sigma model in the functional Schrödinger picture
• ac Josephson effect in superconductingd-wave junctions
• Perturbations on the superconducting state of metallic nanoparticles: influence of geometry and impurities
• Nonrelativistic Banks-Casher relation and random matrix theory for multicomponent fermionic superfluids
• The one dimensional semi-classical Bogoliubov-de Gennes Hamiltonian with PT symmetry: generalized Bohr-Sommerfeld quantization rules
• Effect of pairing correlations on incompressibility and symmetry energy in nuclear matter and finite nuclei
• On the origin of critical temperature enhancement in atomically thin superconductors
• Large surface conductance and superconductivity in topological insulator microstructures
• BCS-Like Bogoliubov Quasiparticles in High-TcSuperconductors Observed by Angle-Resolved Photoemission Spectroscopy
• Dynamic Hubbard model: kinetic energy driven charge expulsion, charge inhomogeneity, hole superconductivity and Meissner effect
• Microscopic linear response calculations based on the Skyrme functional plus the pairing contribution
• Time-reversal invariant superconductivity of Sr2RuO4 revealed by Josephson effects
• THERMODYNAMICS OF ANISOTROPIC-GAP AND MULTIBAND CLEAN BCS SUPERCONDUCTORS
• Link between superconductivity and a Lifshitz transition in intercalated Bi2Se3
• Precise Study of the Resonance at Q0=(1,0,0) in URu2Si2
• THEORY OF SINUSOIDAL MODULATION OF THE RESONANT NEUTRON SCATTERING IN HIGH TEMPERATURE SUPERCONDUCTORS
• Preparation and characterization of high-entropy alloy (TaNb)1−x(ZrHfTi)x superconducting films
• Pairing correlations in finite systems: from the weak to the strong fluctuations regime
• Dynamical correlation functions of the mesoscopic pairing model
• Multiparticle instability in a spin-imbalanced Fermi gas
• Temperature Dependence of the Superconducting Gap in High-TcCuprates
• Simulating complex quantum networks with time crystals
• On the Trail of the Higgs Boson
• Enhanced paraconductivity-like fluctuations in the radiofrequency spectra of ultracold Fermi atoms
• A finite range pairing force for density functional theory in superfluid nuclei
• The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties
• Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations
• Zero-temperature phase diagram of Yukawa bosons
• Ground-state instability in systems of strongly interacting fermions
• Magnon-mediated superconductivity on the surface of a topological insulator
• Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals
• Significant Reduction of Lattice Thermal Conductivity by the Electron-Phonon Interaction in Silicon with High Carrier Concentrations: A First-Principles Study
• Casimir interactions between magnetic flux tubes in a dense lattice
• Visualization of geometric influences on proximity effects in heterogeneous superconductor thin films
• Generalized Ward identity and gauge invariance of the color-superconducting gap
• Noise correlations of the ultracold Fermi gas in an optical lattice
• Crossover from bulk to few-electron limit in ultrasmall metallic grains
• Electron-Phonon Coupling in the Conventional SuperconductorYNi2B2Cat High Phonon Energies Studied by Time-of-Flight Neutron Spectroscopy
• Local electronic structure of defects in superconductors
• High-Pressure Effects on the Intermetallic Superconductor Ti0.85Pd0.15
• A minimal size for granular superconductors
• Evidence for bulk superconductivity in pure bismuth single crystals at ambient pressure
• BCS–BEC CROSSOVER IN RELATIVISTIC FERMI SYSTEMS
• Evidence of a Spin Resonance Mode in the Iron-Based SuperconductorBa0.6K0.4Fe2As2from Scanning Tunneling Spectroscopy
• Method for making 2-electron response reduced density matrices approximately N-representable
• Mean-field based approaches to pairing correlations in atomic nuclei
• New exact solutions of the standard pairing model for well-deformed nuclei
• Temperature and angular dependence of the upper critical field in K2Cr3As3
• Applicability of Bardeen–Cooper–Schrieffer theory to small-sized superconductors: Role of Cooper-pair binding energy
• Exact solution of the nuclear pairing problem
• High‐Tccuprate superconductivity in a nutshell
• Synthesis, phase stability, structural, and physical properties of 11‐type iron chalcogenides
• Effect of atomic disorder and Ce doping on superconductivity ofCa3Rh4Sn13: Electric transport properties under high pressure
• Calibration of cryogenic amplification chains using normal-metal–insulator–superconductor junctions
• Strong coupling expansion of the entanglement entropy of Yang-Mills gauge theories
• Electroweak SU(2)L × U(1)Y model with strong spontaneously fermion-mass-generating gauge dynamics
• Single Cooper pair transfer in stable and in exotic nuclei
• Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover
• Non-Hermitian Pseudo-Gaps
• Superstripes
• COMPARISON OF TWO INTERPRETATIONS OF THE JOSEPHSON EFFECT
• Parity Effect in Ground State Energies of Ultrasmall Superconducting Grains
• Dynamical flavor symmetry breaking by a magnetic field in 2+1 dimensions
• Superconducting phase transition in inhomogeneous chains of superconducting islands
• Derivation of the Gross-Pitaevskii Equation for Condensed Bosons from the Bogoliubov–de Gennes Equations for Superfluid Fermions
• In-plane conductivity of a layered large-bipolaron liquid
• From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature
• Dynamic d-symmetry Bose condensate of a planar-large-bipolaron liquid in cuprate superconductors
• RELATIONSHIP BETWEEN THE FERMI SURFACE AND THE SYMMETRY OF THE GAP FUNCTION IN UNCONVENTIONAL SUPERCONDUCTORS
• Nanomaterials for Quantum Information Science and Engineering
• Basic Variables to Be Reproduced in the First-Principles Theory for Superconductors: Fluctuation of the Particle Number
• Peculiarities in the concentration dependence of the superconducting transition temperature in the bipolaron theory of Cooper pairs
• Critical Slowing Down of Quadrupole and Hexadecapole Orderings in Iron Pnictide Superconductor
• Surface reconstruction and energy gap of superconductingV3Si(001)
• Supersymmetric Nambu-Jona-Lasinio model on 𝒩 = 1/2 four-dimensional non(anti)commutative superspace
• Deconfinement and color superconductivity in cold neutron stars
• Analytic investigation of holographic phase transitions influenced by dark matter sector
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems
• Acoustic attenuation rate in the Fermi-Bose model with a finite-range fermion-fermion interaction
• Electronic multipoles and multiplet pairs induced by Pomeranchuk and Cooper instabilities of Bogoliubov Fermi surfaces
• Engineering holographic phase diagrams
• Spin-flip enhanced thermoelectricity in superconductor-ferromagnet bilayers
• A particle-number-conserving solution to the generalized pairing problem
• Electronic localization in twisted bilayer MoS2 with small rotation angle
• Well-Defined Quasiparticles in Interacting Metallic Grains
• Resonance effects on the crossover of bosonic to fermionic superfluidity
• BCS theory [wikipedia]
• Superconductivity [wikipedia]
• Quantum theory and human perception of the macro-world. [europepmc]
• Citing a Data Repository: A Case Study of the Protein Data Bank. [europepmc]
• Physics of Neutron Star Crusts. [europepmc]
• Imaging the square of the correlated two-electron wave function of a hydrogen molecule. [europepmc]
• Large thermoelectric power factor from crystal symmetry-protected non-bonding orbital in half-Heuslers. [europepmc]
• Andreev bound states and their signatures. [europepmc]
• Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions. [europepmc]
• Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard-Holstein Model. [europepmc]
• Non-equilibrium landscape and flux reveal how the central amygdala circuit gates passive and active defensive responses. [europepmc]
• Structural dynamics of incommensurate charge-density waves tracked by ultrafast low-energy electron diffraction. [europepmc]
• Direct observation of large electron-phonon interaction effect on phonon heat transport. [europepmc]
• A large modulation of electron-phonon coupling and an emergent superconducting dome in doped strong ferroelectrics. [europepmc]
• Large Enhancement of Ferromagnetism under a Collective Strong Coupling of YBCO Nanoparticles. [europepmc]
• Superconductivity in an extreme strange metal. [europepmc]
• Superconductivity up to 243 K in the yttrium-hydrogen system under high pressure. [europepmc]
• High-temperature superconductivity on the verge of a structural instability in lanthanum superhydride. [europepmc]
• Topological triple phase transition in non-Hermitian Floquet quasicrystals. [europepmc]
• Superconducting Materials and Devices Grown by Focused Ion and Electron Beam Induced Deposition. [europepmc]
• Engineering topological states in atom-based semiconductor quantum dots. [europepmc]
• Tunable superconductivity and its origin at KTaO 3 interfaces. [europepmc]
• Evidence of high-temperature exciton condensation in a two-dimensional semimetal. [europepmc]
• Theoretical and Data-Driven Approaches for Biomolecular Condensates. [europepmc]
• Pressure-induced superconductivity at 32 K in MoB 2 . [europepmc]
• High-temperature superconductivity up to 223 K in the Al stabilized metastable hexagonal lanthanum superhydride. [europepmc]
• Quasi-2D Fermi surface in the anomalous superconductor UTe 2 . [europepmc]

Related

• Theory of Superconductivity
• New Theory of Superconductivity
• Calculation of the Superconducting State Parameters with Retarded Electron-Phonon Interaction
• Basic Foundations of the Microscopic Theory of Superconductivity
• A New General Theory of Superconductivity