Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices

Abstract

Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Mueller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of antiferromagnetic fluctuations, and the presence of a mysterious pseudogap phase close to the Mott state, one can conclude that high-Tc superconductors are clearly distinguishable from the well-understood BCS superconductors. The d-wave superconducting state can be understood through a Gutzwiller-type projected BCS wave-function. In this review article, we revisit the Hubbard model at half-filling and focus on the emergence of exotic superconductivity with d-wave symmetry in the vicinity of the Mott state, starting from ladder systems and then studying the dimensional crossovers to higher dimensions. This allows to confirm that short-range antiferromagnetic fluctuations can mediate superconductivity with d-wave symmetry. Ladders are also nice prototype systems allowing to demonstrate the truncation of the Fermi surface and the emergence of a Resonating Valence Bond (RVB) state with preformed pairs in the vicinity of the Mott state. In two dimensions, a similar scenario emerges from renormalization group arguments. We also discuss theoretical predictions for the d-wave superconducting phase as well as the pseudogap phase, and address the crossover to the overdoped regime. Finally, cold atomic systems with tunable parameters also provide a complementary insight into this outstanding problem.

98 pages and 18 figures; Final version (references added and misprints corrected)

References in corpus (48)

• Many-Body Physics with Ultracold Gases
• Fermi-liquid instabilities at magnetic quantum phase transitions
• A Mott insulator of fermionic atoms in an optical lattice
• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Using photoemission spectroscopy to probe a strongly interacting Fermi gas
• Spatial quantum noise interferometry in expanding ultracold atom clouds
• From Fermi Arcs to the Nodal Metal: Scaling of the Pseudogap with Doping and Temperature
• Distinct Fermi-Momentum Dependent Energy Gaps in Deeply Underdoped Bi2212
• A Phenomenological Theory of The Pseudogap State
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+d
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• Two-Dimensional Superconducting Fluctuations in Stripe-Ordered La(1.875)Ba(0.125)CuO(4)
• Dynamical layer decoupling in a stripe-ordered, high T_c superconductor
• Direct evidence for a competition between the pseudogap and high temperature superconductivity in the cuprates
• Molecules of Fermionic Atoms in an Optical Lattice
• From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics
• Anisotropic Scattering and Anomalous Transport in a High Temperature Superconductor
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Modeling the Fermi arc in underdoped cuprates
• The spin-incoherent Luttinger liquid
• Interaction-controlled transport of an ultracold Fermi gas
• Algebraic charge liquids
• Metastable superfluidity of repulsive fermionic atoms in optical lattices
• Correlation between $T_c$ and anisotropic scattering in Tl${}_2$Ba${}_2$CuO${}_{6+\delta }$
• Enhancement of the superconducting transition temperature in La2-xSrxCuO4 bilayers: Role of pairing and phase stiffness
• Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling
• Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires
• Minimum instances of topological matter in an optical plaquette
• Phenomenological description of the two energy scales in underdoped superconducting cuprates
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Myriad phases of the Checkerboard Hubbard Model
• Preparation and detection of d-wave superfluidity in two-dimensional optical superlattices
• Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance
• The electron lifetime in Luttinger liquids
• d-Mott phases in one and two dimensions
• Transport in a spin incoherent Luttinger liquid
• Breakdown of Landau Theory in Overdoped Cuprates near the Onset of Superconductivity
• Enhancement of the superconducting transition temperature in cuprate heterostructures
• Maximizing the Neel temperature of fermions in a simple-cubic optical lattice
• Bipairing and the Stripe Phase in 4-Leg Ladders
• Double-gap superconducting proximity effect in nanotubes
• Experimental investigation of the origin of the cross-over temperature in the cuprates
• Realizing the strongly correlated $d$-Mott state in a fermionic cold atom optical lattice
• Inhomogeneously doped two-leg ladder systems
• SU(2) approach to the pseudogap phase of high-temperature superconductors: electronic spectral functions

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• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Fermions in 2D Optical Lattices: Temperature and Entropy Scales for Observing Antiferromagnetism and Superfluidity
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• Novel phases in twisted bilayer graphene at magic angles as a result of van Hove singularities and interactions
• Competing orders at higher-order Van Hove points
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Pseudo-gap pairing in ultracold Fermi atoms
• Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
• A Theory for the High-T_c Cuprates: Anomalous Normal-State and Spectroscopic Properties, Phase Diagram, and Pairing
• Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry
• Supermetal
• Correlated Dirac Particles and Superconductivity on the Honeycomb Lattice
• Driven dissipative dynamics and topology of quantum impurity systems
• Expansion dynamics in the one-dimensional Fermi-Hubbard model
• Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state
• Comparative Study of BCS-BEC Crossover Theories above $T_c$: the Nature of the Pseudogap in Ultra-Cold Atomic Fermi Gases
• Chiral Bosonic Phases on the Haldane Honeycomb Lattice
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
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• Superconductivity at the onset of spin-density-wave order in a metal
• Competing instabilities, orbital ordering and splitting of band degeneracies from a parquet renormalization group analysis of a 4-pocket model for iron-based superconductors: application to FeSe
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• Effective SU(2) theory for the pseudogap state
• Correlated Topological Phases and Exotic Magnetism with Ultracold Fermions
• Dimensional crossover and cold-atom realization of topological Mott insulators
• Collective modes and superflow instabilities of strongly correlated Fermi superfluids
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• Interacting Stochastic Topology and Mott Transition from Light Response
• Topological proximity effects in a Haldane-graphene bilayer system
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Strong thermal fluctuations in cuprate superconductors in magnetic field above Tc
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• Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys under pressure
• Evolution of spectral and transport quantities with doping in the SU(2) theory of cuprates
• Topological Superconductivity in Two Dimensions with Mixed Chirality
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Topological superconductivity in the extended Kitaev-Heisenberg model
• Controlled hole doping of a Mott insulator of ultracold fermionic atoms
• Magnetic structure of an imbalanced Fermi gas in an optical lattice
• Hopping modulation in a one-dimensional Fermi-Hubbard Hamiltonian
• Superconductivity generated by coupling to a Cooperon in a 2-dimensional array of 4-leg Hubbard ladders
• Diagrammatic Quantum Monte Carlo solution of the two-dimensional Cooperon-Fermion model
• Enhanced nematicity emerging from higher-order van Hove singularities
• Dissipative Preparation of Antiferromagnetic Order in the Fermi-Hubbard Model
• Correcting inconsistencies in the conventional superfluid path integral scheme
• Fluctuations and Higgs mechanism in Under-Doped Cuprates: a Review
• Absence of Luther-Emery Superconducting Phase in the Three-Band Model for Cuprate Ladders
• Triplet FFLO Superconductivity in the doped Kitaev-Heisenberg Honeycomb Model
• Altermagnetism from coincident Van Hove singularities: application to $\kappa$-Cl
• The Crossover from Ordinary to Higher-Order van Hove Singularity in a Honeycomb System: A Parquet Renormalization Group Analysis
• Pairing at a single Van Hove point
• Renormalization group analysis on a neck-narrowing Lifshitz transition in the presence of weak short-range interactions in two dimensions
• Engineering Quantum Spin Liquids and Many-Body Majorana States with a Driven Superconducting Box Circuit
• Unified picture of superconductivity and magnetism in CeRh${}_2$As${}_2$
• Dissipation-induced antiferromagnetic-like frustration in coupled photonic resonators
• On the Origin of the Checkerboard Pattern in Scanning Tunneling Microscopy Maps of Underdoped Cuprate Superconductors
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• Flow equation approach to the linear response theory of superconductors
• Charge and current orders in the spin-fermion model with overlapping hot spots
• The Transformation of the Superconducting Gap to an Insulating Pseudogap at a Critical Hole Density in the Cuprates
• Designing Heterostructures with Higher Temperature Superconductivity
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• Robust topological superconductivity in spin-orbit coupled systems at higher-order van Hove filling
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• Competing superconducting instabilities in the one-dimensional p-band degenerate cold fermionic system
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• Valence Transition Theory of the Pressure-Induced Dimensionality Crossover in Superconducting Sr${}_{14-x}$Ca${}_x$Cu${}_{24}$O${}_{41}$
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• Fluctuation conductivity due to the preformed local pairs