Correlation functions and characteristic lengthscales in flat band superconductors

Abstract

The possibility of an unconventional form of high temperature superconductivity in flat band (FB) material does not cease to challenge our understanding of the physics in correlated systems. Here, we calculate the normal and anomalous one-particle correlation functions in various one and two dimensional FB systems and systematically extract the characteristic lengthscales. When the Fermi energy is located in the FB, it is found that the coherence length ($\xi$) is of the order of the lattice spacing and weakly sensitive to the strength of the electron-electron interaction. Recently, it has been argued that in FB compounds $\xi$ could be decomposed into a conventional part of BCS type (${\xi }_{BCS}$) and a geometric contribution which characterises the FB eigenstates, the quantum metric ($⟨g⟩$). However, by calculating the coherence length in two possible ways, our calculations show that $\xi \ne \sqrt{⟨g⟩.}$ This may suggest that the link between QM and coherence length is more complex, and leaves us with the open question: what is the appropriate definition of the coherence length in flat-band systems?

11 pages, 8 figures

References in corpus (25)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Moire bands in twisted double-layer graphene
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Superfluidity in topologically nontrivial flat bands
• Artificial flat band systems: from lattice models to experiments
• Topological Flat Band Models and Fractional Chern Insulators
• High-temperature surface superconductivity in topological flat-band systems
• The Insulating State of Matter: A Geometrical Theory
• Flat bands in topological media
• Band geometry, Berry curvature and superfluid weight
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Preformed pairs in flat Bloch bands
• Superconductivity, pseudogap, and phase separation in topological flat bands: a quantum Monte Carlo study
• Pairing and superconductivity in the flat band: Creutz lattice
• Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
• The Ginzburg-Landau theory of flat band superconductors with quantum metric
• Pairing and superconductivity in quasi one-dimensional flat band systems: Creutz and sawtooth lattices
• Heuristic bounds on superconductivity and how to exceed them
• Origin of flat-band superfluidity on the Mielke checkerboard lattice
• Designer Flat Bands: Topology and Enhancement of Superconductivity
• Flat band superconductivity in a system with a tunable quantum metric : the stub lattice
• Anomalous Coherence Length in Superconductors with Quantum Metric
• Giant boost of the quantum metric in disordered one dimensional flat band systems

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• Flat Bands and Compact Localised States: A Carrollian roadmap
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Superconducting junctions with flat bands
• Normal state quantum geometry, non-locality and superconductivity
• Correlation lengths of flat-band superconductivity from quantum geometry