Thermodynamics of an Exactly Solvable Model for Superconductivity in a Doped Mott Insulator

Abstract

Computing superconducting properties starting from an exactly solvable model for a doped Mott insulator stands as a grand challenge. We have recently shown that this can be done starting from the Hatsugai-Kohmoto (HK) model which can be understood generally as the minimal model that breaks the non-local ${\mathbb{Z}}_2$ symmetry of a Fermi liquid, thereby constituting a new quartic fixed point for Mott physics [Phillips et al., Nature Physics 16, 1175 (2020); Huang et al., Nature Physics (2022)]. In the current work, we compute the thermodynamics, condensation energy, and electronic properties such as the NMR relaxation rate $1/T_1$ and ultrasonic attenuation rate. Key differences arise with the standard BCS analysis from a Fermi liquid: 1) the free energy exhibits a local minimum at $T_p$ where the pairing gap turns on discontinuously above a critical value of the repulsive HK interaction, thereby indicating a first-order transition, 2) a tri-critical point emerges, thereby demarcating the boundary between the standard second-order superconducting transition and the novel first-order regime, 3) Mottness changes the sign of the quartic coefficient in the Landau-Ginzburg free-energy fuctional relative to that in BCS, 4) as this obtains in the strongly interacting regime, it is Mott physics that underlies the generic first-order transition, 5) the condensation energy exceeds that in BCS theory suggesting that multiple Mott bands might be a way of enhancing superconducting, 6) the heat-capacity jump is non-universal and increases with the Mott scale, 7) Mottness destroys the Hebel-Slichter peak in NMR, and 8) Mottness enhances the fall-off of the ultrasonic attenuation at the pairing temperature $T_p$. As several of these properties are observed in the cuprates, our analysis here points a way forward in computing superconducting properties of strongly correlated electron matter.

accepted in PRB

References in corpus (4)

• Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x
• Particle-hole Asymmetry in the Cuprate Pseudogap Measured with Time-Resolved Spectroscopy
• Topological $s$-wave superconductors driven by electron correlation
• Superconductivity from Luttinger surfaces: Emergent $\infty$-body SYK physics

Cited by in corpus (15)

• Failure of Topological Invariants in Strongly Correlated Matter
• Ground state stability, symmetry, and degeneracy in Mott insulators with long range interactions
• Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
• Two-stage superconductivity in the Hatsugai-Kohmoto-BCS model
• Quantum oscillations in a doped Mott insulator beyond Onsager's relation
• Friedel oscillation in non-Fermi liquid: Lesson from exactly solvable Hatsugai-Kohmoto model
• Topic Review: Hatsugai-Kohmoto models: Exactly solvable playground for Mottness and Non-Fermi Liquid
• Notes on Quantum oscillation for Hatsugai-Kohmoto model
• Emergence of Topological Non-Fermi Liquid Phases in a Modified Su-Schrieffer-Heeger Chain with Long-Range Interactions
• Strong pair-density-wave fluctuations in an exactly solvable doped Mott insulator
• Non-equilibrium dynamics of superconductivity in the Hatsugai-Kohmoto model
• Infinite temperature spin dynamics in the asymmetric Hatsugai-Kohmoto model
• Enhanced Superconducting Diode Effect in the Asymmetric Hatsugai-Kohmoto Model
• Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases
• Interaction enhanced altermagnet in the Hatsugai-Kohmoto model