Thermodynamics of Superconductivity in a Doped Mott Insulator

Being able to compute the superconducting properties starting from a computable model for a doped Mott insulator stands as a grand challenge.  We have recently¹ shown that this can be done starting from the Hatsugai-Kohmoto² model which can be understood³  generally as the minimal model that breaks the non-local Z₂ symmetry of a Fermi liquid, thereby constituting a new quartic fixed point for Mott physics.  In the current work, we go beyond the previous T=0 analysis and compute the thermodynamics, condensation energy, and electronic properties such as the NMR relaxation rate 1/T₁ and ultrasonic attenuation rate.  Key differences arise from the BCS analysis from a Fermi liquid:  1) The pairing gap turns on at a temperature that exceeds T_c defined as the temperature at which the pair susceptibility (computable exactly) diverges, 2) The condensation energy exceeds that in BCS theory suggesting that,  multiple Mott bands might be a way of enhancing T_c, 3) Mottness destroys the Hebel-Slichter peak in NMR, 4) The ultrasonic attenuation has a Mott-induced logarithmic suppression, and 5) Mottness changes the sign of the quartic coefficient in the Landau-Ginzburg free-energy fuctional relative to that in BCS.  As all of these properties are observed in the cuprates, our analysis here points a way forward in computing superconducting properties of strongly correlated electron matter.

[1] P. W. Phillips, L. Yeo, and E. W. Huang, Nature Physics16, 1175 (2020)

[2] Y. Hatsugai and M. Kohmoto, Journal of the Physical Society of Japan61, 2056 (1992), https://doi.org/10.1143/JPSJ.61.2056.

[3] E. W. Huang, G. La Nave, and P. W. Phillips, arXiv e-prints , arXiv:2103.03256 (2021), arXiv:2103.03256 [cond-mat.str-el].