Because the cuprate superconductors are doped Mott insulators, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. We consider the Hatsugai–Kohmoto model^1,2, an exactly solvable system that is a prototypical Mott insulator. Upon either doping or reducing the interaction strength, our exact calculations show that the system becomes a non-Fermi liquid metal with a superconducting instability. In the presence of a weak pairing interaction, the instability produces a thermal transition to a superconducting phase, which is distinct from the traditional state described by Bardeen–Cooper–Schrieffer (BCS) theory, as evidenced by a gap-to-transition temperature ratio exceeding the universal BCS limit. The elementary excitations of this superconductor are not Bogoliubov quasiparticles but rather superpositions of doublons and holons, composite excitations that show that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. An unexpected feature of this model is that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies, as seen in the cuprates³, as well as a suppression of the superfluid density relative to that in BCS theory.

因为铜酸盐超导体是掺杂的Mott绝缘体，所以即使求解同时显示Mottness和超导性的玩具模型，也将是有利的。我们考虑了Hatsugai–Kohmoto模型^1,2，这是一个完全可解决的系统，是典型的Mott绝缘子。掺杂或降低相互作用强度后，我们的精确计算表明该系统成为具有超导不稳定性的非费米液态金属。在弱配对相互作用的存在下，不稳定性会导致向超导相的热转变，这与Bardeen-Cooper-Schrieffer（BCS）理论描述的传统状态是不同的，如间隙与跃迁温度比所证明的那样。超过了通用BCS限制。该超导体的基本激发不是Bogoliubov准粒子，而是双原子和holon的叠加，复合激发表明掺杂的Mott绝缘子的超导基态继承了正常态的非费米液体特性。³，以及相对于BCS理论的超流体密度的抑制。