Dynamic Hubbard model: kinetic energy driven charge expulsion, charge inhomogeneity, hole superconductivity and Meissner effect

Abstract

Conventional Hubbard models do not take into account the fact that the wavefunction of an electron in an atomic orbital expands when a second electron occupies the orbital. Dynamic Hubbard models have been proposed to describe this physics. These models reflect the fact that electronic materials are generically not electron–hole symmetric, and they give rise to superconductivity driven by lowering of kinetic energy when the electronic energy band is almost full, with higher transition temperatures resulting when the ions are negatively charged. We show that the charge distribution in dynamic Hubbard models can be highly inhomogeneous in the presence of disorder, and that a finite system will expel negative charge from the interior to the surface, and that these tendencies are largest in the parameter regime where the models give rise to highest superconducting transition temperatures. High Tc cuprate materials exhibit charge inhomogeneity and they exhibit tunneling asymmetry, a larger tendency to emit electrons rather than holes in normal–insulating–superconducting tunnel junctions. We propose that these properties, as well as their high Tc, are evidence that they are governed by the physics described by dynamic Hubbard models. Below the superconducting transition temperature the models considered here describe a negatively charged superfluid and positively charged quasiparticles, unlike the situation in conventional Bardeen–Cooper–Schrieffer superconductors where quasiparticles are charge neutral on average. We examine the temperature dependence of the superfluid and quasiparticle charges and conclude that spontaneous electric fields should be observable in the interior and in the vicinity of superconducting materials described by these models at sufficiently low temperatures. We furthermore suggest that the dynamics of the negatively charged superfluid and positively charged quasiparticles in dynamic Hubbard models can provide an explanation for the Meissner effect observed in high Tc and low Tc superconducting materials.