Extended Mean-Field Theory for the 2D Hubbard Model in Degenerate Dilute Electron Gases: Fluctuations, Superconducting Dome, and Interaction Mechanisms in Strontium Titanate

TL;DR

This paper develops an extended mean-field theory for the 2D Hubbard model in dilute electron gases like SrTiO3, revealing how fluctuations, competing orders, and interaction mechanisms influence superconductivity and electronic properties.

Contribution

It introduces a novel extended mean-field framework that captures fluctuations, competing orders, and interaction effects in the 2D Hubbard model relevant to SrTiO3.

Findings

Superconducting transition temperature forms a dome shape with doping.

Tunable s-wave and d-wave symmetries are observed.

Charge-density-wave order competes with superconductivity.

Abstract

Strontium titanate ($\mathrm{SrTiO_3, STO}$) dome-shaped superconducting transition temperature as a function of chemical potential, consistent with STO experiments, and shows that tunable s-wave and d-wave symmetries are modulated by doping. Superconducting fluctuations validate the mean-field approximation at low temperatures but destroy pairing at higher temperatures. The charge-density-wave order competes with superconductivity, enhances the effective electron mass inversely with the chemical potential, and increases with the interaction strength $U$ and the temperature $T$. SDW order is rare and fragile, while an additional magnetic term induces subtle band splitting. These findings suggest e-e contributions to STO's transport anomalies and provide criteria to distinguish e-e from e-ph origins, offering insights for engineering higher $T_c$ in dilute systems.