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

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.

Figures (7)

• Figure 1: The relation between the superconducting gap and the wave vector (left panel) and the chemical potential (right panel) is plotted at $U= 0.005 ~\mathrm{a. u.}$
• Figure 2: The difference between the superconducting fluctuations and gaps is plotted with $k_x$ ($k_y$), the x(y)-component total wave vector of electron pairs at $U=0.1 \mathrm{a. u.}, \mu = 0.01 \mathrm{a. u.}$. The radius of the white circles is the critical wave vector at which the superconducting gap vanishes.
• Figure 3: The difference between the superconducting fluctuations and gaps is plotted with $k_x$ ($k_y$), the x(y)-component total wave vector of electron pairs at $U=0.1 \mathrm{a. u.}, \mu = 0.05 \mathrm{a. u.}$. The radius of the white circles is the critical wave vector at which the superconducting gap vanishes.
• Figure 4: The difference between the superconducting fluctuations and gaps is plotted with $k_x$ ($k_y$), the x(y)-component total wave vector of electron pairs at $U=0.05 \mathrm{a. u.}, \mu = 0.01 \mathrm{a. u.}$. The radius of the white circles is the critical wave vector at which the superconducting gap vanishes.
• Figure 5: The charge density wave order parameter is plotted $k_x$ ($k_y$), the wave vector magnitude of incident (scattered) electrons at $U=0.01 \mathrm{a. u.}, \mu = 0.001 \mathrm{a. u.}$.