Ab-initio superfluid weight and superconducting penetration depth

Abstract

Machine learning and high-throughput screening approaches to superconductor discovery require physically meaningful descriptors that capture essential physics while remaining computationally tractable. The superfluid weight is an ideal descriptor as it is a prerequisite for superconductivity, determines the magnetic penetration depth and the Berezinskii-Kosterlitz-Thouless transition temperature in two-dimensional materials, may limit the critical temperature in unconventional superconductors through phase coherence, and reveals quantum geometric contributions to supercurrent transport. We develop a computationally efficient framework for calculating the zero-temperature, mean-field superfluid weight for uniform pairing from density functional theory band structures and Bloch wavefunctions. We separately evaluate the conventional contribution from band curvature and the geometric contribution from quantum geometry. To validate the method, we calculate London penetration depths for a few conventional superconductors (Al, Pb, Nb, MgB$_2$, LuRu$_3$B$_2$ and YRu$_3$B$_2$) and find good agreement with experiment after accounting for nonlocal corrections, strong-coupling effects, and sample quality. The conventional contribution dominates by orders of magnitude in these wide-band materials, as expected. This framework provides a foundation for large-scale screening of superconducting candidates and exploring quantum geometric effects in unconventional superconductors.

Figures (3)

• Figure 1: A comparison between calculated penetration depths $\lambda_L^\text{calc}$ and experimental estimates of the London penetration depth $\lambda_L^\text{exp}$ from Equations \ref{['eq:el-ph']} and \ref{['eq:london_L-n-meff']}. See Table \ref{['tab:exp-data']} for details on the experimental parameters used.
• Figure 2: High-symmetry path of Pb and Nb's electronic band structure colored by the magnitude of the superfluid weight's conventional contribution $D_\text{conv}$ (a)/(g) xx (b)/(h) yy and (c)/(i) zz component, and the geometric contribution $D_\text{geom}$ (d)/(j) xx (e)/(k) yy and (f)/(l) zz component. The superfluid weights have been computed with their corresponding experimental gaps, 1.33meV for Pb and 1.55meV for Nb. The conventional contribution clearly dominates by around 4 orders of magnitude for both materials and is strongly localized to the fermi surface.
• Figure 3: The superfluid weight dependence on the superconducting gap $\Delta$ for several materials with the geometric contribution in the top panel and the conventional in the bottom panel. The conventional term is is nearly constant with respect to the gap while the geometric term increases with the superconducting gap.