London penetration depth and thermal fluctuations in the sulphur hydride 203 K superconductor

Recently, compressed H$_2$S has been shown to become superconducting at 203 K under a pressure of 155 GPa. One might expect fluctuations to dominate at such temperatures. Using the magnetisation critical current, we determine the ground-state London penetration depth, $lambda_0$=189 nm, and the superconducting energy gap, $Delta_0$=27.8 meV, and find these parameters are similar to those of cuprate superconductors. We also determine the fluctuation temperature scale, $T_{textrm{fluc}}=1470$ K, which shows that, unlike the cuprates, $T_c$ of the hydride is not limited by fluctuations. This is due to its three dimensionality and suggests the search for better superconductors should refocus on three-dimensional systems where the inevitable thermal fluctuations are less likely to reduce the observed $T_c$.