RSAVS superconductors: Materials with a superconducting state that is robust against large volume shrinkage

The transition temperature (${T}_{\mathrm{C}}$) between normal and superconducting states usually exhibits a dramatic increase or decrease with increasing applied pressure. Here we present, in contrast, a type of superconductor that exhibits the exotic feature that ${T}_{\mathrm{C}}$ is robust against large volume shrinkages (RSAVS, so naming them ``RSAVS superconductors'') induced by applied pressure. Extraordinarily, our previous studies found that the ${T}_{\mathrm{C}}$ in the two materials stays almost constant over a large pressure range, e.g., over 136 GPa in the ${(\mathrm{TaNb})}_0.67{(\mathrm{HfZrTi})}_0.33$ high-entropy alloy and 141 GPa in the NbTi commercial alloy. Here, we show that the RSAVS behavior also exists in another high-entropy alloy, ${(\mathrm{ScZrNbTa})}_0.6{(\mathrm{RhPd})}_0.4$, and in superconducting elemental Ta and Nb, indicating that this behavior occurs universally in a certain kind of superconductor, composed of only transition metal elements, with a body-centered cubic lattice. Our electronic structure calculations indicate that in the RSAVS state the contribution of the degenerate ${d}_{{x}²\ensuremath{-}{y}²}$ and ${d}_{{z}²}$ orbital electrons remains almost unchanged at the Fermi level, suggesting that these are the electrons that may play a crucial role in stabilizing the ${T}_{\mathrm{C}}$ in the RSAVS state. We preliminarily analyzed the reasonability and validity of this suggestion by the Homes law.