Valley-dimensionality locking of superconductivity in cubic phosphides.

Two-dimensional superconductivity is primarily realized in atomically thin layers through extreme exfoliation, epitaxial growth, or interfacial gating. Apart from their technical challenges, these approaches lack sufficient control over the Fermiology of superconducting systems. Here, we offer a Fermiology-engineering approach, allowing us to desirably tune the coherence length of Cooper pairs and the dimensionality of superconducting states in arsenic phosphides As _x P _{1- x} under hydrostatic pressure. We demonstrate how this turns these compounds into tunable two-dimensional superconductors with a dome-shaped phase diagram even in the bulk limit. This peculiar behavior is shown to result from an unconventional valley-dimensionality locking mechanism, driven by a delicate competition between three-dimensional hole-type and two-dimensional electron-type energy pockets spatially separated in momentum space. The resulting dimensionality crossover is further discussed to be systematically controllable by pressure and stoichiometry tuning. Our findings pave a unique way to realize and control superconducting phases with special pairing and dimensional orders.