Microscopic Phase-Transition Framework for Gate-Tunable Superconductivity in Monolayer WTe$_2$
The recently reported gate-tunable superconductivity in monolayer WTe$_2$ [Science 362, 922 (2018); Science 362, 926 (2018); Nat. Phys. 20, 269 (2024); PRR 7, 013224 (2025)] exhibits several striking anomalies beyond the standard paradigm, including a contrasting carrier-density dependence of the transition temperature $T_c$ in weakly and strongly disordered regimes and more surprisingly, the sudden disappearance of superconducting fluctuations below a critical carrier density. To understand these features, we go beyond mean-field theory and develop a microscopic framework that treats the gap and superfluid density by explicitly and self-consistently incorporating both Nambu-Goldstone phase fluctuations and Berezinskii-Kosterlitz-Thouless fluctuations. We show that these fluctuations are minimal in the weak-disorder regime but become crucial under strong disorder, where the zero-temperature gap renormalized by NG quantum fluctuations becomes density-dependent while the BKT fluctuations drive the $T_c$ below the gap-closing temperature. Simulations within this unified framework combining with the density-functional-theory input to account for the excitonic instability quantitatively reproduced nearly all key experimental observations, providing a consistent understanding of reported anomalies.