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Microscopic Phase-Transition Framework for Gate-Tunable Superconductivity in Monolayer WTe$_2$

F. Yang, G. D. Zhao, Y. Shi, L. Q. Chen

Abstract

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.

Microscopic Phase-Transition Framework for Gate-Tunable Superconductivity in Monolayer WTe$_2$

Abstract

The recently reported gate-tunable superconductivity in monolayer WTe [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 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 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.

Paper Structure

This paper contains 8 equations, 3 figures.

Figures (3)

  • Figure 1: Simulation results of superconductivity in ML WTe$2$ at relatively high carrier density. ( a) $T_c$ (dashed) and $T_{\rm os}$ (solid) for weak disorder ($\gamma=0.12$ meV) and strong disorder ($\gamma=3.2$ meV). ( b) Temperature dependence of the SC gap under strong disorder ($\gamma=3.2$ meV) at two different densities. ( c) Bare (curve) and BKT-renormalized (circles) superfluid density corresponding to the results in panel ( b). ( d, e) Zero-temperature gap $|\Delta(0)|$ and the temperature difference $T_{\rm os}-T_c$ versus density and disorder, respectively. The pairing potential is fixed and specified in the Supplemental Materials.
  • Figure 2: ( a) DFT calculation of the band structure of ML WTe$_2$. ( b), ( c), inset of ( c) and ( d): experimentally measured $T_c$ from Refs. song2024unconventional, fatemi2018electrically, sajadi2018gate and PhysRevResearch.7.013224, respectively, compared with our calculated $T_c$ (dashed curves) obtained by fitting $E_g$ and disorder strength. Crosses in ( b) denote our calculated $T_{\rm os}$. Inset of ( b): experimentally measured Nernst signal $V_n(T=45~\text{mK}, H=23~\text{mT})$ in Ref. song2024unconventional. The orange line marks our calculated $n_c$ where $T_{\rm os}$ vanishes, and the light blue region indicates the regime where our $T_{\rm os}-T_c$ [Fig. \ref{['figyc3']}( b)] is maximized. The chain curve in ( d) is extracted from the experimentally observed superconductivity that survives at $H=50$ mT PhysRevResearch.7.013224.
  • Figure 3: Calculation of ( a) the critical field $H_{c2}(0)$ and ( b) the temperature dependence of $T_{\rm os}-T_c$ as a function of density, corresponding to simulation in Fig. \ref{['figyc2']}( b). Inset of ( a): experimentally measured Nernst signal $V_n(T=45~\text{mK})$ (in unit of nV) from Ref. song2024unconventional; the dashed line indicates the field at which the signal vanishes in experiment.