Low-temperature anomaly and anisotropy of critical magnetic fields in transition-metal dichalcogenide superconductors

TL;DR

This work explains why spin-singlet superconductivity in monolayer transition-metal dichalcogenides can persist beyond the Pauli limit under an in-plane Zeeman field. By solving the Gor'kov equations for a two-valley Ising-TMD model, it identifies two spin-triplet pairing channels: an odd-frequency channel that destabilizes superconductivity and an even-frequency channel induced by the interaction of Zeeman field and Ising SOC that stabilizes it, with the latter arising from the cross product $m{eta} imes m{H}$. The paper connects these channels to the temperature- and orientation-dependent behavior of the superfluid density, revealing how Ising protection is anisotropic and enhanced at low temperatures. These results provide a microscopic mechanism for the observed Pauli-limit violation and clarify how additional spin-orbit components (e.g., Rashba) and impurities modulate the effect.

Abstract

We clarify why spin-singlet superconductivity persists in monolayer transition-metal dichalcogenides even in high magnetic fields beyond the Pauli limit. The phenomenon called Ising protection is caused by two magnetically active potentials: a Zeeman field and an Ising spin-orbit interaction. These potentials induce two spin-triplet pairing correlations in a spin-singlet superconductor. One belonging to odd-frequency symmetry class arises solely from a Zeeman field and always makes the superconducting state unstable. The other belonging to even-frequency symmetry class arise from the interaction between the two magnetic potentials and eliminate the instability caused by odd-frequency pairs. The presence or absence of even-frequency spin-triplet pairs explains the anisotropy of the Ising protection. The analytical expression of the superfluid weight enables us to conclude that even-frequency spin-triplet Cooper pairs support spin-singlet superconductivity in high Zeeman fields.

Figures (2)

• Figure 1: The critical magnetic field $H_{c}$ is plotted as a function of temperature $T$ for several values of the Ising spin-orbit interactions $\beta$ in (a). The arrow on the vertical axis indicates the Pauli limit $\mu_{\mathrm{B}} H_{p} = \Delta_{0}/\sqrt{2}$. The superfluid weights along the transition line in (a) is shown for $\bm{\beta} \parallel \bm{H}$ in (b) and $\bm{\beta} \perp \bm{H}$ in (c), where the strength of the Ising SOI is fixed at $\beta = \Delta_{0}$. The critical field $H_c(T)$ is obtained from the data in (a) for each temperature.
• Figure 2: The critical Zeeman field $H_{c}$ at $T = 0.1 T_{0}$ is plotted as a function of the angle $\theta$ between $\bm{\beta}$ and $\bm{H}$ for two values of the Ising spin-orbit interactions $\beta$. The angles $\theta = 0$ and $\theta = \pi / 2$ correspond to the out-of-plane and in-plane magnetic fields, respectively.