Three-dimensional Ising superconductors designed via inversion-symmetry breaking in intercalated NbSe${}_2$ and NbTe${}_2$

Abstract

Ising superconductors exhibit in-plane upper critical fields far exceeding the Pauli paramagnetic limit, a hallmark first established in two-dimensional (2D) monolayer transition-metal dichalcogenides (TMDs). This field resilience requires the coexistence of strong spin-orbit coupling (SOC) and broken inversion symmetry, yet three-dimensional (3D) bulk realizations remain scarce because equilibrium stacking typically restores inversion symmetry. Here we demonstrate that intercalation provides a practical route to break this symmetry, systematically designing 16 NbSe${}_2$- and NbTe${}_2$-based compounds from four intercalants (In, Sn, Pb, Bi) across two polytypes: non-centrosymmetric $P\bar{6}m2$ and centrosymmetric $P{6}_3/mmc$. Four compounds in the $P\bar{6}m2$ phase, InNbSe${}_2$, SnNbSe${}_2$, PbNbSe${}_2$, and PbNbTe${}_2$, emerge as promising 3D Ising superconductors. They exhibit SOC splittings of 80-100 meV near the Fermi level, dominant out-of-plane spin polarization, and anisotropic superconductivity with $T_c=2.6$-$5.4$ K. Notably, spin-texture analysis reveals that the efficiency of Ising protection is governed not by the magnitude of SOC splitting alone but by the out-of-plane spin purity on the Fermi surface. Bogoliubov-de Gennes (BdG) calculations predict in-plane upper critical fields reaching 4-7 times the Pauli limit. These findings establish intercalation as a promising symmetry-engineering strategy for realizing 3D Ising superconductors in TMDs.