A unified tight-binding description of the electronic structure and Ising protection of superconductivity in misfit layered compounds

Abstract

Misfit layered compounds (MLCs) offer a unique bulk platform for realizing exotic quantum states typically associated with two-dimensional transition-metal dichalcogenides (TMDs), most notably Ising-protected superconductivity. Yet a theoretical description capturing their electronic structure beyond the simplistic picture of electronically isolated TMD layers has been lacking. Here, we develop a unified tight-binding model for metal dichalcogenide-based MLCs, parameterized by extensive density-functional theory (DFT) calculations across multiple structural configurations and chemical compositions. We show that the intervening tetragonal layers play an active role beyond charge reservoirs: they mediate a significant interlayer spin-orbit coupling entirely absent in the standard rigid-band picture. This emergent interlayer spin-orbit coupling is essential for reproducing the DFT band structure of bulk MLCs and, when incorporated into Bogoliubov--de Gennes calculations, provides a microscopic mechanism for the Ising protection of superconductivity by strongly enhancing the in-plane critical field. Our framework establishes MLCs as a distinct class of three-dimensional materials with intrinsically coupled layers and emergent spin-orbit phenomena.