Singlet, Triplet and Pair Density Wave Superconductivity in the Doped Triangular-Lattice Moir\'e System

TL;DR

This study uses density matrix renormalization group calculations to explore how a spin-dependent hopping phase influences superconductivity in a triangular-lattice Hubbard model relevant to twisted bilayer TMDs, revealing coexistence of various pairing states.

Contribution

It demonstrates the emergence of diverse superconducting phases, including singlet and triplet pairings with pair density waves, driven by the spin-dependent hopping phase in a triangular-lattice model.

Findings

Identification of quasi-long-range superconductivity with charge and spin density waves for 0<θ<π/3.

Discovery of dominant d-wave singlet and subdominant p-wave triplet pairings.

Observation of triplet pair density waves and coexistence with charge density wave and ferromagnetism for π/3<θ<2π/3.

Abstract

Recent experimental progress has established the twisted bilayer transition metal dichalcogenide (TMD) as a highly tunable platform for studying many-body physics. Particularly, the homobilayer TMDs under displacement field are believed to be described by a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase $\theta$. To explore the effects of $\theta$ on the system, we perform density matrix renormalization group calculations for the relevant triangular lattice t-J model. By changing $\theta$ at small hole doping, we obtain a region of quasi-long-range superconducting order coexisting with charge and spin density wave within $0<\theta<\pi/3$. The superconductivity is composed of a dominant spin singlet $d$-wave and a subdominant triplet $p$-wave pairing. Intriguingly, the $S_z=\pm 1$ triplet pairing components feature pair density waves. In addition, we find a region of triplet superconductivity coexisting with charge density wave and ferromagnetism within $\pi/3<\theta<2\pi/3$, which is related to the former phase at smaller $\theta$ by a combined operation of spin-flip and gauge transformation. Our findings provide insights and directions for experimental search for exotic superconductivity in twisted TMD systems.