Chiral and nodal superconductors in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi><mml:mtext>−</mml:mtext><mml:mi>J</mml:mi></mml:mrow></mml:math> model with valley contrasting flux on a triangular moiré lattice
Boran Zhou, Ya-Hui Zhang
Abstract
Recent experimental progress has made it possible to simulate spin-1/2 Hubbard model on triangular lattice in moir\'e materials formed by transition metal dichalcogenide (TMD) heterobilayer or homobilayer. In twisted TMD homobilayer, a vertical electric field can induce a valley contrasting flux in the hopping term. In this paper we study possible superconductors from a $t\text{\ensuremath{-}}J$ model with valley contrasting flux $\mathrm{\ensuremath{\Phi}}$ using the slave boson mean-field theory. We obtain a phase diagram with doping $x$ and $\mathrm{\ensuremath{\Phi}}$. A finite $\mathrm{\ensuremath{\Phi}}$ breaks spin rotation symmetry and the pairing symmetry is a superposition of spin singlet $d\ensuremath{-}id$ and spin triplet $p+ip$. There are two topological phase transitions when tuning $\mathrm{\ensuremath{\Phi}}$ from 0 to $\ensuremath{\pi}$, with three Dirac nodes at one transition and one single Dirac node at the other transition. We also discuss the effects of Van Hove singularity and a three-site correlated hopping term on the pairing strength. Lastly, we demonstrate that a small anisotropy term breaking the ${C}_{3}$ rotation can lead to a time-reversal invariant nodal superconductor connected to the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductor on square lattice.