Thermodynamic-Limit Evidence for Chiral Superconductivity Induced by Doping Chiral Topological Phases

TL;DR

This paper provides thermodynamic-limit evidence for chiral superconductivity emerging from doped chiral topological states in a triangular Hofstadter-Hubbard model, revealing complex winding behaviors near the Mott transition.

Contribution

It introduces a tensor-network method capturing both superconducting and topological orders, demonstrating chiral superconductivity in a strongly correlated fermionic system.

Findings

Identification of a robust chiral spin liquid as a parent state

Observation of a uniform chiral superconducting phase upon doping

Detection of complex phase winding and topological features in the superconducting state

Abstract

The emergence of chiral superconductivity from strongly correlated Mott regimes in purely repulsive, genuinely two-dimensional fermionic systems poses a key challenge, particularly when topology and superconducting long-range order must be treated on equal footing. Here we provide direct thermodynamic-limit evidence for chiral superconductivity in the triangular Hofstadter-Hubbard model relevant to moir\'e materials. This is achieved by advancing a simplex tensor-network formulation that simultaneously captures superconducting long-range order and chiral topological order in interacting fermionic systems with intrinsic charge fluctuations. We show that a chiral spin liquid occupies a broad intermediate-$U$ regime, forming a robust undoped parent state. Upon hole doping, we identify a uniform chiral superconducting phase in the infinite system, diagnosed directly by a finite complex pairing order parameter and chiral entanglement spectrum. The superconducting phase exhibits an almost universal phase winding across a wide interaction-doping region, together with a distinct pocket of opposite winding near the Mott criticality. These results establish thermodynamic-limit chiral superconductivity emerging from doped chiral topological states, revealing richer winding competition near the Mott transition point of the undoped system while preserving a common chiral topological character throughout the superconducting region.