Chiral superconductivity in the doped triangular-lattice Fermi-Hubbard model in two dimensions

Vinicius Zampronio1,2 and Tommaso Macrì3,2

1Institute for Theoretical Physics, Utrecht University, 3584CS Utrecht, Netherlands
2Departamento de Física Teórica e Experimental, Federal University of Rio Grande do Norte 59078-950 Natal-RN, Brazil
3ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA

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The triangular-lattice Fermi-Hubbard model has been extensively investigated in the literature due to its connection to chiral spin states and unconventional superconductivity. Previous simulations of the ground state of the doped system rely on quasi-one-dimensional lattices where true long-range order is forbidden. Here we simulate two-dimensional and quasi-one-dimensional triangular lattices using state-of-the-art Auxiliary-Field Quantum Monte Carlo. Upon doping a non-magnetic chiral spin state, we observe evidence of chiral superconductivity supported by long-range order in Cooper-pair correlation and a finite value of the chiral order parameter. With this aim, we first locate the transition from the metallic to the non-magnetic insulating phase and the onset of magnetic order. Our results pave the way towards a better understanding of strongly correlated lattice systems with magnetic frustration.

Chiral superconductivity is a fascinating new phenomenon where Cooper pairs exhibit motion in a direction determined by their spin orientation, resulting in an intriguing interplay between spin and motion. One remarkable characteristic of chiral superconductors is the presence of robust chiral edge currents that remain unaffected by impurities, making them highly useful for applications in quantum computing. Chirality commonly arises in magnetic-frustrated lattice systems, characterized by interactions between magnetic moments that cannot be mutually satisfied, leading to complex and disordered magnetic states such as quantum spin liquids. The behavior of chiral spin states in frustrated lattices can be effectively described by the Fermi-Hubbard model, a fundamental concept in condensed-matter physics. The Hubbard Hamiltonian, which accounts for on-site interactions, extends beyond conventional band theory and successfully captures the intricate physics of Mott insulators, quantum spin liquids, and unconventional superconductors, although our understanding of these systems remains incomplete. Despite its simplicity, the Hubbard model is analytically tractable only in a few scenarios, and numerical methods are generally preferred. In our study, we utilized Quantum Monte Carlo simulations to investigate the Hubbard model on the triangular lattice, the simplest form of a frustrated lattice. Our results demonstrate the existence of a non-magnetic chiral spin state at intermediate interactions and at half filling. Moreover, below half filling, we observe the emergence of chiral superconductivity. Significantly, our Quantum Monte Carlo method enables simulations of two-dimensional systems and, for the first time, provides evidence of true long-range order in the ground state of this particular system.

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[2] Ji-Si Xu, Zheng Zhu, Kai Wu, and Zheng-Yu Weng, "Hubbard Model on Triangular Lattice: Role of Charge Fluctuations", arXiv:2306.11096, (2023).

[3] Yang Yu, Shaozhi Li, Sergei Iskakov, and Emanuel Gull, "Magnetic phases of the anisotropic triangular lattice Hubbard model", Physical Review B 107 7, 075106 (2023).

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