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Physical review. B./Physical review. B

Emergent pairing states and tunable symmetry in the anisotropic triangular lattice

Da-Fei Sun, Zuodong Yu, Weijian Li, Shun-Li Yu, Yuan Zhou

Published Apr 9, 2025• 0 citations
Publisher

Abstract

The superconducting pairing symmetry is significantly constrained by lattice symmetry, yet how this pairing symmetry evolves with changes in lattice symmetry remains unclear. In this study, through variational quantum Monte Carlo simulations on the Hubbard model, we investigate the evolution of the superconducting ground state on an anisotropic triangular lattice with smoothly tunable frustration. At half-filling, we identify a hidden ${C}_{6}$-like $s+d+id$-wave superconductivity, which breaks time-reversal symmetry, emerging for moderate frustrations. This occurs as the lattice symmetry transitions from ${C}_{4}$ to ${C}_{2}$, where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and $s+{d}_{xy}$-wave superconducting ground states dominate, respectively. Notably, we find an isotropic-like $d+id$-wave superconducting phase at ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.7$, much lower than the expected value ${t}^{\ensuremath{'}}/t=1$ predicted by most previous studies. At high electron doping levels, we further discover an unexpected quasi-one-dimensional ${d}_{xy}^{\ensuremath{'}}$-wave superconductivity characterized by strong pairing on the next-nearest-neighbor bond, despite the absence of direct hopping. The numerical data also reveal that pairing symmetries, belonging to distinct irreducible representations of the given point group, can mix together, beyond the conventional theories based on the linear gap equations.

DOI
10.1103/physrevb.111.134508

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In this thesis we try to understand the unconventional superconducting mechanism on cuprates and organic superconductors (or sodium cobaltates) which can be modeled by a two-dimensional square- and triangular-lattice Hubbard model respectively. The formation of the superconducting dome requires explanations of feasible scenarios. Generally speaking, pairing strength is provided by magnetic fl_x001D_uctuations in the strongly correlated region and the structure of the Fermi surface in this region will favor superconducting pairings with a certain type of symmetry. For the cuprate physics, a superconducting dome composed of d-wave pairings has been identified experimentally. We study the Hubbard model on square lattices and _x001C_find that the pairing strength is originated from anti-ferromagnetic instabilities, and the nearly nested Fermi surface with the square symmetry further supports the d-wave pairing. Moreover, our results show there is a quantum critical point (QCP) beneath the superconducting dome. The QCP is a zero-temperature instability which separates the Fermi liquid and pseudogap regions and exhibits the quantum _x001D_fluctuations which may lead to a high superconducting transition temperature. Above the QCP, a V-shape marginal Fermi liquid region associated with the quantum critical phenomena is also identi_x001C_fied. Using next-nearest-neighbor hopping, chemical potential, and temperature as control parameters, there is a line of Lifshitz transition associated with the change of topology of the Fermi surface. Along the Lifshitz line with t'<=0, the marginal Fermi liquid region prevails, the peak of density of states crosses the Fermi level, and the bare d-wave pairing susceptibility shows a universal scaling with the exponent consistent with theoretical proposals. For the triangular-lattice Hubbard model in the strongly correlated region, we _x001C_find a d+id superconducting pairing on the hole-doped side of the phase diagram. Here the pairing strength comes from the instabilities of the anti-ferromagnetic order (120-degree-spin structure), and the nested hexagon-deformed Fermi surface with the triangular symmetry further boosts the d+id symmetry. Due to the strong competition between electronic interactions and geometric frustrations, the superconductivity and other novel features of the system equal to or above half fi_x001C_lling requires future studies. The numerical tool we apply to study these systems is the dynamical cluster approximation with continuous-time quantum Monte Carlo as the solver. Our approach includes nonlocal correlations embedded in a mean _x001C_field host and is a most up-to-date and reliable approach in dealing with the above mentioned strongly correlated systems valid in the thermodynamic limit. Our _x001C_findings shine light on future investigations of the nature