Quantum criticality in the metal-superconductor transition of interacting Dirac fermions on a triangular lattice

TL;DR

This paper uses large-scale quantum Monte Carlo simulations to study the quantum critical behavior of a Dirac fermion system transitioning from a semimetal to a superconductor on a triangular lattice, revealing critical exponents consistent with chiral XY universality.

Contribution

It provides the first accurate estimation of critical exponents for the Dirac fermion superconductor transition on a triangular lattice, confirming theoretical predictions of chiral XY universality class.

Findings

Critical exponents match those of the chiral XY class.

Superconducting order parameter exhibits expected scaling behavior.

Emergent U(1) symmetry observed at the transition.

Abstract

We investigate a semimetal-superconductor phase transition of two-dimensional Dirac electrons at zero temperature by large-scale and essentially unbiased quantum Monte Carlo simulations for the half-filled attractive Hubbard model on the triangular lattice, in the presence of alternating magnetic $\pi$-flux, that is introduced to construct two Dirac points in the one-particle bands at the Fermi level. This phase transition is expected to describe quantum criticality of the chiral XY class in the framework of the Gross-Neveu model, where, in the ordered phase, the $U(1)$ symmetry is spontaneously broken and a mass gap opens in the excitation spectrum. We compute the order parameter of the s-wave superconductivity and estimate the quasiparticle weight from the long-distance behavior of the single-particle Green's function. These calculations allow us to obtain the critical exponents of this transition in a reliable and accurate way. Our estimate for the critical exponents is in good agreement with those obtained for a transition to a Kekul\'{e} valence bond solid, where an emergent $U(1)$ symmetry is proposed [Z.-X. Li et al., Nat. Commun. 8, 314 (2017)].