The interplay of phase fluctuations and nodal quasiparticles: ubiquitous Fermi arcs in two-dimensional d-wave superconductors

Abstract: We propose that the pseudogap and Fermi arcs can universally emerge due to thermal (static) phase fluctuations in the normal state of 2D nodal superconductors. By considering a minimal phenomenological model with spatially fluctuating superconducting pairings, we theoretically investigate the role of superconducting phase fluctuations in generic 2D superconductors with disorder-average technique. It is shown for nodal d-wave superconductors that phase fluctuations mediate the scattering of d-wave quasiparticles, smearing out the nodal quasiparticle gap and further leading to pseudogap and Fermi arcs. Moreover, the evolution of Fermi arcs is quantitatively described by two emergent characteristic length scales of the system: one is the finite superconducting correlation length $\xi(T)$, and another the nodal BCS coherence length $\xi_\text{BCS}(k)$. To support our theoretical findings, we numerically report the observation of Fermi arcs in a Hubbard-like model, proposed originally by X. Y. Xu and T. Grover in Phys. Rev. Lett. $\textbf{126}$, 217002 (2021), with sign-problem-free determinant quantum Monte Carlo (DQMC) calculations. As far as we noticed, it is the first time in a correlated model that Fermi arcs are identified with unbiased simulations. The numerical results for the scattering rate $\Gamma_\text{pf}$ of Cooper pairs exhibit excellent agreements with our theoretical predictions, where $\Gamma_\text{pf}$ is expected to scale linearly with the inverse superconducting correlation length $\xi(T)^{-1}$. This convergence of theory and numerics thereby strongly validates the universal connection between phase fluctuations and Fermi arcs in 2D nodal superconductors.