Fermi arcs and pseudogap phase in a minimal microscopic model of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave superconductivity
Dheeraj Kumar Singh, Samrat Kadge, Yunkyu Bang, Pinaki Majumdar
Abstract
We conclusively show that a pseudogap state can arise at $T>{T}_{c}$, for reasonable pairing interaction strength, from order parameter fluctuations in a two-dimensional minimal model of $d$-wave superconductivity. The occurrence of the pseudogap requires neither strong correlation nor the presence of competing order. We study a model with attractive nearest-neighbor interaction and establish our result using a combination of a cluster-based Monte Carlo method for the order parameter field and a twisted-boundary scheme to compute the momentum-resolved spectral function. Apart from a dip in the density of states that characterizes the pseudogap, the momentum and frequency resolution on our effective lattice size $\ensuremath{\sim}160\ifmmode\times\else\texttimes\fi{}160$ allows two major conclusions: (i) at $T<{T}_{c}$, despite the presence of thermal phase fluctuations, the superconductor has only nodal Fermi points while all non-nodal points on the normal state Fermi surface show a two-peak spectral function with a dip at $\ensuremath{\omega}=0$, and (ii) for $T>{T}_{c}$, the Fermi points develop into arcs, characterized by a single quasiparticle peak, and the arcs connect up to recover the normal state Fermi surface at a temperature ${T}^{*}>{T}_{c}$. We show the variation of ${T}_{c}$ and ${T}^{*}$ with coupling strength and provide detailed spectral results at a coupling where ${T}^{*}\ensuremath{\sim}1.5{T}_{c}$.