Effects of inhomogeneities and thermal fluctuations on the spectral function of a model d-wave superconductor

TL;DR

This study analyzes how inhomogeneities and thermal fluctuations influence the spectral function of a model high-temperature superconductor, revealing effects near specific momentum points and implications for spectral peak splitting.

Contribution

It introduces a model considering spatial inhomogeneity with regions of different gap sizes and examines their impact on the spectral function at various temperatures.

Findings

Inhomogeneity near (π,0) significantly alters the spectral function.

A large gap difference can produce split peaks, but unlikely causes of a second dispersion branch.

Thermal fluctuations broaden peaks and shift spectral weight to zero energy at high temperatures.

Abstract

We compute the spectral function $A({\bf k}, \omega)$ of a model two-dimensional high-temperature superconductor, at both zero and finite temperatures $T$. We assume that an areal fraction $c_{\beta}$ of the superconductor has a large gap $\Delta$ ($\beta$ regions), while the rest has a smaller $\Delta$ ($\alpha$ regions), both of which are randomly distributed in space. We find that $A({\bf k}, \omega)$ is most strongly affected by inhomogeneity near the point $\mathbf k = (\pi, 0)$ (and the symmetry-related points). For $c_\beta\simeq 0.5$, $A({\bf k}, \omega)$ exhibits two double peaks (at positive and negative energy) near this k-point if the difference between $\Delta_\alpha$ and $\Delta_\beta$ is sufficiently large in comparison to the hopping integral. The strength of the inhomogeneity required to produce a split spectral function peak suggests that inhomogeneity is unlikely to be the cause of a second branch in the dispersion relation. Thermal fluctuations also affect $A({\bf k}, \omega)$ most strongly near $\mathbf k = (\pi,0)$. Typically, peaks that are sharp at $T = 0$ become reduced in height, broadened, and shifted toward lower energies with increasing $T$; the spectral weight near $\mathbf k = (\pi, 0)$ becomes substantial at zero energy for $T$ greater than the phase-ordering temperature.