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

Abstract

We compute the spectral function $A(\mathbf{k},\omega )$ 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 $A(\mathbf{k},\omega )$ is most strongly affected by inhomogeneity near the point $\mathbf{k}=(\pi ,0)$ (and the symmetry-related points). For $c_{\beta }\simeq 0.5$, $A(\mathbf{k},\omega )$ 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 $A(\mathbf{k},\omega )$ 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.

arXiv commentAccepted for publication in Phys. Rev. B. Scheduled Issue: 01 Jan 2008. 26 Pages and 10 figures

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