Model for the temperature dependence of the quasiparticle interference pattern in the measured scanning tunneling spectra of underdoped cuprate superconductors

Abstract

In this paper we explore the behavior of the quasiparticle interference (QPI) pattern of scanning tunneling microscopy as a function of temperature $T$, for moderately underdoped cuprates. After ensuring a minimal consistency with angle-resolved photoemission spectroscopy, we find that the QPI pattern is profoundly sensitive to quasiparticle coherence and that it manifests two energy-gap scales. In particular, we find that the superconducting QPI pattern vanishes at the same temperature as that at which the Fermi arcs appear. Experimental support for this conclusion comes from the observation of a nearly dispersionless QPI pattern which has been observed to appear above ${T}_{c}$ in moderately underdoped cuprates. To illustrate the important two energy scale physics we present predictions of the QPI-inferred energy gaps as a function of $T$ for future experiments on moderately underdoped cuprates. This defines the so-called ``Bogoliubov arcs,'' which we find have an extinction point controlled by the size of the superconducting order parameter. This extinction, thus, seems unrelated to the magnetic zone boundary. Moreover, the calculated Bogoliubov arcs persist across the full nodal region, as might be expected, since that is where the superconductivity is thought to be dominant. A second larger energy scale is implied from extrapolation to the antinodes, presuming a simple $d$-wave shape and that the temperatures are not too close to ${T}_{c}$. This corresponds to the pseudogap energy scale in the literature.