Phenomenology of the low-energy spectral function in high-Tcsuperconductors

Abstract

We introduce a simple phenomenological form for the self-energy which allows us to extract important information from angle resolved photoemission data on the high Tc superconductor Bi2212. First, we find a rapid suppression of the single particle scattering rate below Tc for all doping levels. Second, we find that in the overdoped materials the gap ∆ at all k-points on the Fermi surface has significant temperature dependence and vanishes near Tc. In contrast, in the underdoped samples such behavior is found only at k-points close to the diagonal. Near (π, 0), ∆ is essentially T -independent in the underdoped samples. The filling-in of the pseudogap with increasing T is described by a broadening proportional to T − Tc, which is naturally explained by pairing correlations above Tc.PACS numbers: 71.25. Hc, 74.25.Jb, 74.72.Hs, 79.60.Bm Angle-resolved photoemission spectroscopy (ARPES) has played a major role in developing our understanding of the high T c superconductors. The momentum and frequency resolved information contained in the one-particle spectral function [1] probed by ARPES provides critical insights difficult to obtain from other techniques. However, an important open problem in interpreting ARPES data is the absence of simple representations of the spectral lineshape, analogous to the Drude formula for optical studies.In this paper, we take a step in this direction by introducing a simple phenomenological form for the selfenergy which captures much of the important low frequency information contained in the ARPES data for the normal, superconducting and pseudogap phases of high T c superconductors. We first test this on ARPES data at k F for overdoped Bi2212, from which we determine the T -dependence of the superconducting (SC) gap and the one-particle scattering rate, the latter found to decrease rapidly in the SC state, leading to the appearence of sharp quasiparticles at low temperatures.We then turn to underdoped Bi2212, where a highly anisotropic pseudogap is known to persist well above T c [2-4]. The magnitude of this gap and its smooth evolution through T c establish a strong connection between the normal state pseudogap and the SC gap below T c , and suggest that the pseudogap arises from pairing correlations in a state without long range phase coherence [5]. Here, we use our simple self energy to gain insight into the ARPES lineshape in the pseudogap regime. We find that near (π, 0) ∆ is T -independent, and the pseudogap fills in due to a T -dependent broadening which is naturally explained by pairing correlations above T c .Finally, we use our analysis to shed more light on the very recent surprising result that the pseudogap at different k-points turns off at different temperatures, leading to gapless arcs above T c which expand in length until the entire Fermi surface is recovered at T * [6]. We show below that the T -dependence of the underdoped lineshape away from (π, 0) is rather different, with the vanishing of the pseudogap controlled instead by a T -dependent ∆.The data analysed b...

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