Two-energy-gap preformed-pair scenario for cuprate superconductors: Implications for angle-resolved photoemission spectroscopy Chih-Chun Chien, 1 Yan He, 1 Qijin Chen, 2,1 and K. Levin 1 1 Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA 2 Department of Physics and Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China Received 15 April 2009; published 25 June 2009 We show how, within a preformed-pair scenario for the cuprate pseudogap, the nodal and antinodal re- sponses in angle-resolved photoemission spectroscopy necessarily have very different temperature T depen- dences. We examine the behavior and the contrasting T dependences for a range of temperatures both below and above T c . Previously, the distinct nodal and antinodal responses have provided strong support for the “two-gap scenario” of the cuprates in which the pseudogap competes with superconductivity. Instead, our theory supports a picture in which the pseudogap derives from pairing correlations, identifying the two-gap components with noncondensed and condensed pairs. Our calculations are based on a microscopic diagram- matic approach for addressing pairing correlations in a regime where the attraction is stronger than BCS and the coherence length is anomalously short. This many body theory-based scheme takes as a starting point the BCS ansatz for the ground-state wave function and incorporates finite temperature effects through coupled equations for the single particle and pair propagators or T matrix. It leads to reasonably good agreement with a range of different photoemission measurements in the moderately underdoped regime and we emphasize that here there is no explicit curve fitting. We briefly address the more heavily underdoped regime in which the behavior is more complex. DOI: 10.1103/PhysRevB.79.214527 PACS numbers: 74.20.z, 74.25.Jb, 74.72.Hs, 79.60.i I. INTRODUCTION A. Background literature An important dichotomy is emerging in descriptions of the mysterious pseudogap phase of the cuprates which has resulted in different theoretical scenarios. 1 At the heart of this dispute is whether the pseudogap observed in the normal state is derived from the superconductivity itself or whether it results from a competing, but somewhat elusive order pa- rameter. Experiments i which directly study this anomalous normal phase have provided evidence for both points of view. 2–5 However, there is an even larger class of recent ex- periments ii which address the superconducting phase. These are based on angle-resolved photoemission 6–8 and Ra- man scattering 9,10 as well as scanning tunneling microscopy. 11–14 They quite generally reveal that there are two distinct temperature dependences associated with the be- havior of the spectral function and related properties in the nodal and antinodal regions of momentum space. The nodal response appears to reflect superconducting order whereas the antinodal response is much less sensitive to T c . For this reason, it is speculated that the pseudogap may derive from a competing order parameter. Finally, there is a third class of experiments iii which probe the behavior as the system evolves from above to just below T c and establish that the transition is clearly second order. Here, for example, one sees a very smooth evolution of the angle-resolved photoemission spectroscopy ARPES response in the antinodal direction. 15,16 Many other properties 17,18 which depend on the excitation gap show no clear signature of T c . This is generally interpreted as evidence in favor of a precursor- superconductivity origin to the pseudogap. It is the last two classes of experiments which are the focus of this paper. Indeed, there is very little in the theoret- ical literature which addresses these phenomena. Rather the emphasis has been on the ground state or on the normal, pseudogap phase. Our goal is to show how to reconcile, in particular, the experiments of class ii with a preformed-pair scenario. Moreover, it is possible that the arguments pre- sented here can be viewed as “modular” in the sense of ap- plying to alternate precursor-superconductivity approaches such as the “phase fluctuation” approach 19 or the resonant valence bond RVB scheme. 20 We stress that there appear to be no counterpart studies of the intermediate temperature broken symmetry state within the more widely espoused phase fluctuation scheme. 19 Our explanation of the di- chotomy is built around a picture in which the short coher- ence length cuprates are somewhere between BCS and Bose- Einstein condensed BEC systems. This crossover scheme seems to be gaining in support 1,21 and is now widely studied in the cold Fermi gases. 17,22,23 Our emphasis here is on mod- erately underdoped cuprates where at the lowest tempera- tures the spectral properties appear to conform to that of a simple d-wave BCS-like state. 7,24 While the behavior ap- pears to be much more complex in the heavily underdoped regime, nevertheless, there is a smooth evolution with dop- ing and all the indications for distinct nodal and antinodal responses are present at moderate underdoping. Thus, we feel the same qualitative physics regarding the origin of the pseudogap is appropriate to both moderately and heavily un- derdoped cuprates. We build on a d-wave BCS-like ground state where the variational parameters are determined in conjunction with a self-consistency condition for the chemical potential, . This self-consistent treatment of  which is close to but different from E F  is necessary 25,26 to accommodate the relatively short coherence length of the cuprates. Our contribution in the past 17,27 has been to address the associated finite tempera- PHYSICAL REVIEW B 79, 214527 2009 1098-0121/2009/7921/21452711 ©2009 The American Physical Society 214527-1