We argue that the experimentally observed nonmonotonic gap in electron-doped cuprates at optimal doping is the lowest quasiparticle excitation energy in the coexisting antiferromagnetic (AF) and superconducting (SC) state. The idea is implemented by studying the coexistence of AF and SC orders with the t-t ′ -t ′′ -J model. Although the pairing gap itself is assumed to be the simplest d wave which is monotonic, we have found that the quasiparticle excitation gap in the coexisting state is nonmonotonic, with the maxima around the hot spots where the Fermi surface is missing due to the AF gap. Within the same framework of the coexisting state the spectral function is also calculated at optimal doping. The obtained results are all consistent with experiments.PACS numbers: 74.72.Jt, 74.20.Mn, 74.25.Jb, 74.25.Ha The pairing symmetry is a central issue for understanding the notable superconducting (SC) properties in cuprate superconductors. While for hole-doped compounds the pairing symmetry is generally accepted to be d wave, it is still under debate for electron-doped (edoped) ones. Originally it was thought to be s wave, 1 but later suggested to be d wave as in hole-doped materials, by a number of experimental measurements such as phase sensitive, 2 angle-resolved photoemission spectroscopy (ARPES), 3 penetration depth, 4 etc. On the other hand, recent experimental evidence disfavoring the typical d wave 5,6,7 or supporting a transition from d to s wave with increasing doping 8 was also found. In this regard, it is of great interest to notice the measurements by Raman scattering 5 and ARPES 6 on e-doped compounds Nd 2−x Ce x CuO 4 (NCCO) at x = 0.15 and Pr 1−x LaCe x CuO 4 (PLCCO) at x = 0.11, respectively. They are both on optimally doped samples and have reached the same conclusion, i.e., the observed gap does not fit the simplest commonly assumed d-wave function cos k x − cos k y , but exhibits a nonmonotonic behavior with the gap maxima locating midway between the Brillouin zone (BZ) boundaries and the zone diagonals.So far, the theoretical explanations for the so called nonmonotonic d-wave gap 5,6,9,10,11 are limited to extending the SC gap out of the simplest d wave, e.g., by inclusion of high-order d-wave harmonics.Here an alternative idea is proposed to explain the observed nonmonotonic gap. The new idea highlights the antiferromagnetic (AF) order in the SC phase, which is motivated by the following facts. First, in e-doped cuprates the AF order is robust to survive a broad doping range, which coexists with the SC order around the AF/SC phase boundary and even at optimal doping.
12,13Actually, for the SC samples of NCCO at x = 0.15, the Néel temperature T N is usually much higher than the SC transition temperature T c .12,14,15 Second, recent ARPES measurements have revealed the intriguing doping evolution of the Fermi surface (FS) in NCCO.16 It was found that at optimal doping the FS consists of two inequivalent pockets around (π, 0) and (π/2, π/2). This suggests the two-band modeling to study the SC pr...