Superconductivity, Pair Density Wave, and Néel Order in Cuprates**Supported by the National Key Research and Development Program of China under Grant Nos. 2016YFA0300401 and 2016YFA0300202, the National Natural Science Foundation of China under Grant Nos. 11574134, 11874205 and 11774306, and the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDB28000000).

Abstract

We investigate in underdoped cuprates possible coexistence of the superconducting order at zero momentum and pair density wave (PDW) at momentum Q = (π, π) in the presence of a Néel order. By symmetry, the d-wave uniform singlet pairing dS0 can coexist with the d-wave triplet PDW dTQ, and the p-wave singlet PDW pQ can coexist with the p-wave uniform triplet pT0. At half filling, we find that the novel pSQ+ pT0 state is energetically more favorable than the dS0 + dTQ state. At finite doping, however, the dS0 + dTQ state is more favorable. In both types of states, the variational triplet parameters dTQ and pT0 are of secondary significance. Our results point to a fully symmetric Z2 quantum spin liquid with spinon Fermi surface in proximity to the Néel order at zero doping, which may not be adiabatically connected to the d-wave singlet superconductivity at finite doping with intertwining d-wave triplet PDW fluctuations and spin moment fluctuations. The results are obtained by variational quantum Monte Carlo simulations.