Superconductivity, Pair Density Wave, and Néel Order in Cuprates

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 Neel order.By symmetry,the d-wave uniform singlet pairing dS0can coexist with the d-wave triplet PDW dTQ,and the p-wave singlet PDW pSQcan coexist with the p-wave uniform triplet pT0.At half filling,we find that the novel pSQ+pT0state is energeticall.y more favorable than the dS0+dTQstate.At finite doping,however,the dS0+dTQstate is more favorable.In both types of states,the variational triplet parameters dTQand pTo are of secondary significance.Our results point to a fully symmetric Z2quantum spin liquid with spinon Fermi surface in proximity to the Neel order at zero doping,which may not be adiabatically connected to the d-wave singlet superconductivity at Bnite doping with intertwining d-wave triplet PDW fluctuations and spin moment fluctuations.The results are obtained by variational quantum Monte Carlo simulations.