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Register a new userComplementary Pair Density Wave and d-wave Checkerboard Order in High Temperature Superconductors
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The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that there is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or globally through phase fluctuation should induce both orders in underdoped cuprates. The presence of both DWCB and PDW orders with $4a times 4a$ periodicity can explain the checkerboard modulation observed in FT-STS from STM and the puzzling dichotomy between the nodal and antinodal regions as well as the characteristic features such as non-dispersive Fermi arc in the pseudogap state.
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Pair density wave superconductivity constitutes a novel electronic condensate proposed to be realized in certain unconventional superconductors. Establishing its potential existence is important for our fundamental understanding of superconductivity in correlated materials. Here we compute the dynamical magnetic susceptibility in the presence of a pair density wave ordered state, and study its fingerprints on the spin-wave spectrum including the neutron resonance. In contrast to the standard case of d-wave superconductivity, we show that the pair density wave phase exhibits neither a spin-gap nor a magnetic resonance peak, in agreement with a recent neutron scattering experiment on underdoped La$_{1.905}$Ba$_{0.095}$CuO$_4$ [Z. Xu et al., Phys. Rev. Lett. 113, 177002 (2014)].
We investigate in underdoped cuprates possible coexistence of the superconducting (SC) order at zero momentum and pair density wave (PDW) at momentum ${bf Q}=(pi, pi)$ in the presence of a Neel order. By symmetry, the $d$-wave uniform singlet pairing $dS_0$ can coexist with the $d$-wave triplet PDW $dT_{bf Q}$, and the $p$-wave singlet PDW $pS_{bf Q}$ can coexist with the $p$-wave uniform triplet $pT_0$. At half filling, we find the novel $pS_{bf Q}+pT_0$ state is energetically more favorable than the $dS_0+dT_{bf Q}$ state. At finite doping, however, the $dS_0+dT_{bf Q}$ state is more favorable. In both types of states, the variational triplet parameters, $dT_{bf Q}$ and $pT_0$, are of secondary significance. Our results point to a fully symmetric $mathrm{Z_2}$ quantum spin liquid with spinon Fermi surface in proximity to the Neel order at zero doping, and to intertwined $d$-wave triplet PDW fluctuations and spin moment fluctuations along with the dominant $d$-wave singlet SC at finite doping. The results are obtained by variational quantum Monte Carlo simulations.
Neutron crystal-field spectroscopy experiments in the Y- and La-type high-temperature superconductors HoBa2Cu3O6.56, HoBa2Cu4O8, and La1.81Sr0.15Ho0.04CuO4 are reviewed. By this bulk-sensitive technique, information on the gap function is obtained from the relaxation behavior of crystal-field transitions associated with the Ho3+ ions which sit as local probes close to the superconducting copper-oxide planes. The relaxation data exhibit a peculiar change from a convex to a concave shape between the superconducting transition temperature Tc and the pseudogap temperature T* which can only be modelled satisfactorily if the gap function of predominantly d-wave symmetry includes an s-wave component of the order of 20-25%, independent of the doping level. Moreover, our results are compatible with an unusual temperature dependence of the gap function in the pseudogap region (Tc<T<T*), i.e., a breakup of the Fermi surface into disconnected arcs.
When the Mott insulating state is suppressed by charge carrier doping, the pseudogap phenomenon emerges, where at the low-temperature limit, superconductivity coexists with some ordered electronic states. Within the framework of the kinetic-energy-driven superconductivity, the nature of the pair-density-wave order in cuprate superconductors is studied by taking into account the pseudogap effect. It is shown that the onset of the pair-density-wave order does not produce an ordered gap, but rather a novel hidden order as a result of the interplay of the charge-density-wave order with superconductivity. As a consequence, this novel hidden pair-density-wave order as a subsidiary order parameter coexists with the charge-density-wave order in the superconducting-state, and is absent from the normal-state.
Using a dynamical cluster quantum Monte Carlo approximation we investigate the d-wave superconducting transition temperature $T_c$ in the doped 2D repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings $tp$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2times2$ plaquette and $tp$ is the hopping between the plaquettes. We find inhomogeneity suppresses $T_c$. The characteristic spin excitation energy and the strength of d-wave pairing interaction decrease with decreasing $T_c$ suggesting a strong correlation between these quantities.
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