Amperean pairing and the pseudogap phase of cuprate superconductors

The enigmatic pseudogap phase in underdoped cuprate high T_c superconductors has long been recognized as a central puzzle of the T_c problem. Recent data show that the pseudogap is likely a distinct phase, characterized by a medium range and quasi-static charge ordering. However, the origin of the ordering wavevector and the mechanism of the charge order is unknown. At the same time, earlier data show that precursive superconducting fluctuations are also associated with this phase. We propose that the pseudogap phase is a novel pairing state where electrons on the same side of the Fermi surface are paired, in strong contrast with conventional BCS theory which pair electrons on opposite sides of the Fermi surface. In this state the Cooper pair carries a net momentum and belong to a general class called pair density wave (PDW). The microscopic pairing mechanism comes from a gauge theory formulation of the resonating valence bond (RVB) picture, where electrons traveling in the same direction feel an attractive force in analogy with Ampere's effects in electromagnetism. We call this Amperean pairing. Charge order automatically appears as a subsidiary order parameter. Our theory gives a prediction of the ordering wavevector which is in good agreement with experiment. Furthermore, the quasiparticle spectrum from our model explains many of the unusual features reported in photoemission experiments. The Fermi arc and the unusual way the tip of the arc terminates also come out naturally. We also discuss how the onset of the Kerr effect in this state can be accommodated. Finally, we propose an experiment which can directly test the notion of Amperean pairing.Comment: (v4) added phase diagram, Appendix A on the incompatibility of CDW model, and more discussion of low-temperature properties; (v3) expanded supplementary section, added figures and discussion on Fermi arc; (v2) added references, improved figures, corrected typo in Eq.(4

Pseudogaps in Underdoped Cuprates

It has become clear in the past several years that the cuprates show many unusual properties, both in the normal and superconducting states, especially in the underdoped region. In particular, gap-like behavior is observed in magnetic properties, c-axis conductivity and photoemission, whereas in-plane transport properties are only slightly affected by the pseudogap. I shall argue that these experimental evidences must be viewed in the context of the physics of a doped Mott insulator and that they support the notion of spin charge separation. I shall review recent theoretical developments, concentrating on studies based on the t-J model. I shall describe a model based on quasiparticle excitations, which predicts the doping dependence of T_c and anomalous energy-gap-to-T_c ratios. Finally, I shall outline how the model may be derived from a microscopic formulation of the t-J model. After a brief review of the U(1) formulation, I shall explain some of the difficulties encountered there, and how a new SU(2) formulation can resolve some of the difficulties.Comment: 9 pages, 4 figure

Staggered-flux normal state in the weakly doped t-J model

A normal (non-superconducting) ground state of the t-J model may be variationally approximated by a Gutzwiller-projected wave function. Within this approximation, at small hole doping near half-filling, the normal state favors staggered-flux ordering. Such a staggered-flux state may occur in vortex cores of underdoped high-temperature cuprate superconductors. From comparing the energies of the staggered-flux state and of the superconducting state, we numerically obtain the condensation energy. Extracting the superfluid density directly from the projected superconducting wave function, we can also estimate the coherence length at zero temperature.Comment: 5 pages, 4 figure

A Proposal to Use Neutron Scattering to Measure Scalar Spin Chirality Fluctuations in Kagome Lattices

In the theory of quantum spin liquids, gauge fluctuations are emergent excitations at low energy. The gauge magnetic field is proportional to the scalar spin chirality, S1.(S2xS3). It is therefore highly desirable to measure the fluctuation spectrum of the scalar spin chirality. We show that in the Kagome lattice with a Dzyaloshinskii-Moriya term, the fluctuation in Sz which is readily measured by neutron scattering contains a piece which is proportional to the chirality fluctuation.Comment: 8 Pages, 2 Figure