Amperean Pairing and the Pseudogap Phase of Cuprate Superconductors

Abstract

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 quasistatic charge ordering. However, the origin of the ordering wave vector 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 Bardeen-Cooper-Schrieffer theory which pairs electrons on opposite sides of the Fermi surface. In this state the Cooper pair carries a net momentum and belongs to a general class called pair density wave. The microscopic pairing mechanism comes from a gauge theory formulation of the resonating valence bond (RVB) picture, where spinons 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 even when long-range pair order is destroyed by phase fluctuations. Our theory gives a prediction of the ordering wave vector 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, the unusual way the tip of the arc terminates, and the relation of the spanning vector of the arc tips to the charge ordering wave vector also come out naturally. Finally, we propose an experiment that can directly test the notion of Amperean pairing. DOI: 10.1103/PhysRevX.4.031017 Subject Areas: Condensed Matter Physics, SuperconductivitySince the early days of cuprate superconductivity research, the pseudogap phase has been identified as a central piece of the high-T c puzzle [1]. The pseudogap opens below a temperature T Ã much above T c in underdoped cuprates, and it is visible in the spin susceptibility as detected by the Knight shift, in tunneling spectroscopy and in c-axis conductivity. Angle-resolved photoemission (ARPES) shows that the pseudogap opens in the antinodal region near ð0; πÞ (we set the lattice constant a to unity), leaving behind ungapped "Fermi arcs" centered around the nodes. Recent x-ray scattering data [2][3][4][5] reveal that the pseudogap is likely to be a distinct phase, characterized by the onset of a charge density wave (CDW) with wave vectors at ð0; AEδÞ and ðAEδ; 0Þ, where δ decreases with increasing doping, thus confirming evidence for charge order found earlier by scanning tunneling microscope (STM) [6][7][8][9] and nuclear magnetic resonance (NMR) experiments [10]. Recent advances include STM and x-ray studies on the same Bi 2 Sr 2 CaCu 2 O 8þx (Bi-2212) samples [11]. Other signatures include Kerr rotation [12], the emergence of anisotropy in the Nernst effect, etc. [13]. (Another set of exp...

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

“…4(c), similar to a recent theoretical proposal (see, e.g., Ref. [90]). The inhomogeneity is mainly observed with t 0, corresponding to the hole-doped cuprates.…”

“…In this region, a variety of spin-density [25,43,45,46,49,[83][84][85], charge-density [25,[86][87][88], pair-density wave [88][89][90][91], and stripe orders [30,32,51,52,85,[92][93][94][95] have been posited in both the Hubbard model and the simpler t-J model, with different types of orders seen in different simulation methods. These inhomogeneous phases are proposed to be relevant in the pseudogap physics [89,90,[96][97][98][99][100]. Recent projected entangled pair state (PEPS) studies of the t-J model and Hubbard model at large U 8 suggest that inhomogeneous and homogeneous states are near degenerate at low doping and can be stabilized with small changes in the model parameters [95,101].…”

Wiedemann-Franz law in the underdoped cuprate superconductorYBa2Cu3Oy

“…[25][26][27]40 Note that even though the vortex state ends at H c2 , superconducting fluctuations can exist beyond H c2 . 41,42 In YBCO at p = 0.11 -0.12, they are detected up to ∼ 30 T in the low-temperature magnetization 29,43 and Nernst signal.…”

Visualising the Charge and Cooper-Pair Density Waves in Cuprates

“…A. Lee has put forward a detailed argument that the anti-nodal gap present for T < T * , as observed by ARPES on Bi 2 Sr 2 CuO 6+δ , is compatible with a PDW and incompatible with a CDW or uniform d -wave pairing [184].…”