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Title: The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond
We review the physics of pair-density wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as charge-density wave, and discuss related vestigial states that emerge as a consequence of partial melting of the PDW order. We review and critically discuss the mounting experimental evidence for such PDW order in the cuprate superconductors, the status of the theoretical microscopic description of such order, and the current debate on whether the PDW is a mother order or another competing order in the cuprates. In addition, we give an overview of the weak coupling version of PDW order, Fulde–Ferrell–Larkin–Ovchinnikov states, in the context of cold atom systems, unconventional superconductors, and noncentrosymmetric and Weyl materials.
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Publication Date:
Journal Name:
Annual Review of Condensed Matter Physics
Page Range or eLocation-ID:
231 to 270
Sponsoring Org:
National Science Foundation
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  5. Abstract

    A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effectivet-J-Vmodel, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around theKand$${K}^{\prime}$$Kpoints in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central chargec ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.