Theory of the striped superconductor

Abstract

We define a distinct phase of matter, a pair density wave (PDW), in which the superconducting order parameter, φ( r, r ′ ), varies periodically as a function of position such that when averaged over the center of mass position, ( r + r ′ )/2, all components of φ vanish identically. Specifically, we study the simplest, unidirectional PDW, the "striped superconductor," which we argue may be at the heart of a number of spectacular experimental anomalies that have been observed in the failed high temperature superconductor, La2−xBaxCuO4. We present a solvable microscopic model with strong electron-electron interactions which supports a PDW groundstate. We also discuss, at the level of Landau theory, the nature of the coupling between the PDW and other order parameters, and the origins and some consequences of the unusual sensitivity of this state to quenched disorder. I. A NEW PHASE OF MATTERSuperconductivity which arises from the pairing of electrons in time reversed states is well understood as a weak coupling "Fermi surface" instability -a consequence of arbitrarily weak effective attractive interactions. 1 In this paper we explore a new type of superconducting state, a "pair density wave" (PDW), which is a distinct state of matter, and which does not occur under generic circumstances in the weak coupling limit -it requires interactions in excess of a critical strength. The PDW spontaneously breaks the global gauge symmetry, in precisely the same way as a conventional superconductor does. Thus, the order parameter is a charge 2e complex scalar field, φ. However, it also spontaneously breaks some of the translational and point group symmetries of the host crystal, in the same way as a conventional charge-density wave (CDW). In a PDW, for fixed r − r ′ , the order parameteris a periodic function of the center of mass coordinate, R ≡ ( r + r ′ )/2. Here, ψ † σ ( r) is the electron creation operator at position r with spin polarization σ. We will focus on the case in which translational symmetry is broken only in one direction, i.e. a unidirectional PDW or equivalently a "striped superconductor."Accompanying the PDW there is, as we will show below, induced CDW order with half the period of the PDW. However, the PDW differs from a state of coexisting superconducting and CDW order 2 , which has also been previously called a "pair-density wave". 3 Unlike the pair-density-wave state of Ref.[2], the average value of the superconducting order parameter vanishes for the PDW state we discuss here. This is a defining symmetry property of this state. The PDW is more closely analogous to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state 5 which arises, under appropriate circumstances, when the electron gas is partially polarized by an applied magnetic field. However, explicit time-reversal symmetry breaking is an essential ingredient of the FFLO state, and is responsible for lifting the degeneracy ("nesting") between time-reversed pairs of quasiparticle states. In the absence of quenched disorder, the PDW state preserves time-r...

Fluctuations and phase transitions in Larkin-Ovchinnikov liquid-crystal states of a population-imbalanced resonant Fermi gas

“…It is not exhibited by crystalline FFLO phases with multiple non-collinear ordering wavevectors [78,79], that, in contrast are characterized by the long-range positional order and a nonzero pair-condensate, that is stable to thermal fluctuations. As with treatments of the LO state, where long-range order is assumed [113,118], in this algebraic LO phase we also find an unusual topological excitation -a half vortex bound to a half dislocation -in addition to integer vortices and dislocations. These are illustrated in Figs.8,9, and 10.…”

“…However, as we will see, despite enhanced fluctuations the LO state studied here does lead to a number of novel features recently discussed in the literature, such as the fractional vortex-dislocation defects, "charge"-4 superfluidity, Andreev-like mid-gap states, and many others [113,118].…”

Sensing Magnetic Fields with a Giant Quantum Wave

“…We highlight here one such application for which the SQCRAMscope is suited. The possible emergence of the unconventional pair-density-wave superfluid state in cuprate, high-T c superconductors and the theory of striped superconductors is the subject of much interest and speculation [47,48]. A key signature of such a state is the spontaneous generation of dc currents around domains of the emerging chiral superconductor as the temperature is tuned below the transition at approximately 30 K. Imaging transport may reveal these spontaneously generated current loops.…”

Quasi-one-dimensional pair density wave superconducting state

“…A negative sign induces a π phase shift between two neighboring LE liquids. It was shown by Berg et al 7 that two superconductors that are proximity coupled to each other through a 1D weakly doped Hubbard model have a broad regime of parameters (in particular, doping) in which the effective Josephson coupling is negative. Here, in order to incorporate this physics, we will introduce a set of Ising degrees of freedom mediating the interactions between the LE liquids which emulate different doping profiles of the electronic Luttinger liquids.…”