Interplay between unidirectional and bidirectional charge-density-wave orders in underdoped cuprates

Abstract

We analyze the interplay between charge-density-wave (CDW) orders with axial momenta (Q, 0) and (0, Q) (∆x and ∆y respectively), detected in the underdoped cuprates. The CDW order in real space can be uni-directional (either ∆x or ∆y is non-zero) or bi-directional (both ∆x and ∆y are non-zero). To understand which of the two orders develop, we adopt the magnetic scenario, in which the CDW order appears due to spin-fluctuation exchange, and derive the Ginzburg-Landau action to the sixth order in ∆x and ∆y. We argue that, at the mean-field level, the CDW order is bi-directional at the onset, with equal amplitudes of ∆x and ∆y, but changes to uni-directional inside the CDW phase. This implies that, at a given temperature, CDW order is uni-directional at smaller dopings, but becomes bi-directional at larger dopings. This is consistent with recent x-ray data on YBCO, which detected tendency towards bi-directional order at larger dopings. We discuss the role of discrete symmetry breaking at a higher temperature for the interplay between bi-directional and uni-directional CDW orders and also discuss the role of pair-density-wave (PDW) order, which may appear along with CDW. We argue that PDW with the same momentum as CDW changes the structure of the bi-directional charge order by completely replacing either ∆x or ∆y CDW components by PDW. However, if an "Amperean" PDW order, which pairs fermions with approximately the same momenta, is also present, both ∆x and ∆y remain non-zero in the bidirectional phase, albeit with non-equal amplitudes. This is again consistent with x-ray experiments, which at larger doping found non-equal ∆x and ∆y in every domain.

Dynamical charge density waves rule the phase diagram of cuprates

“…This is the well-known frustrated-phase-separation instability [27,28] underlying the formation of CDWs near optimal doping [6,24,25]. We notice that, although λ might have a magnetic contribution, the present mechanism of CDW formation, contrary to other proposals [30][31][32][33], does not require the proximity to a magnetic QCP. The same CDW-mediated interactions are also active in the Cooper channel, providing a high-temperature d-wave pairing mechanism [34].…”

Charge-stripe crystal phase in an insulating cuprate

“…In sharp contrast to the charge ordered phases in the pseudogap phase manifested at low energies near the Fermi level, the striped hole crystal phase is detected in the insulating state and likely tied to the spatial modulations of the high-energy charge transfer gap. Given the long-standing debate on whether the stripes (checkerboard) that break (preserve) the C4 rotational symmetry of the crystal are favored in cuprates 31,32 , our work provides a real-space evidence that clearly indicates the preference of lightly-doped cuprates to form charge stripes over the checkerboard. Our observation of large phase-coherent regions indicates that the striped hole crystal may exist as a stable ground state of a lightly-doped Mott insulator stabilized by long-range Coulomb interaction 3 .…”

Influence of the spatially inhomogeneous gap distribution on the quasiparticle current inc-axis junctions involvingd-wave superconductors with charge density waves

“…The observations demonstrate either a unidirectional (stripe) or a bidirectional (checkerboard) configuration of two-dimensional CDWs (or even three-dimensional ones [38,42]). Their attribution [43,44] and mutual interplay are also a hot issue [45][46][47]. The violation of the C 4 symmetry and the emergence of the C 2 (nematic or smectic) charge order in cuprates compose a very interesting topic, which is intensively studied concerning not only cuprates but also other materials [37,[48][49][50][51][52][53][54][55][56][57][58][59][60][61].…”