Quenched disorder and vestigial nematicity in the pseudogap regime of the cuprates

Abstract

The cuprate high-temperature superconductors have been the focus of unprecedentedly intense and sustained study not only because of their high superconducting transition temperatures, but also because they represent the most exquisitely investigated examples of highly correlated electronic materials. In particular, the pseudogap regime of the phase diagram exhibits a variety of mysterious emergent behaviors. In the last few years, evidence from NMR and scanning tunneling microscopy (STM) studies, as well as from a new generation of X-ray scattering experiments, has accumulated, indicating that a general tendency to short-rangecorrelated incommensurate charge density wave (CDW) order is "intertwined" with the superconductivity in this regime. Additionally, transport, STM, neutron-scattering, and optical experiments have produced evidence-not yet entirely understood-of the existence of an associated pattern of long-range-ordered point-group symmetry breaking with an electron-nematic character. We have carried out a theoretical analysis of the LandauGinzburg-Wilson effective field theory of a classical incommensurate CDW in the presence of weak quenched disorder. Although the possibilities of a sharp phase transition and long-range CDW order are precluded in such systems, we show that any discrete symmetry-breaking aspect of the charge order-nematicity in the case of the unidirectional (stripe) CDW we consider explicitlygenerically survives up to a nonzero critical disorder strength. Such "vestigial order," which is subject to unambiguous macroscopic detection, can serve as an avatar of what would be CDW order in the ideal, zero disorder limit. Various recent experiments in the pseudogap regime of the hole-doped cuprates are readily interpreted in light of these results. Because the spontaneous breaking of a continuous symmetry is forbidden (1) in the presence of "random-field" disorder in dimension d ≤ 4, effects of disorder are significant for the physics of incommensurate charge density wave (CDW) ordering, even in crystalline materials, such as the high-temperature superconductor YBCO, which can in other respects be considered extremely well ordered. However, because d = 2 is the lower critical dimension for breaking a discrete symmetry, as in the random-field Ising model (1-3), if a putative CDW ground state breaks a discrete symmetry (e.g., a point-group symmetry), a finite temperature transition at which this symmetry is broken will persist in the presence of weak disorder in d = 3.Here, with the case of the cuprates in mind, we study a model of a layered system with tetragonal symmetry that in the absence of disorder undergoes a transition to a unidirectional incommensurate CDW (stripe-ordered) phase. We thus express the density at positionr in plane m aswhere Q is the magnitude of the CDW ordering vector, ψ α (with α = x; y) are the two components of a slowly varying complex vector field, and the ellipsis refers to higher harmonics. Broken symmetries are defined, as usual, by taking the asymptotic long-dis...

Ideal charge-density-wave order in the high-field state of superconducting YBCO

“…Our results also lend support to the existence of nematic components in the proximate phases to the 3D CDW in the phase diagram, and to their interpretation as arising from remnant unidirectional 3D CDW correlations (19,30).…”

“…Thus, the properties of the quasi-2D CDW are likely strongly affected by disorder and only indirectly represent the true nature of the underlying CDW correlations. Indeed, X-ray scattering shows that the onset of the quasi-2D order is gradual without a sharp transition (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), consistent with the influence of quenched disorder on an incommensurate CDW (19)(20)(21). Furthermore, whereas Y-based and La-based cuprates exhibit a clear competition between CDW and superconductivity (7,8,(12)(13)(14)(15), such competition is not apparent in the families of Bi-based and Hg-based cuprate compounds (9-11)-a discrepancy that probably reflects different degrees of quenched disorder among cuprate families.…”

“…On theoretical ground (19), an incommensurate CDW phase exists as a sharply defined phase of matter (i.e., with true long-range order) only in the ideal limit of vanishing disorder. However, as shown in Fig.…”

“…However, as shown in Fig. 5, for a unidirectional CDW in a tetragonal system, a sharply defined nematic phase, a form of "vestigial" CDW order (19) that spontaneously breaks the pointgroup symmetry, exists so long as the disorder strength, σ, is less than a finite critical value, σc. The phase transition at σ = σc is rounded in an orthorhombic system, but so long as the symmetry breaking field is weak there remains a sharp cross-over from an approximately bidirectional phase (i.e., isotropic) for σ > σc to a strongly unidirectional phase for σ < σc.…”

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

“…In the real materials, a CDW order is likely pinned by impurities 29 and is shortrange, albeit static.…”