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

Significance Recent experiments show that a tendency toward charge density wave (CDW) order, long documented in certain structurally special members of the cuprate family, is a ubiquitous feature of the pseudogap regime in these high-temperature superconductors. We show that quenched disorder plays a key role in this problem, inevitably limiting the growth of CDW correlations even in the most perfect existing crystals and rounding the associated phase transitions. However, weak disorder operating on a unidirectional CDW leaves behind a sharply defined vestigial point-group symmetry breaking and an associated phase transition. We suggest that such electron-nematic order is an essential feature of the pseudogap phase and that the associated quantum critical point may play an essential role in the physics of high-temperature superconductivity. 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-range–correlated 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 Landau–Ginzburg–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 explicitly—generically 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.