Remnant of stripe order.

At a phenomenological level, the superconducting phase of the cuprate high Tc phase diagram shown in Fig. 1A can be characterized as a BCS (named for three theorists: Bardeen, Cooper, and Schrieffer) superconductor with a d-wave gap. However, a suitable phenomenological description of the so-called “pseudogap” region indicated by the yellow shaded region in Fig. 1A has been missing. This region is characterized by the absence of low-energy single-particle states with momenta near the part of the Fermi surface, where a maximum d-wave gap opens in the superconducting phase, leading to it being called the pseudogap region. A variety of experiments show evidence of short-range unidirectional charge and in some cases spin order in this region. However, there remained questions of whether the boundary shown as the black T* curve in Fig. 1Amarks a cross-over or an actual phase transition, and if the latter, what characterizes the pseudogap phase. In PNAS, Nie et al. (1) discuss a phenomenological Landau– Ginzburg–Wilson theory of an incommensurate unidirectional charge density wave (stripes) in the presence of weak quenched disorder. The authors find that although long-range stripe order, schematically illustrated in Fig. 1B, is destroyed by the disorder, a remnant nematic order, shown in Fig. 1C, can survive. As Nie et al. discuss, this theory provides a framework for interpreting a number of experiments, as well as the basis for experimental protocols that can provide further tests for nematic order. The authors note that although the spontaneous breaking of a continuous symmetry will not occur in the presence of random field disorder for dimensions less than or equal to four, the breaking of a discrete symmetry is possible for weak disorder in three dimensions. Specifically, Nie et al. (1) analyze a Landau– Ginzburg–Wilson model of a layered tetragonal lattice, which in the absence of disorder would have a unidirectional incommensurate striped phase, schematically illustrated in Fig. 1B. The authors explain that although this striped phase is destroyed by random quenched impurities, a remnant of it, associated with the x or y orientation of the stripes, remains provided there is coupling between the planes. This remnant of the striped phase appears as a nematic phase, schematically illustrated in Fig. 1C, which consists of stripe segments in which the longrange charge and spin order has melted, but the orientation of the segments along the x or y Cu-O-Cu bonds remains. An important prediction of this theory is that there is a thermodynamic phase transition at the boundary of the pseudogap regime and a quantum critical point where T* goes to zero. However, as discussed by Nie et al. (1), the thermodynamic signal of the phase transition may be weak because the nematic order is not expected to open gaps on the Fermi surface. Nevertheless, ultrasonic measurements of the temperature dependence of the elastic moduli of YBa_2Cu_3O_{6+y} crystals have reported thermodynamic evidence that the pseudogap region is a distinct phase bounded by a line of phase transitions (2). Evidence that the pseudogap region is characterized by a phase with short-range charge order, consistent with nematic order, is seen in a variety of experimental NMR, scanning tunneling microscopy, and X-ray studies referred to by Nie et al. (1). For example, the symmetry-breaking that makes the Ox and Oy planar oxygen sites of the CuO2 unit cell electronically inequivalent is AF PG