In the high-transition-temperature (high-T(c)) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO(2) unit cell. We analyse spectroscopic-imaging scanning tunnelling microscope images of the intra-unit-cell states in underdoped Bi(2)Sr(2)CaCu(2)O(8 +) (delta) and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90 degrees -rotational symmetry within every CuO(2) unit cell.

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classical nematics generally occur in liquids of rod-like molecules; given that electrons are point like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. Dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr(3)Ru(2)O(7) in a strong magnetic field in 2007 established that such phases exist in nature. In this article, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr(3)Ru(2)O(7) experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors

. † These authors contributed equally to this project. The existence of electronic symmetry breaking in the underdopedcuprates, and its disappearance with increased hole-density p, are now widely reported. However, the relationship between this transition and the momentumspace ( ⃗ -space) electronic structure underpinning the superconductivity has not been established. Here we visualize the ⃗ =0 (intra-unit-cell) and ⃗ ≠0 (density wave) broken-symmetry states simultaneously with the coherent ⃗ -space topology, for Bi2Sr2CaCu2O8+d samples spanning the phase diagram 0.06≤p≤0.23.We show that the electronic symmetry breaking tendencies weaken with increasing p and disappear close to pc=0.19. Concomitantly, the coherent ⃗ -space topology undergoes an abrupt transition, from arcs to closed contours, at the same pc. These data reveal that the ⃗ -space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point. 2The highest known superconducting critical temperature Tc (1-3) occurs atop the Tc(p) 'dome' of hole-doped cuprates (Fig. 1A). In addition to the superconductivity, electronic broken-symmetry states (4) have also been reported at low p in many such compounds. Wavevector ⃗ =0 (intra-unit-cell) symmetry breaking, typically of 90 orotational (C4) symmetry, is reported in YBa2Cu3O6+, . Finite wavevector ⃗ ≠0 (density wave) modulations breaking translational symmetry, long detected in underdoped 16), are now also reported in underdoped YBa2Cu3O6+, . Summarizing all such reports in Fig. 1A reveals some stimulating observations.First, although the ⃗ =0 and ⃗ ≠0 states are detected by widely disparate techniques and are distinct in terms of symmetry, they seem to follow approximately the same phasediagram trajectory (shaded band Fig. 1A) as if facets of a single phenomenon (26). The second implication is that a critical point (perhaps a quantum critical point) associated with these broken-symmetry states may be concealed beneath the Tc(p) dome.Numerous earlier studies reported sudden alterations in many electronic/magnetic characteristics near p=0.19 (2,3,27), but whether these phenomena are caused by electronic symmetry changes (28) at a critical point was unknown. 3In ⃗ -space, the hole-doped cuprates also exhibit an unexplained transition in electronic structure with increasing hole density. Open contours or "Fermi arcs" (29)(30)(31)(32) are reported at low p in all compounds studied, while at high p closed hole-like pockets surrounding ⃗ = (±1, ±1) / 0 are observed (33,34). One possibility is that such a transition could occur due to the disappearance of an electronic ordered state, with the resulting modifications to the Brillouin zone geometry altering the topology of the electronic bands (28). 4Our strategy is therefore a simultaneous examination of both the ⃗ -space 11,36) or at the Bragg wavevectors (11,26,35). But the complete doping dependence of these broken-symmetry signatures was unknown. 6To determine the ⃗ -space t...