Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking

Abstract

. † 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...

Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

“…Although Bogoliubov QPI is LETTERS observed as expected everywhere on the Fermi surface in overdoped cuprates 32 , in underdoped samples it evolves as expected only until the energy E ≈ ∆ 0 , at which the terminations of the Bogoliubov coherent k-space arcs (Fig. 3e) are observed [30][31][32] . Here, the set of seven dispersive scattering interference modulations q 1 , q 2 , .…”

“…Moreover, we demonstrate that the dFF-DW modulations at E = −∆ 1 (filled states) occur with relative phase π compared to those at E = ∆ 1 (empty states). Finally, we show that the conventionally defined dFF-DW Q corresponds to scattering between the 'hot frontier' regions of momentum-space beyond which Bogoliubov quasiparticles cease to exist [30][31][32] . These data indicate that the cuprate dFF-DW state involves particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in momentum space where the pseudogap opens.…”

“…But which energy gap (if any) is associated with the dFF-DW state found in underdoped cuprates is unknown. Figure 3a shows how a typical tunnelling conductance spectrum representative of strongly underdoped cuprates exhibits two characteristic energies [30][31][32] . Whereas the lower-energy scale ∆ 0 represents the maximum energy at which Bogoliubov quasiparticle excitations exist [30][31][32] (see Fig.…”

“…Figure 3a shows how a typical tunnelling conductance spectrum representative of strongly underdoped cuprates exhibits two characteristic energies [30][31][32] . Whereas the lower-energy scale ∆ 0 represents the maximum energy at which Bogoliubov quasiparticle excitations exist [30][31][32] (see Fig. 3b), the higher-energy scale (dashed blue line) is the cuprate 'pseudogap' as determined from its comparison with the doping dependence of the pseudogap scale in tunnelling and photoemission.…”

“…Such information was not previously available from measurements of the modulation wavevectors from STM images lacking sublattice-phase-resolved segregation 14 intoÕ x (q) andÕ y (q). Figure 3e shows the measured k-space locus where Bogoliubov quasiparticles exist [30][31][32] as a function of hole density. When the dispersive 'octet' of Bogoliubov scattering interference disappears, a transition occurs to an ultraslow dispersing density wave modulation (Fig.…”