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Researchers Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking
In recent years, several experimental probes have reported broken symmetries In underdoped cuprates of almost linearly decreasing onset temperatures with doping. However, how the real-space ordering and fluctuations are related to the momentum space electronic structure that hosts high temperature superconductivity and its apparent topology change is not well established. It is primarily because the techniques used are single-sided; scattering experiments can only see periodic arrangements in real space, while photoemission reveals electronic bands with no direct access to real space. In contrast, SI-STM can, and only SI-STM can simultaneously investigate both real and momentum space from a single measurement. The doping evolution of the broken symmetry as well as the Fermi surface transition are studied here with Bi
[1] Out of the seven distinct quasi-particle interference (QPI) peaks connecting the octet regions of high density of states,
d-wave superconducting energy gap Δ(k_{F}) on two opposing segments of the Fermi surface. The q_{4} wavevector for the octet scattering process q_{4}(E=Δ(k_{F}))=2k_{F} that always passes through the Brillouin zone symmetry point (0, 0) is indicated for several Δ(k_{F}) by colored arrows B, By focusing on q_{4}(E) one can then determine the location of the Fermi surface because it is the set of wavevectors k=q_{4}(0<E<Δ_{0})/2. This is demostrated using the correspondence between the colored arrows q_{4}(E) in A and the colored arrows k(Δ)=q_{4}(E=Δ(k_{F}))/2. Here we show the resulting k_{F} that we measure for a sample with p=0.23. C, The measured Λ(q), Z(q, E) integrated up to the SC energy scale for underdoped p=0.14 sample. No complete contour for q_{4} can be detected; instead, the coherent Bogoliubov QPs are found to be restricted to four arcs terminating at AFZB. D, The measured Λ(q) for overdoped p=0.23 sample. A complete closed contour for q_{4} surrounding (±1,±1)Δ/a_{0} can be identified immediately. E, The measured doping dependence of the k-space topology of coherent BG QP in Bi2212 using q_{4} technique. The transition from arcs terminating at AFZB to complete hole-pockets surrounding (π,π) points at p~0.19 is strikingly clear.[2] Electronic intra-unit-cell rotational symmetry breaking and incommensurate charge modulation are best characterized in real space. The former is captured with the inequivalence of electronic density of states at the two oxygen sites lying along x and y direction off a Cu atom. Statistics on the spatial distribution of the nematic order parameter clearly exhibits monotonously vanishing average magnitude along with increasing spread (more disordered) toward ~19% doping. The domain sizes of opposite ising nematic order parameter become comparable beyond ~19% leading to zero average, i. e., disappearance of global nematicity.
_{1}) for p=0.08. Incommensurate bidirectional modulations are clearly seen. B, Measured Z(r, E~Δ_{1}) for p=0.23. No specific q-vector for modulations is seen although the QPI signature of Bogoliubov quasiparticles does produce a jumbled standing wave pattern. C, Measured Z(r, E~Δ_{1}) for p=0.08 from A. The two wavevectors universally reported in SI-STM experiments for the broken-symmetry states, q_{1}* and q_{5}* are indicated using violet and orange circles, respectively. The two Bragg peaks are shown using red circles. D, Measured Z(r, E~Δ_{1}) for p=0.08 from B. No specific broken-symmetry state wavevectors are apparent, while the residual dispersive effects of Bogoliubov quasiparticles are seen. E, Measured Q=0 C_{4} broken-symmetry order parameter O_{N}^{q}(r, E~Δ_{1}) for p=0.06; the whole field of view is a single color indicating that long range Q=0 intra-unit-cell C_{4} breaking exists. F, Measured intra-unit-unit cell broken C_{4} symmetry O_{N}^{q}(r, E~Δ_{1}) for p=0.22; long-range order has been lost but nanoscale domains of opposite nematicity persist. Broken circle represents the spatial resolution of the analysis. G, Measured intensity of incommensurate modulation with wavevector q_{5}*: I(q_{5}*). The incommensurate modulations do not show long-range order in contrast to the intra-unit-cell nematicity. Instead, the modulations show severe spatial fluctuation in phase and amplitude; such fluctuations are reflected in how broad the modulation peaks are in C. Nevertheless, the intensity of the modulation peaks initially increase upon doping peaking near p~1/8, and then diminish to reach zero at p~0.19. H, Filled square symbols indicate measured spatial average value of the Q=0 C_{4} broken symmetry |O_{N}^{q}(r, E~Δ_{1})| which diminishes steadily with increasing p, to reach zero at p=0.19. Triangles indicate measured standard deviation of the Q=0 C_{4} broken symmetry O_{N}^{q}(r, E~Δ_{1}) which increases as the spatial range of fluctuations increases. Both spatial ordering phenomena disappear between 17% and 20% doping at which the Fermi surface undergoes abrupt transition from arc to closed full contour. The simultaneous transitions of real and momentum space electronic structures implies that the broken symmetries are closely linked with the Fermi surface topology. Moreover, the fact that all transitions occur at around 19% doping points toward quantum critical point concealed underneath the superconducting dome.
p~0.19. B, The k-space area proportional to hole-density p is observed between the arc and the AFZB. This transitions with the appearance of the closed FS at p~0.19, to a diminishing area of electron count 1-p (as would be expected conventionally for uncorrelated electrons). C, The wavevectors k of states at which Bogoliubov quasiparticle scattering interference disappears q_{E}/2 (closed circles), and those of the quasistatic broken-symmetry modulations with q_{1}/2 and (2π-q_{5}*)/2 (closed squares). It is unknown why all these wavevectors, characteristic of both termination in the Bogoliubov QPI and the Q≠0 broken symmetry states, are associated so closely with the AFZB. D, T-matrix scattering interference simulation for Λ(q) for band structure with a complete Fermi surface upon which a d-wave gap opens and for conventional (time-reversal preserving) scattering. E, Measured Λ(q) for p=0.14 showing the combined effects of all detectable Bogoliubov QPI. In stark contrast to the simulation result in D, the energy-integrated QPI data reveals finer features near the nodal direction resulting from the dispersion of "octet" peaks characteristic of underdoped cuprates, while the set of scattering q-vectors dispersed unexpectedly with energy are limited to a set of four arcs. Conventional Bogoliubov scattering on the complete Fermi surface (D) definitely fails to reproduce all these notable hallmarks. F, For p=0.23, on the contrary, Λ(q) conforms very nicely to the conventional d-wave Bogoliubov scattering scheme in that the FS is fully closed and that the large nodal 'blobs' are unresolvable. The clear distinction between E and F, and the excellent correspondence between D and F, strongly suggests that p~0.19 is also associated with the critical change of the underlying QP scattering mechanism.These results were published in Science Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states
A route to find the mechanism of cuprate superconductivity is to understand the physics of pseudogap states. We use SI-STM to probe the electronic property of pseudogap states in underdoped Bi
We have discovered an evidence for electronic nematicity of the states close to the pseudogap energy of strongly underdoped Bi
We have visualized the spatial components of coexisting smectic modulations and intra-unit-cell nematicity in the pseudogap states of underdoped Bi
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