Cu/Fe High Temperatue Superconductors
Cu/Fe High-Tc Superconductors
On the electron pairing mechanism of CuO2 high temperature superconductivity,
Essence: The hypothetical charge-transfer superexchange electron-pairing mechanism of high temperature CuO2 superconductivity – as proposed by both Anderson and Emery in 1987 - was tested directly for the first time at atomic scale. We simultaneously visualized the charge transfer energy ε and the electron-pair wavefunction amplitude squared npas the evolve together. By comparison to theory, the charge-transfer superexchange pairing mechanism is validated quantitatively and in detail for canonical cuprate Bi2Sr2CaCu2O8.
Left: Atomic-resolution SJTM image of the electron-pair density nP(r) in Bi2Sr2CaCu2O8. Center:Atomic-resolution image of the charge transfer energy ε(r) in Bi2Sr2CaCu2O8 Right: Comparison of measured nP versus ε to charge-transfer superexchange theory predictions for nP versus ε (yellow cone).
The elementary CuO2 plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO5 pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate t/ℏ and across the charge-transfer energy gap ε, generate 'superexchange' spin-spin interactions of energy J≈4t4/ε3 in an antiferromagnetic correlated-insulator state. However, hole doping the CuO2 plane converts this into a very high temperature superconducting state whose electron-pairing is exceptional. A leading proposal for the mechanism of this intense electron-pairing is that, while hole doping destroys magnetic order it preserves pair-forming superexchange interactions governed by the charge-transfer energy scale ε. To explore this hypothesis directly at atomic-scale, we combined single-electron and electron-pair (Josephson) scanning tunneling microscopy to visualize the interplay of ε and the electron-pair density nP in Bi2Sr2CaCu2O8+x. The responses of both ε and nP to alterations in the distance between planar Cu and apical O atoms are then determined. These data reveal the empirical crux of strongly correlated superconductivity in CuO2, the response of the electron-pair condensate to varying the charge transfer energy. Concurrence of predictions from strong-correlation theory for hole-doped charge-transfer insulators with these observations, indicates that charge-transfer superexchange is the electron-pairing mechanism of superconductive Bi2Sr2CaCu2O8+x.
Discovery of Orbital Ordering in Bi2Sr2CaCu2O8+x
Nature Materials, 23, 492, 2024
Essence: The measured charge-transfer energy ε is demonstrated to be distinctly different for the two O atoms within each CuO2 unit cell in Bi2Sr2CaCu2O8+x. The observed ~ 50meV energy splitting between them reveals a Q=0 orbitally ordered state in underdoped cuprates.
Top: Average topographic structure measured inside the CuO2 unit cell in the two Ising domains of orbital order - they are indistinguishable. Bottom: Comparison of measure charge-transfer energy ε inside the CuO2 unit cell in the two Ising domains of orbital order. They are rotated by 90-degrees relative to each other and in each case the average energetic separation between oxygen sites is ~50mV.
Within the high temperature superconductive CuO2 unit cell theoretical attention usually concentrates on the intra-atom Coulombic interactions dominating the 3d9 and 3d10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p6 orbitals of each planar oxygen atom, spontaneous orbital ordering should split their energy levels. This long-predicted intra-unit cell symmetry breaking should generate an orbital ordered phase, for which the charge-transfer energy ε separating the 2p6 and 3d10 orbitals is distinct for the two oxygen atoms. We introduced sublattice resolved ε (r) imaging techniques to CuO2 studies and discovered intra-unit-cell rotational symmetry breaking of ε (r), with energy-level splitting between the two oxygen atoms on the ~50 meV scale. Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order and within whose domain walls low energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q=0 orbitally ordered state that splits the energy levels of the oxygen orbitals by ~50 meV, in underdoped CuO2.
Discovery of Orbital-Selective Cooper Pairing in FeSe
Essence: By visualizing the momentum-space structure of the energy gaps Δi(k) in FeSe we show both gaps are extremely anisotropic but nodeless, and exhibit gap maxima oriented orthogonally and have opposite sign with respect to each other. This configuration reveals the first example of orbital-selective Cooper pairing, in FeSe based preferentially on electrons from the dyz orbitals of the iron atoms.
Top left: The three active Fe orbitals in FeSe. Top right: QPI measured momentum-space structure of the energy gaps in FeSe. Bottom row: Comparison between orbital selective cooper pairing theory for FeSe (left) and the measured Δi(k) including their signed values.
For the superconductor FeSe we used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the bands surrounding the Γ=(0,0) and X=(π/aFe,0) points of FeSe, and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless, and exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing which, in FeSe, is based preferentially on electrons from the dyz orbitals of the iron atoms.
Commensurate 4a0-period Charge Density Modulations of the Pseudogap Regime.
Essence: We introduced phase-resolved electronic structure visualization for determination of the fundamental wavevector of the cuprate density wave state. This reveales a virtually doping independent locking of the local wavevector at |Q0|=2π/4a0 throughout the underdoped phase diagram of the canonical cuprate Bi2Sr2CaCu2O8, indicating that Fermi surface nesting is not the source of the density wave since it evolves with carrier density.
A-E: Phase residue characterization of the density wave at five different carrier density in underdoped Bi2Sr2CaCu2O8 – the minimum reside occurs in theory at the dominant wavevector. F. In all cases the observed density wave wavevector is Q=2π/4a0 and does not disperse with carrier density as it would in the case of a Fermi surface nesting mechanism.
Theories based upon strong real space (r-space) electron interactions have long predicted that unidirectional charge density modulations (CDM) with four unit cell (4a0) periodicity should occur in the hole doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p was reported to cause the conventionally defined wavevector QA of the CDM to evolve continuously as if driven primarily by momentum space (k-space) effects. We introduced phase resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this new technique revealed a virtually doping independent locking of the local CDM wavevector at |Q0|=2π/4a0 throughout the underdoped phase diagram of the canonical cuprate Bi2Sr2CaCu2O8. These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi surface) based picture of the cuprate CDM but are consistent with strong coupling r-space based theories. Our findings imply that it is the latter that provide the intrinsic organizational principle for the cuprate CDM state.
Atomic-scale Structure of d-Symmetry Form Factor Density Wave State in CuO2.
Nature Physics 12, 150 (2015).
Essence: The detailed atomic-scale electronic structure, including its d-symmetry form factor and is bond-center register, of the charge density modulation in underdoped cuprates rates was revealed by direct visualization.
Sequence of typical STM images of the density wave in underdoped cuprates showing that it this is a disorder arrangement of predominantly 4a0 commensurate modulations, that are bond-centered, and that they have a d-symmetry form factor (blue dot represents oxygen and black dot copper).
The cuprate density wave state always exhibits wave vector Q parallel to the planar Cu-O-Cu bonds along with a predominantly d-symmetry form factor (dFF-DW). We used energy-resolved sublattice visualization of electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy Δ1. Moreover, we demonstrated that the dFF-DW modulations at E=−Δ1 (filled states) occur with relative phase π compared to those at E=Δ1 (empty states). Finally, we show that the dFF-DW wavevector corresponds directly to scattering between the 'hot frontier' regions of k-space beyond which Bogoliubov quasiparticles cease to exist. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in k-space where the pseudogap opens.
Simultaneous Transitions in CuO2 k-Space Topology and Symmetry Breaking.
Essence: By visualizing the carrier density p dependence of electronic symmetry breaking we reveal how it weakens with increasing p and disappears close to pc=0.19; concomitantly we discovered that the coherent k -space topology undergoes an abrupt transition, from arcs to closed contours at the same pc. These data revealed that the cuprate k-space topology transformation is linked intimately with the disappearance of the electronic symmetry breaking, at a concealed critical point pc=0.19.
Top row: N(q,V) the FT of quasiparticle density of states images N(r,V) in the superconductive state at two carrier densities - left p<pc and right p>pc. Bottom, k-space locate of quasiparticles detected by QPI as a function of carrier density p; there is an abrupt transition at p=pc=0.19+-0.01.
The existence of electronic symmetry breaking in the underdoped cuprates, and its disappearance with increased hole-density p, are now widely reported. However, the relationship between this transition and the momentum space (k-space) electronic structure underpinning the superconductivity has not been established. Here we visualize the Q⃗=0 (intra-unit-cell) and Q⃗ ≠0 (density wave) broken-symmetry states simultaneously with the coherent k-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 k-space topology undergoes an abrupt transition, from arcs to closed contours, at the same pc. These data reveal that the k⃗-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.
Direct phase-sensitive identification of a d-symmetry density wave in cuprates
Essence: We demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intra-unit-cell states that exhibit a predominantly d-symmetry form factor (dFF).This is the first dFF density wave ever observed, and its form factor points towards a unique new mechanism for the CuO2 density wave state.
Left: elementary components of underdoped cuprate density wave Q=2π/4a0 modulating from left to right. Right: model of a d-symmetry form factor density wave modulating from left to right. They are detailed agreement.
The identity of the fundamental broken symmetry (if any) in the underdoped cuprates was long unresolved. We carried out site-specific measurements within each CuO2 unit-cell, segregating the results into three separate electronic structure images containing only the Cu sites (Cu(r)) and only the x/y-axis O sites (Ox(r) and Oy(r)). Phase resolved Fourier analysis reveals directly that the modulations in the Ox(r) and Oy(r) sublattice images consistently exhibit a relative phase of π. We confirmed this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intra-unit-cell states that exhibit a predominantly d-symmetry form factor.