Doping dependence of the electron-phonon and electron-spin fluctuation interactions in the high-$ T_ {c} $ superconductor Bi $ _ {2} $ Sr $ _ {2} $ CaCu $ _ {2} $ O $ … (original) (raw)
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Interplay of electron-lattice interactions and superconductivity in Bi2Sr2CaCu2O8+∂
Formation of electron pairs is essential to superconductivity. For conventional superconductors, tunnelling spectroscopy has established that pairing is mediated by bosonic modes (phonons); a peak in the second derivative of tunnel current d 2 I/dV 2 corresponds to each phonon mode 1-3 . For high-transition-temperature (high-T c ) superconductivity, however, no boson mediating electron pairing has been identified. One explanation could be that electron pair formation 4 and related electron-boson interactions are heterogeneous at the atomic scale and therefore challenging to characterize. However, with the latest advances in d 2 I/dV 2 spectroscopy using scanning tunnelling microscopy, it has become possible to study bosonic modes directly at the atomic scale 5 . Here we report d 2 I/dV 2 imaging 6-8 studies of the high-T c superconductor Bi 2 Sr 2 CaCu 2 O 81d . We find intense disorder of electron-boson interaction energies at the nanometre scale, along with the expected modulations in d 2 I/dV 2 (refs 9, 10). Changing the density of holes has minimal effects on both the average mode energies and the modulations, indicating that the bosonic modes are unrelated to electronic or magnetic structure. Instead, the modes appear to be local lattice vibrations, as substitution of 18 O for 16 O throughout the material reduces the average mode energy by approximately 6 per cent-the expected effect of this isotope substitution on lattice vibration frequencies 5 . Significantly, the mode energies are always spatially anticorrelated with the superconducting pairing-gap energies, suggesting an interplay between these lattice vibration modes and the superconductivity.
New Journal of Physics, 2013
Using ultrafast optical techniques, we detect two types of bosons strongly coupled to electrons in the family of Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) from the underdoped to overdoped regimes. The different doping dependences of the electron-boson coupling strengths enable us to identify them as phonons and 8 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Rapid change of superconductivity and electron-phonon coupling through critical doping in Bi-2212
Science, 2018
Electron-boson coupling plays a key role in superconductivity for many systems. However, in copper-based high-temperature (Tc) superconductors, its relation to superconductivity remains controversial despite strong spectroscopic fingerprints. Here we use angle-resolved photoemission spectroscopy to find a striking correlation between the superconducting gap and the bosonic coupling strength near the Brillouin zone boundary in Bi2Sr2CaCu2O8+δ. The bosonic coupling strength rapidly increases from the overdoped Fermi-liquid regime to the optimally doped strange metal, concomitant with the quadrupled superconducting gap and the doubled gap-to-Tc ratio across the pseudogap boundary. This synchronized lattice and electronic response suggests that the effects of electronic interaction and the electron-phonon coupling re-enforce each other in a positive feedback loop upon entering the strange metal regime, which in turn drives a stronger superconductivity. Main Text: The phase diagram of cuprate high temperature superconductors hosts a number of complex orders, types of fluctuations and interactions (1-4). In the non-Fermi liquid strange metal regime, a hierarchy of microscopic interactions are intimately at play but not fully understood (1, 2, 4). Although the experimental evidence for d-wave superconductivity (5-7) naturally points to an electron-electron interaction based pairing mechanism (8-12), the omnipresent charge order (3) points to the role of electron-phonon coupling (EPC), especially in a new context of enhanced EPC by electronic correlation (13, 14) and multichannel boosted superconductivity (15-17). Although there have been reports of EPC imprinting on the electronic structure of many cuprate superconductors (18-21), little evidence directly correlates EPC with the intertwined orders in the phase diagram (1-2). Focusing on the overdoped side in Bi2Sr2CaCu2O8+δ (Bi-2212), we find via angle-resolved photoemission spectroscopy (ARPES) a set of striking effects rapidly crossing
Science, 2008
Identifying the mechanism of superconductivity in the high-temperature cuprate superconductors is one of the major outstanding problems in physics. We report local measurements of the onset of superconducting pairing in the high–transition temperature ( T c ) superconductor Bi 2 Sr 2 CaCu 2 O 8+δ using a lattice-tracking spectroscopy technique with a scanning tunneling microscope. We can determine the temperature dependence of the pairing energy gaps, the electronic excitations in the absence of pairing, and the effect of the local coupling of electrons to bosonic excitations. Our measurements reveal that the strength of pairing is determined by the unusual electronic excitations of the normal state, suggesting that strong electron-electron interactions rather than low-energy (<0.1 volts) electron-boson interactions are responsible for superconductivity in the cuprates.
Disentangling the Electronic and Phononic Glue in a High-Tc Superconductor
Science, 2012
Unveiling the nature of the bosonic excitations that mediate the formation of Cooper pairs is a key issue for understanding unconventional superconductivity. A fundamental step toward this goal would be to identify the relative weight of the electronic and phononic contributions to the overall frequency (Ω) dependent bosonic function, Π(Ω). We perform optical spectroscopy on Bi2Sr2Ca0.92Y0.08Cu2O 8+δ crystals with simultaneous time-and frequency-resolution; this technique allows us to disentangle the electronic and phononic contributions by their different temporal evolution. The strength of the interaction (λ∼1.1) with the electronic excitations and their spectral distribution fully account for the high critical temperature of the superconducting phase transition. Lattice vibrations [1] and excitations of electronic origin, like spin or electric polarizability fluctuations[2] and loop currents[3], are generally considered potential mediators of Cooper-pairing in the copper-oxide high-temperature superconductors (cuprates). The generic interaction of fermionic quasiparticles (QPs) with bosonic excitations is accounted for by the bosonic function Π(Ω) (usually indicated as α 2 F (Ω) for phonons and I 2 χ(Ω) for spin fluctuations), a dimensionless function that depends on the density of states of the excitations and the strength of their coupling to QPs. Because both the energy dispersion and lifetime of QPs are strongly affected by the interactions, signatures of QP-boson coupling have been observed in experiments that probe the electronic properties at equilibrium. The ubiquitous kinks in the QP dispersion at ∼70 meV, measured by angle-resolved photoemission spectroscopy (ARPES)[4], have been interpreted in terms of coupling to either optical Cu-O lattice modes[5, 6] or spin excitations[7]. Inelastic neutron and X-ray scattering experiments found evidence for both QP-phonon anomalies[8] and bosonic excitations attributed to spin fluctuations[7, 9] and loop currents[10]. Dip features in tunnelling experiments have been used to alternatively support the scenarios of dominant electron-phonon interactions or antiferromagnetic spin fluctuations . The frequency-dependent dissipation of the Drude optical conductivity, σ (ω), measured by equilibrium optical spectroscopies, has been interpreted as the coupling of electrons to bosonic excitations, in which the separation of the phononic and electronic contributions is impeded by their partial coexistence on the same energy scale (<90 meV).
The interaction between phonons and high-energy excitations of electronic origin in cuprates and their role on the superconducting phenomenon is still controversial. Here, we use coherent vibrational time-domain spectroscopy together with density functional and dynamical mean-field theory calculations to establish a direct link between the c-axis phonon modes and the in-plane electronic charge excitations in optimally doped YBCO. Our findings clarify the nature of the anomalous high-energy response associated to the formation of the superconducting phase in the cuprates.
Imaging the Essential Role of Spin Fluctuations in High-T_{c} Superconductivity
Physical Review Letters, 2009
We have used scanning tunneling spectroscopy to investigate short-length electronic correlations in three-layer Bi2Sr2Ca2Cu3O 10+δ (Bi-2223). We show that the superconducting gap and the energy Ω dip , defined as the difference between the dip minimum and the gap, are both modulated in space following the lattice superstructure, and are locally anti-correlated. Based on fits of our data to a microscopic strong-coupling model we show that Ω dip is an accurate measure of the collective mode energy in Bi-2223. We conclude that the collective mode responsible for the dip is a local excitation with a doping dependent energy, and is most likely the (π, π) spin resonance. PACS numbers: 74.50.+r, 74.20.Mn, 74.72.Hs The presence of phonon signatures in the electron tunneling spectra of classical superconductors [1], and their quantitative explanation by the Eliashberg equations [2, 3], stand among the most convincing validations of the BCS phonon-mediated pairing theory . For high-T c superconductors, the pairing mechanism still remains an intriguing mystery. Several cuprate superconductors present a spectroscopic feature, known as the dip-hump , that resembles the phonon signatures of classical superconductors. There is still no consensus on the origin of the dip-hump nor its connection to high-T c superconductivity. In this work we report on a scanning tunneling microscopy (STM) study of the three-layer compound Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ (Bi-2223). We observe that the gap magnitude, a direct measure of the pairing strength, is periodically modulated on a lengthscale of about 5 crystal unit-cells. This variation follows the superstructure, a periodic modulation of atomic positions naturally present in Bi-based cuprates. By fitting the STM data with a strong-coupling model we demonstrate that the dip feature originates from a collective excitation. This allows us to image the collective mode energy (CME) at the atomic scale and reveal a modulation that also follows the superstructure. The CME and the gap are locally anti-correlated. These findings support that the collective mode probed in our study is related to superconductivity, and is most likely the anti-ferromagnetic spin resonance detected by neutron scattering [10]. Our results, in particular the CME value of 30-40 meV, are in agreement with the spin-fluctuation-mediated pairing scenario , in which the spin resonance in high-T c 's is a consequence of pairing.
Strength of the spin-fluctuation-mediated pairing interaction in a high-temperature superconductor
2009
Theories based on the coupling between spin fluctuations and fermionic quasiparticles are among the leading contenders to explain the origin of high-temperature superconductivity, but estimates of the strength of this interaction differ widely 1. Here, we analyse the charge-and spin-excitation spectra determined by angle-resolved photoemission and inelastic neutron scattering, respectively, on the same crystals of the high-temperature superconductor YBa 2 Cu 3 O 6.6. We show that a self-consistent description of both spectra can be obtained by adjusting a single parameter, the spin-fermion coupling constant. In particular, we find a quantitative link between two spectral features that have been established as universal for the cuprates, namely high-energy spin excitations 2-7 and 'kinks' in the fermionic band dispersions along the nodal direction 8-12. The superconducting transition temperature computed with this coupling constant exceeds 150 K, demonstrating that spin fluctuations have sufficient strength to mediate high-temperature superconductivity. Looking back at conventional superconductors, the most convincing demonstration of the electron-phonon interaction as the source of electron pairing was based on the quantitative correspondence between features in the electronic tunnelling conductance and the phonon spectrum measured by inelastic neutron scattering (INS; for reviews, see the articles by Scalapino, McMillan and Rowell in ref. 13). The rigorous comparison of fermionic and bosonic spectra was made possible by the Eliashberg theory, which enabled the tunnelling conductance to be derived from the experimentally determined phonon spectrum. Various difficulties have impeded a similar approach to the origin of high-temperature superconductivity. First, the d-wave pairing state found in these materials implies a strongly momentum-dependent pairing interaction. A more elaborate analysis based on data from momentum-resolved experimental techniques such as INS and angle-resolved photoemission spectroscopy (ARPES) is thus required. These methods, in turn, impose conflicting constraints on the materials. To avoid surface-related problems, most ARPES experiments have been carried out on the electrically neutral BiO cleavage plane in Bi 2 Sr 2 Ca n−1 Cu n O 2(n+2)+δ (ref. 8). However, as a consequence of electronic inhomogeneity, this family of materials exhibits broad INS spectra that greatly complicate a quantitative comparison with ARPES data 7. Conversely, compounds with sharp spin excitations, including YBa 2 Cu 3 O 6+x , have generated problematic ARPES spectra due to polar surfaces with charge distributions different from the bulk 8. Finally, an analytically rigorous treatment of the spin-fluctuation-mediated pairing
Enhanced electron–phonon coupling and its irrelevence to high Tc superconductivity
Solid State Communications, 1998
It is argued that the origin of the buckling of the CuO2 planes in certain cuprates as well as the strong electron-phonon coupling of the B1g phonon is due to the electric field across the planes induced by atoms with different valence above and below. The magnitude of the electric field is deduced from new Raman results on YBa2Cu3O6+x and Bi2Sr2(Ca1−xYx)Cu2O8 with different O and Y doping, respectively. In the latter case it is shown that the symmetry breaking by replacing Ca partially by Y enhances the coupling by an order of magnitude, while the superconducting Tc drops to about two third of its original value.