Abstract
In strongly correlated systems the electronic properties at the Fermi energy (E_{F}) are intertwined with those at highenergy scales. One of the pivotal challenges in the field of hightemperature superconductivity (HTSC) is to understand whether and how the highenergy scale physics associated with Mottlike excitations (E−E_{F}>1 eV) is involved in the condensate formation. Here, we report the interplay between the manybody highenergy CuO_{2} excitations at 1.5 and 2 eV, and the onset of HTSC. This is revealed by a novel optical pumpsupercontinuumprobe technique that provides access to the dynamics of the dielectric function in Bi_{2}Sr_{2}Ca_{0.92}Y_{0.08}Cu_{2}O_{8+δ} over an extended energy range, after the photoinduced suppression of the superconducting pairing. These results unveil an unconventional mechanism at the base of HTSC both below and above the optimal hole concentration required to attain the maximum critical temperature (T_{c}).
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Introduction
The highT_{c} copperoxide (cuprate) superconductors are a particular class of strongly correlated systems in which the interplay^{1} between the Cu3d and the O2p states determines both the electronic structure close to the Fermi level as well as the highenergy properties related to the formation of Zhang–Rice singlets^{2} (hole shared among the four oxygen sites surrounding a Cu, and antiferromagnetically coupled to the Cu spin; energy E_{ZR}∼0.5 eV) and to the chargetransfer processes^{3} (Δ_{CT}∼2 eV). One of the unsolved issues of highT_{c} superconductivity is whether and how the electronic manybody excitations at highenergy scales are involved in the condensate formation in the under and overdoped regions of the superconducting dome. Solving this problem would provide a benchmark for unconventional models of highT_{c} superconductivity, at variance with the BCS theory of conventional superconductivity, where the opening of the superconducting gap induces a significant rearrangement of the quasiparticle excitation spectrum over an energy range of only a few times 2Δ_{SC} (ref. 4).
As the knowledge of the dielectric function ɛ(ω) provides direct information about the underlying electronic structure, optical spectroscopic techniques have been widely used to investigate highT_{c} superconductors^{5,6,7,8,9,10,11,12,13,14,15,16,17}. Recently, equilibrium techniques revealed a superconductivityinduced modification of the CuO_{2}planes' optical properties involving energy scales in excess of 1 eV (refs 7, 11, 12, 14, 15, 16, 17). These results suggested a possible superconductivityinduced gain in the inplane kineticenergy on the underdoped side of the phase diagram^{18,19,20}. However, the identification of the highenergy electronic excitations involved in the onset of hightemperature superconductivity (HTSC) has remained elusive because they overlap in energy with the temperaturedependent narrowing of the Drudelike peak.
Here we solve this question adopting a nonequilibrium approach to disentangle the ultrafast modifications of the highenergy spectral weight (, σ_{1}(ω)=ɛ_{2}(ω)·ω/4πi being the real part of the optical conductivity) from the slower broadening of the Drudelike peak induced by the complete electronboson thermalization. As the superconducting gap (2Δ_{SC}) value is related to the total number of excitations^{21}, an impulsive suppression^{22} of 2Δ_{SC} is achieved by photoinjecting excess quasiparticles in the superconducting Bi_{2}Sr_{2}Ca_{0.92}Y_{0.08}Cu_{2}O_{8+δ} crystals (YBi2212), through an ultrashort light pulse (pump). Exploiting the supercontinuum spectrum produced by a nonlinear photonic crystal fibre^{23} we are able to probe the highenergy (1.2–2.2 eV) modifications of the abplane optical properties at low pump fluences (<10 μJ cm^{−2}), avoiding the complete vaporization of the superconducting phase^{22,24}. This novel timeresolved optical spectroscopy (Methods) allows us to demonstrate the interplay between manybody electronic excitations at 1.5 and 2 eV and the onset of superconductivity both below and above the optimal hole concentration required to attain the maximum T_{c}.
Results
Equilibrium optical properties of Bi_{2}Sr_{2}Ca_{0.92}Y_{0.08}Cu_{2}O_{8+δ}
The interpretation of timeresolved optical spectroscopy relies on the detailed knowledge of the equilibrium (intragap transitions) ɛ(ω) of the system. In Figure 1a, we report the real (ɛ_{1}) and imaginary (ɛ_{2}) parts of the dielectric function, measured on an optimally doped sample (T_{c}=96 K, labelled OP96) by spectroscopic ellipsometry at 20 K (Methods). Below 1.25 eV, ɛ(ω) is dominated by the Drude response of free carriers coupled to a broad spectrum of bosons I^{2}χ(Ω) (refs 25,26). In the highenergy region (ℏω>1.25 eV), the interband transitions dominate. The best fit to the data (solid black lines) is obtained by modelling the equilibrium dielectric function as a sum of an extended Drude term (ɛ_{D}) and Lorentz oscillators at 0.5 eV and higher energies (ɛ_{L}, indexed by i): ɛ_{eq}(T,ω)=ɛ_{D}(T,ω)+Σ_{i}ɛ_{Li}(T,ω) (Supplementary Note 1). The highenergy region of ɛ(ω) is characterized by interband transitions at {\omega}_{{0}_{i}} ∼1.46, 2, 2.72 and 3.85 eV. The attribution of the interband transitions in cuprates is a subject of intense debate. As a general phenomenological trend, the chargetransfer (CT) gap edge (hole from the upper Hubbard band with {d}_{{\text{x}}^{\text{2}}{\text{y}}^{\text{2}}} symmetry to the O2p_{x,y} orbitals, Fig. 1b,c) in the undoped compounds is about 2 eV (ref. 5). Upon doping, a structure reminiscent of the CT gap moves to higher energies, while the gap is filled with states (intragap transitions) at the expense of spectral weight at ℏω>2 eV (ref. 5, Fig. 1d). Dynamical mean field calculations of the electron spectral function and of the abplane optical conductivity for the holedoped threeband Hubbard model recently found that the Fermi level moves into a broad (∼2 eV) and structured band of mixed Cu–O character, corresponding to the Zhang–Rice singlet states^{27}. The empty upper Hubbard band, which involves Cu–3d^{10} states, is shifted to higher energies with respect to the undoped compound, accounting for the blue shift of the optical CT edge to 2.5–3 eV. The structures appearing in the optical conductivity at 1–2 eV, that is, below the remnant of the CT gap, are mostly related to transitions between manybody Cu–O states at binding energies as high as 2 eV (for example singlet states) and states at the Fermi energy.
Timeresolved optical spectroscopy
In Figure 2, we report the time and frequencyresolved reflectivity variation in the 1.2–2 eV spectral range (δR/R(ω,t)=R_{neq}(ω,t)/R_{eq}(ω,t)1, where R_{neq}(ω,t) and R_{eq}(ω,t) are the nonequilibrium (pumped) and equilibrium (unpumped) reflectivities), for the normal (top row), pseudogap (middle row), and superconducting (bottom row) phases at three different dopings. In the normal state, δR/R(ω,t) is positive, with a fast decay over the whole spectrum, and independent of doping. At T=100 K, our frequencyresolved measurement reveals a more structured ωdependence of δR/R(ω,t). In under and optimally doped samples a positive variation is measured below ∼1.35 eV, whereas a negative signal, with a fast decay time (∼0.5 ps), extends up to 2 eV. The temperatures, at which the highenergy negative signal appears (T*∼220 K for UD83, T*∼140 K for OP96), linearly decrease as the doping increases and correspond to the onset of the universal pseudogap phase with broken timereversal symmetry^{28}. In the overdoped sample, the negative response is nearly absent, whereas the positive structure at 1.3 eV persists. Below T_{c}, a slow δR/R(ω,t) dynamics appears. This response is strongly dopingdependent, reversing sign when moving from the under to the overdoped samples. The timetraces of the δR/R(ω,t) scans at 1.5 eV probe energy (Fig. 2) exactly reproduce the timeresolved reflectivities obtained in the standard singlecolour configuration^{29,30}, that is, with fixed probe wavelength. The sudden increase of the decay time in the superconducting phase is generally attributed to a bottleneck effect in which the dynamics of quasiparticles is dominated by gapenergy bosons (ℏΩ∼2Δ_{SC}) emitted during the recombination of Cooper pairs^{31,32,33}. The experimental evidence of this bottleneck in a dwave superconductor, where the nodal quasiparticles do not emit finiteenergy bosons, strongly suggests that the dynamics is dominated by antinodal excitations^{31} and is characterized by a transient nonthermal population in the kspace, as recently shown by timeresolved photoemission experiments^{34}. These results are a benchmark for the development of realistic nonequilibrium models^{6,35,36} of strongly correlated superconductors, aimed at clarifying the nature of the bosonic glue responsible for highT_{c} superconductivity.
Normal and pseudogap phases
Good spectral resolution is mandatory to obtain a reliable fit of a differential dielectric function δɛ(ω,t)=ɛ_{neq}(ω,t)−ɛ_{eq}(ω,t), where ɛ_{neq}(ω,t) and ɛ_{eq}(ω,t) are the nonequilibrium and equilibrium dielectric functions, to the measured δR/R(ω,t) (Supplementary Note 2). In Figure 3a,b,c we report the maximum δR/R(ω,t), measured in the normal and pseudogap phases at t=200 fs. At T=300 K the fit to the data (black lines) is obtained by assuming an increase of the effective temperature, for all the doping levels. As the pseudogap phase is entered, the measured δR/R(ω,t) becomes incompatible with a simple heating of the system. The nearly flat negative signal above ∼1.5 eV is well reproduced assuming an impulsive modification of the extended Drude model parameters, such as a weakening of the electron–boson coupling, without invoking any variation of the interband oscillators.
Superconducting phase
In Figure 4a, we report the maximum δR/R(ω,t), measured in the superconducting phase in the 1.2–2.2 eV energy range. At all doping levels, the data cannot be reproduced by modifying the extended Drude model parameters. The structured variation of the reflectivity at high energies can be only accounted for by assuming a modification of both the 1.5 and 2 eV oscillators (Supplementary Note 2). The fits to the data automatically satisfy the Kramers–Kronig relations, because they are obtained as a difference between Kramers–Kronigconstrained Lorentz oscillators, and are used to calculate the relative variation of the optical conductivity (δσ_{1}/σ_{1}(ω,t) shown in the inset of Figure 4a). The trend from positive δσ_{1}/σ_{1}(ω,t) in the underdoped to a slightly negative δσ_{1}/σ_{1}(ω,t) in the overdoped samples reveals that the interband spectral weight variation (δSW_{tot}=δω^{2}_{p}(1.5)/8+δω^{2}_{p}(2)/8, ω_{p}(1.5) and ω_{p}(2) being the plasma frequencies of the 1.5 and 2 eV oscillators) strongly depends on the doping. We remark that, at higher probe energies (3.14 eV), a negligible δR/R(t) value for OP96 is observed, confirming that the transitions at energies larger than 2 eV are not significantly affected by the 2Δ_{SC} suppression.
Discussion
In the simple energygap model for conventional superconductors^{37,38}, small changes of the interband transitions, over a narrow frequency range of the order of ω_{0i}±Δ_{SC}/ℏ, can arise from the opening of the superconducting gap at the Fermi level. In contrast to this model, the partial suppression of 2Δ_{SC} photoinduced by the pump pulse, induces a change of R(ω,t) over a spectral range (∼1 eV) significantly broader than 2Δ_{SC}∼80 meV (ref. 39). This result reveals a dramatic superconductivityinduced modification of the Cu–O electronic excitations at 1.5 and 2 eV.
In the timedomain, we obtain that the dynamics of δSW_{tot} (reported in Fig. 4b) is nearly exponential with a time constant ô=2.5±0.5 ps. The δSW_{tot} variation is completely washed out at longer times (>5 ps), when the complete electron–boson thermalization broadens the Drude peak, overwhelming the contribution of δSW_{tot}. It is worth noting that the photoinduced modifications of δSW_{tot} vanish as T_{c} is approached from below (Fig. 4c), demonstrating that this effect is exclusively related to the impulsive partial suppression of 2Δ_{SC}. Further evidence of the direct relation between 2Δ_{SC} and δSW_{tot} is obtained from a comparison with timeresolved experiments with probe energy in the midinfrared^{40} and THz regions^{41,42}, directly showing a recovery time of the superconducting gap and condensate ranging from 2 to 8 ps, for different families of cuprates and different experimental conditions (that is, temperature and pump fluence). The correspondence between these timescales and the recovery time of δSW_{tot} finally demonstrates the interplay between the excitations at 1.5 and 2 eV and the superconducting gap 2Δ_{SC}. In addition, our results clarify the origin of the doping and temperaturedependent δR/R(t) signal measured in singlecolour experiments^{24,29,30,31,32,33} at highenergy scales and demonstrate that the dynamics of 2Δ_{SC}(t) can be reconstructed exploiting the δR/R(t) signal measured at highenergies (Fig. 4d and Supplementary Note 4).
Assuming that the total spectral weight change of the interband transitions is compensated by an opposite change of the Drudelike optical conductivity, we can estimate a superconductivityinduced kinetic energy decrease of ∼1–2 meV per Cu atom for the underdoped sample (Methods). This value is very close to the superconductivityinduced kinetic energy gain predicted by several unconventional models^{43,44}. As we move from the under to the overdoped side of the superconducting dome (Fig. 4e), we obtain that the modification of the SW of optical transitions, involving excitations at 1.5 and 2 eV, completely accounts for the transition from a superconductivityinduced gain to a loss of kinetic energy^{12,17,18,19,20}, estimated by equilibrium optical spectroscopies, directly measuring the lowenergy optical properties, and singlecolour timeresolved reflectivity measurements^{29}. This result indicates that most of the superconductivityinduced modifications of the excitation spectrum and optical properties at the lowenergy scale are compensated by a variation of the inplane electronic excitations at 1.5 and 2 eV, demonstrating that these excitations are at the base of an unconventional superconductive mechanism both in the under and overdoped sides of the superconducting dome.
In conclusion, we have exploited the timeresolution of a novel pumpsupercontinuumprobe optical spectroscopy to unambiguously demonstrate that, in Bi_{2}Sr_{2}Ca_{0.92}Y_{0.08}Cu_{2}O_{8+δ}, the superconductive transition is strongly unconventional both in the under and overdoped sides of the superconducting dome, involving inplane Cu–O excitations at 1.5 and 2 eV. When moving from below to above the optimal hole doping, the spectral weight variation of these features entirely accounts for a crossover from a superconductivityinduced gain to a BCSlike loss of the carrier kinetic energy^{4,19,20}.
Superconductivityinduced changes of the optical properties at highenergy scales (ℏω>100Δ_{SC}) seem to be a universal feature of hightemperature superconductors^{5,7,11}, indicating that the comprehension of the interplay between lowenergy excitations and the highenergy scale physics, associated with Mottlike excitations, will be decisive in understanding hightemperature superconductivity.
Methods
Pumpsupercontinuumprobe technique
The optical pumpprobe setup is based on a cavitydumped Ti:sapphire oscillator. The output is a train of 800 nm–140 fs pulses with an energy of 40 nJ per pulse. A 12cmlong photonic crystal fibre, with a 1.6μm core, is seeded with 5 nJ per pulse focused onto the core by an aspherical lens. The supercontinuum probe output is collimated and refocused on the sample through achromatic doublets in the nearIR/visible range. The 800 nm oscillator output (pump) and the supercontinuum beam (probe), orthogonally polarized, are noncollinearly focused onto the sample. The superposition on the sample and the spot dimensions (40 μm for the IRpump and 20 μm for the supercontinuum probe) are monitored through a chargecoupled device camera. The pump fluence is ∼10 μJ cm^{−2}. The probe beam impinges on the sample surface nearly perpendicularly, ensuring that the abplane reflectivity is measured. The reflected probe beam is spectrally dispersed through an SF11 equilateral prism and imaged on a 128pixellinear photodiode array (PDA), capturing the 620–1,000 nm spectral region. A spectral slice, whose width ranges from 2 at 620 nm to 6 at 1,000 nm, is acquired by each pixel of the array. The probe beam is sampled before the interaction with the pump and used as a reference for the supercontinuum intensity. The outputs of the two PDAs are acquired through a 22 bit/2 MHz fast digitizer, and are divided pixel by pixel to compensate the supercontinuum intensity fluctuations, obtaining a signal to noise ratio of the order of 10^{−4} acquiring 2,000 spectra in about 1 s. The differential reflectivity signal is obtained modulating the pump beam with a mechanical chopper and performing the difference between unpumped and pumped spectra. The spectral and temporal structure of the supercontinuum pulse has been determined either by exploiting the switching character of the photoinduced insulatortometal phase transition in a VO_{2} multifilm^{23} or by standard XFROG techniques. The data reported in Figure 2 have been corrected taking into account the spectral and temporal structure of the supercontinuum pulse.
Spectroscopic ellipsometry
The abplane dielectric function of the Bi_{2}Sr_{2}Ca_{0.92}Y_{0.08}Cu_{2}O_{8+δ} samples has been obtained by applying the Kramers–Kronig relations to the reflectivity for 50 cm^{−1}<ω/2πc<6,000 cm^{−1} and directly from ellipsometry for 1,500 cm^{−1}<ω/2πc<36,000 cm^{−1}. This combination allows a very accurate determination of ɛ(ω) in the entire combined frequency range. Due to the offnormal angle of incidence used with ellipsometry, the abplane pseudodielectric function had to be corrected for the caxis admixture.
Samples
The Ysubstituted Bi2212 single crystals were grown in an image furnace by the travellingsolvent floatingzone technique with a nonzero Y content in order to maximize T_{c} (ref. 45). The underdoped samples were annealed at 550 °C for 12 days in a vacuumsealed glass ampoule with copper metal inside. The overdoped samples were annealed in a quartz test tube under pure oxygen flow at 500 °C for 7 days. To avoid damage of the surfaces, the crystals were embedded in Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} powder during the annealing procedure. In both cases, the quartz tube was quenched to icewater bath after annealing to preserve the oxygen content at annealing temperature. For the optimally doped sample (OP96), the critical temperature reported (T_{c}=96 K) is the onset temperature of the superconducting phase transition, the transition being very narrow (ΔT_{c}<2 K). As a meaningful parameter for the under (T_{c}=83 K, UD83) and overdoped (T_{c}=86 K, OD86) samples, which have respective transition widths of ΔT_{c}∼8 K and ΔT_{c}∼5 K, we report the transition midpoint temperatures. The hole concentration p is estimated through the phenomenological formula^{46} T_{c}/T_{c,max}=1–82.6·(p−0.16)^{2}, where T_{c,max} is the critical temperature of the optimally doped sample.
Kinetic energy
Below the critical temperature T_{c}, possible modifications of the highenergy spectral weight , including the contribution to the optical conductivity from all the possible interband transitions i, must compensate the spectral weight of the condensate zerofrequency δfunction, SW_{δ}, and the variation of the spectral weight of the Drudelike optical conductivity, , related to the free carriers in the conduction band. This is expressed by the Ferrell–Glover–Tinkham sum rule^{4}:
where the superscripts refer to the normal (N) and superconducting (SC) phases.
In the special case of a single conduction band within the nearestneighbour tightbinding model^{43,44}, the total intraband spectral weight SW_{D} can be related to the kinetic energy T_{δ} of the charge carriers (holes) associated to hopping process in the δ direction, via the relation^{43}:
where a_{δ} is the lattice spacing in the Cu–O plane, projected along the direction determined by the inplane polarization δ of the incident light and V_{Cu} is the volume per Cu atom. We obtain 〈K〉=2〈T_{δ}〉 from the spectral weight variation of the interband oscillators, through the relation:
Considering V_{Cu}=V_{unit cell}/8∼1.1·10^{−22} cm^{3} and a_{δ}=a_{unit cell}/√2∼3.9 Å, we obtain that the kinetic energy can be calculated as 〈K〉=8ℏ^{2}[SW_{h}^{N}–SW_{h}^{SC}]·(83 meV/eV^{2}), where 8ℏ^{2}[SW_{h}^{N}–SW_{h}^{SC}] is the interband spectral weight variation expressed in eV^{2}. A finite value of SW_{h}^{N}–SW_{h}^{SC} thus implies a superconductivityinduced variation of the kinetic energy. To obtain the total kinetic energy variation related to the condensate formation, we estimate a photoinduced breaking of ∼3–7% of the Cooper pairs (Supplementary Note 3), and we extrapolate the measured SW_{h}^{N}–SW_{h}^{SC} values, reported in Figure 4c–e, to the values corresponding to the breaking of 100% of the Cooper pairs.
Additional information
How to cite this article: Giannetti, C. et al. Revealing the highenergy electronic excitations underlying the onset of hightemperature superconductivity in cuprates. Nat. Commun. 2:353 doi: 10.1038/ncomms1354 (2011).
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Acknowledgements
We acknowledge valuable discussion from M. Capone, E. van Heumen, P. Marchetti, F. Carbone and P. Galinetto. F.C., G.C., and F.P. acknowledge the support of the Italian Ministry of University and Research under Grant Nos. FIRBRBAP045JF2 and FIRBRBAP06AWK3. The crystal growth work was supported by DOE under Contracts No. DEFG0399ER45773 and No. DEAC0376SF00515 and by NSF under Grant No. DMR9985067. The work at UBC was supported by the Killam Program (A.D.), the Alfred P. Sloan Foundation (A.D.), the CRC Program (A.D.), NSERC, CFI, CIFAR Quantum Materials, and BCSI.
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C.G. and F.P. conceived the project and the timeresolved experiments. C.G. coordinated the research activities with input from all the coauthors, particularly F.P., A.D., D.vdM. and M.G. C.G., F.C. and G.F. designed and developed the pumpsupercontinuumprobe technique. C.G., F.C., S.D.C. and G.C. performed the timeresolved measurements and analysed the data. M.R., R.L., H.E., M.G. and A.D. produced and characterized the crystals. H.M. and D.vdM performed the equilibrium spectroscopic ellipsometry measurements. The text was drafted by C.G. with inputs from F.P., A.D. and D.vdM. All authors extensively discussed the results and the interpretation, and revised the manuscript.
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Giannetti, C., Cilento, F., Conte, S. et al. Revealing the highenergy electronic excitations underlying the onset of hightemperature superconductivity in cuprates. Nat Commun 2, 353 (2011). https://doi.org/10.1038/ncomms1354
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DOI: https://doi.org/10.1038/ncomms1354
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