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Ultrafast Mid-Infrared Response of YBa2Cu3O7-δ

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Science  21 Jan 2000:
Vol. 287, Issue 5452, pp. 470-473
DOI: 10.1126/science.287.5452.470

Abstract

Optical spectra of high-transition-temperature superconductors in the mid-infrared display a gap of in-plane conductivity whose role for superconductivity remains unresolved. Femtosecond measurements of the mid-infrared reflectivity of YBa2Cu3O7-δ after nonequilibrium optical excitation are used to demonstrate the ultrafast fill-in of this gap and reveal two gap constituents: a picosecond recovery of the superconducting condensate in underdoped and optimally doped material and, in underdoped YBa2Cu3O7-δ, an additional subpicosecond component related to pseudogap correlations. The temperature-dependent amplitudes of both contributions correlate with the antiferromagnetic 41-millielectronvolt peak in neutron scattering, supporting the coupling between charges and spin excitations.

A number of energy-sensitive studies on high-transition-temperature (highT C) cuprate superconductors including tunneling (1), angular-resolved photoemission (2), neutron scattering (3), Raman scattering (4), and infrared reflectivity (5–8) suggest that understanding the elementary excitations in the mid-infrared energy range (ℏ︀ω ≈ 40 to 200 meV) in the vicinity of the superconducting gap is essential for clarifying the mechanisms behind formation of the superconducting condensate. In particular, the low-energy electromagnetic response of such cuprates contains valuable information on electronic excitations and their correlated dynamics. When temperature T is lowered below the superconducting transition in optimally doped materials, the most pronounced changes of the reflectivityR(ω,T) for light of frequency ω polarized parallel to the superconducting CuO2 planes [(ab)-plane reflectivity] appear in the spectral range around ℏ︀ω ≈ 100 meV. These reflectivity changes (Fig. 1A) are directly connected with a strong depression of the in-plane conductivity (Fig. 1C), which has been attributed to the opening of a gap for electronic transitions involving inelastic collisions. A straightforward association with the superconducting gap, however, is hampered by the observation that, in underdoped cuprates, such features already occur at temperaturesT* substantially higher thanT C (Fig. 1, B and D) and are termed pseudogap (5–8).

Figure 1

Stationary reflectivity and conductivity spectra of the samples studied in the femtosecond experiments. (Aand B) ChangeR(T a) −R(T b) of the stationary reflectivityR(T) when temperature was raised fromT b to T afor optimally doped [T C = 88 K] (A) and underdoped [T C = 68 K] (B) YBCO. (Cand D) Real part of optical conductivity σ1(ω,T) normalized to its value atT = 200 K as obtained from Kramers- Kronig analysis of the reflectivity spectra at various lattice temperatures for optimally doped (C) and underdoped (D) (T C = 68 K) YBCO.

While stationary infrared spectroscopy measures the total of all contributions to the mid-infrared reflectivity and cannot clearly discern spectrally similar components in the pseudogap regime, nonlinear time-resolved spectroscopy could provide such a distinction by separating the components in the time domain. Previous ultrafast optical experiments with high-T C superconductors have given information on the time scales of carrier and condensate relaxation dynamics by nonequilibrium excitation of the carrier system at photon energies of 1.5 eV and subsequently studying its dynamics either at the same interband energies (9–11) or in the far-infrared around ℏ︀ω ≈ 0 to 3 meV (12). Here, we present experimental results probing the mid-infrared spectra in high-T C superconductors on ultrafast time scales.

The superconductor is excited by 20-fs (pump) pulses at 1.6 eV from a mode-locked, cavity-dumped Ti:sapphire laser operating at a 2-MHz repetition rate. Mid-infrared (probe) pulses broadly tunable from 60 to 180 meV are derived from a newly developed difference frequency mixing scheme, with pulse durations typically of 150 fs (13). We present results for optimally doped (T C = 88 ± 0.7 K) and underdoped (T C = 68 ± 1.5 K) thin films of YBa2Cu3O7-δ (YBCO). We achieved underdoping (deoxygenation) by sintering optimally doped films at reduced oxygen pressure (14, 15). The 200-nm-thick twinned films are c-axis oriented; thus the mid-infrared beam, polarized parallel to the sample surface, probes directly the (ab)-plane reflectivity. The change of the reflected mid-infrared intensity induced by the pump pulse is recorded as a function of delay and spectral position E probeof the probe pulses (16).

In the time-resolved mid-infrared response of optimally doped YBCO at E probe = 90 meV (Fig. 2A), a fast, subpicosecond reflectivity increase to ΔR/R 0 ≈ 3 × 10−3 is followed by a decay on a much longer time scale of about 5 ps. With increasing sample temperature, the amplitude of ΔR/R 0 decreases and, aroundT C, changes its sign accompanied by a relaxation speedup. This distinction between reflectivity changes at temperaturesT < T C and T >T C is confirmed by the transient spectra of ΔR/R 0 (Fig. 2, C and D). Below T C (Fig. 2C) (T = 14 K), the spectra peak sharply at E probe = 90 meV. The energy position of this peak and the zero crossing at 70 meV remains constant for all delay times. The same holds true for other temperatures below T C. Above T C(Fig. 2D) (T = 94 K), the behavior drastically changes to a spectrally flat response.

Figure 2

Optimally doped YBCO. (A) Transient reflectivity change ΔR/R 0 = [R(t) −R 0]/R 0[R(t) and R 0 are reflectivity with and without excitation, respectively] as a function of time delay between near-infrared pump and mid-infrared probe pulses (probe photon energy E probe = 90 meV;T, sample temperature). (B) Solid squares, temperature dependence ofA N(T) =A(T)/A(10 K), shown for data below T C, whereA(T) = max(ΔR/R 0) denotes maximum amplitude of transients at temperature T. Open circles, amplitude of the 41-meV resonance peak obtained from inelastic neutron scattering in (3) normalized to the 10 K value. (Cand D) Transient differential reflectivity spectra at different time delays between pump and probe. Sample temperatures areT = 14 K ≪ T C (C) andT = 94 K > T C(D).

We now compare the time-resolved reflectivity spectra to the changes induced in the stationary (ab)-plane reflectivity R(ω,T) as the sample temperature is raised from below to above T C. InFig. 1 (A and C), the difference of reflectivity spectra of our samples above T C (95 K) and belowT C (20 K) is shown along with the normalized optical conductivity as obtained from Kramers-Kronig analysis. The optical conductivity, which is a measure of the oscillator strength, exhibits a broad depletion below about 100 meV, which occurs with the onset of superconductivity and corresponds to a peak in the difference reflectivity spectra around 100 meV. The shape of this peak closely matches our transient reflectivity spectra belowT C (Fig. 2C), which confirms that the ultrafast transients directly show the ultrafast fill-in and subsequent recovery of this mid-infrared conductivity gap.

Below T C, the dynamics in the optimally doped sample is dominated by the slow relaxation of about 5 ps. Experiments probing the electrodynamic signature of the superconducting condensate in the far-infrared (12) have shown that absorption of near-infrared photons strongly reduces the condensate density (with a concurrent increase of Drude-like quasiparticle absorption), which re-forms on the same 5-ps time scale observed here. A comparison with such results is straightforward as the far-infrared response obeys basic electrodynamic properties generally valid for any superconducting condensate. Thus, the conductivity gap dynamics in the mid-infrared is directly determined by the depletion and re-formation of the superconducting condensate. With increasing sample temperature, the initial density of the condensate, and thus the amplitude of the reflectivity change, decreases (Fig. 2B, solid squares) (E probe = 90 meV).

Much faster dynamics and featureless spectra are found for the reflectivity changes above T C (Fig. 2, A and D). This is attributed to cooling of a hot quasi-equilibrium electron gas, giving rise to reflectivity changes similar to those observed in metals (17).

A direct association of the conductivity gap found belowT C with the superconducting gap has been impeded by the fact that the stationary reflectivity of underdoped cuprates shows a similar conductivity decrease to occur already below the pseudogap temperature T* >T C (T* ≈ 160 K in our underdoped sample) (5–8). Here, our femtosecond data provide a much clearer picture. Figure 3shows time-resolved ΔR/R 0 data for the underdoped sample at two different spectral positions ofE probe = 90 and 145 meV. The data taken below T C (blue and black lines, lower panels) display an overall dynamics, which extend well into the picosecond regime and cannot be described by a single—for example, exponentially decaying—component. Above T C, the transients are dominated by a fast component at early delay.

Figure 3

Underdoped YBCO. Transient reflectivity changes ΔR(t)/R 0 atE probe = 90 meV (A andB) and E probe = 145 meV (C and D) for different sample temperatures. (E) Temperature dependence of the normalized amplitudeA N(T) (solid squares) defined as in Fig. 2B compared with amplitude of the 41-meV resonance peak (open circles) of a T C = 63 K underdoped YBCO sample, from (3).

We analyzed the data of Fig. 3 and results for other probe frequencies by singular value decomposition, a standard numerical procedure previously applied to, for example, analysis of transient femtosecond spectra in biomolecular spectroscopy (18). It finds the number of mutually independent—that is, uncorrelated—components in a given input matrix containing the experimental data, where rows and columns represent temporal and spectral positions, respectively. The resulting orthonormal basis set of functions is used to construct physically meaningful components by linear combination. As additional constraints, we have assumed that the (normalized) transients decay monotonically and that subpicosecond components have totally decayed for times longer than about 30 ps. The total signal is written ΔR(ω,t) = Σi ai (ω) ×bi (t), whereai (ω) andbi (t) are spectrum and time evolution of the ith component. The results of this analysis are shown in Fig. 4. The ΔR/R 0 transients are essentially described by two components, one with a slow decay (about 5 ps) and one with a much faster decay (about 700 fs). The slow component exhibits a decay dynamics (Fig. 4A) and a spectrum (Fig. 4B) almost identical with that of the condensate in the optimally doped sample. In particular, it disappears completely above T C. The fast component (Fig. 4A, spectra in Fig. 4C) exists both below and aboveT C up to T* ≈ 160 K where the reflectivity transients change their sign and the decay rate becomes even faster (Fig. 3, A and C, brown curves).

Figure 4

Results of the singular value decomposition applied to the full data set for the underdoped sample, as explained in text. (A) Two components as normalized transients (black lines) obtained from decomposition atT = 14 K. Fast component retains its dynamics over temperature. For comparison, data at T = 100 K (magenta) are shown, where only the fast component exists. (Band C) Differential reflectivity spectra of the slow and fast transients at different temperatures: T = 14 K (red squares), 50 K (olive circles), 75 K (magenta up triangles), 100 K (cyan down triangles), 145 K (blue diamonds). (D) Amplitudes at E probe = 90 meV of the fast (open circles) and slow (solid diamonds) components obtained from decomposition in (B) and (C) together with the totalA N(T) (solid line) from Fig. 3E.

The existence of the two dynamic components in the underdoped sample results in a temperature dependence of the ΔR/R 0 amplitudes that is different from the optimally doped sample. At E probe= 90 meV, a large fraction of the optically induced reflectivity changes has faded out at T C but a substantial part remains even for significantly higher temperatures (Fig. 3E, solid squares). The above decomposition shows that this results from separate contributions of fast and slow components (Fig. 4D, as determined from the singular value decomposition amplitudes atE probe = 90 meV) (19).

The observation of two different reflectivity components on a femtosecond time scale allows us to draw a new picture of the mid-infrared response of underdoped cuprates. Ultrafast excitation of the electronic system leads to a breakup of both condensed pairs and a second type of correlated carriers. The decomposition in Fig. 4D gives the relative contribution of those two types of quasiparticles. The dominating slow (about 5 ps) component follows the gap related to condensed pairs and fades out at T C as in optimally doped samples. In contrast, the fast (about 700 fs) component exists up to the pseudogap temperature T*. It results from the breakup and re-formation of carrier correlations, which have been ascribed to preformed pairs (20) or antiferromagnetic couplings (21).

The electronic response probed at mid-infrared energies far below the plasma frequency (≈15,000 cm−1) is determined by intraband processes ≲ 100 meV close to the Fermi energy, which are indirect transitions formed by a charge excitation plus a momentum-conserving boson. Recent theories of the stationary infrared properties of cuprates (22, 23) suggest that the coupling to 41-meV antiferromagnetic (AF) spin fluctuations, which were observed as a resonance peak in inelastic neutron scattering (3) and treated theoretically in (21,24), represents the dominant process in momentum conservation. As a result, the conductivity gap does not occur simply at twice the superconducting gap 2Δ00 ≈ 25 meV in YBCO) but includes the energy of the AF spin fluctuation. This model is strongly supported by a comparison of our femtosecond data with the strength of the 41-meV AF resonance peak. The amplitude of this peak decreases with temperature, as shown in Figs. 2B and 3E (open circles). Our optical measurements show an identical behavior of the ΔR/R 0 amplitudes. The fact that charge-and-spin–related amplitudes are proportional gives independent support for a prominent role of AF spin fluctuations in the mid-infrared absorption process.

A recent theoretical analysis of stationary infrared spectra has shown that coupling of quasiparticles to AF spin fluctuations is strong enough to support superconductivity up toT C = 100 K (22), neglecting, however, the pseudogap behavior in underdoped materials. Our data give evidence that the mid-infrared response below T Cof both optimally and underdoped material is dominated by the superconducting condensate. This strongly suggests that indeed AF spin fluctuations play a prominent role for coupling in the superconducting condensate.

In summary, ultrafast nonlinear optical experiments allow us to separate the superconducting gap from the pseudogap contributions in the mid-infrared response of YBCO by monitoring their distinctly different dynamics.

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