We report measurements of the photoinduced change in reflectivity of an
untwinned single crystal of YBa2Cu3O6.5 in the ortho II structure. The decay
rate of the transient change in reflectivity is found to decrease rapidly with
decreasing temperature and, below Tc, with decreasing laser intensity. We
interpret the decay as a process of thermalization of antinodal quasiparticles,
whose rate is determined by an inelastic scattering rate of quasiparticle
pairs.Comment: 4 pages, 4 figure

Bonn, D. A.

Gedik, N.

Hardy, W. N.

Liang, Ruixing

Orenstein, J.

Segre, G. P.

English

arXiv

G. P. Segre

N. Gedik

J. Orenstein

D. A. Bonn

Ruixing Liang

W. N. Hardy

Crossref

Physical Review Letters

Photoinduced Changes of Reflectivity in Single Crystals of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>YBa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>6.5</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>(Ortho II)

We report measurements of the photoinduced change in reflectivity of an untwinned single crystal of YBa2Cu3O6.5 in the ortho II structure. The decay rate of the transient change in reflectivity is found to decrease rapidly with decreasing temperature and, below Tc, with decreasing laser intensity. We interpret the decay as a process of thermalization of antinodal quasiparticles, with a rate determined by inelastic scattering of quasiparticle pairs

Segre, Gino P.

Gedik, Nuh

Orenstein, Joseph

Bonn, Doug A.

Hardy, Walter N.

UNT (University of North Texas) Digital Library

VOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 20021Photoinduced Changes of Reflectivity in Single Crystals of YBa2Cu3O6.5 (Ortho II)G. P. Segre, N. Gedik, and J. OrensteinMaterials Sciences Division, Lawrence Berkeley National Laboratory and Physics Department, University of California,Berkeley, California 94720D. A. Bonn, Ruixing Liang, and W. N. HardyUniversity of British Columbia, Vancouver, Canada(Received 15 July 2001; published 14 March 2002)We report measurements of the photoinduced change in reflectivity of an untwinned single crystal ofYBa2Cu3O6.5 in the ortho II structure. The decay rate of the transient change in reflectivity is found todecrease rapidly with decreasing temperature and, below Tc , with decreasing laser intensity. We interpretthe decay as a process of thermalization of antinodal quasiparticles, with a rate determined by inelasticscattering of quasiparticle pairs.DOI: 10.1103/PhysRevLett.88.137001 PACS numbers: 74.25.Gz, 78.47.+pThe desire to understand the pseudogap phenomenoncontinues to dominate research in the high-Tc cuprates.At issue is the nature of the partial gap that onsets wellabove Tc in underdoped materials. The gap is likely to bea manifestation of either fluctuating or long-range order.A key question is whether this order competes with orenhances superconductivity, or is, in fact, a fluctuatingform of the superconducting phase itself.One approach to answering this question is to studythe dynamics of nonequilibrium quasiparticles, which canbe extremely sensitive to a gap [1,2]. A promising tech-nique to study such dynamics is optical pump and probespectroscopy. In this type of experiment a pulse of lightstimulates a nonequilibrium state with excess energy andquasiparticle density. A weaker pulse, which is delayedrelative to the pump, probes the nonequilibrium state bydetecting changes in the absorptance or reflectance. Dy-namics can be measured with subpicosecond time reso-lution while anisotropy can be explored by varying thepolarization of the pump and probe beams.In this paper we report pump and probe measurementsperformed on an untwinned single crystal of YBa2Cu3O6.5(Ortho II). Together with YBa2Cu4O8 it is one of two un-derdoped materials in which doping does not introducedisorder. We find, in contrast with an earlier report [3]on underdoped films, that the decay rate of the photoin-duced change in reflectivity, DRR, depends strongly onthe excitation density and temperature. Because it van-ishes in the limit that both tend to zero, we interpret thedecay rate as an inelastic scattering rate of quasiparticlepairs. We present evidence that the decay corresponds toa process of thermalization, rather than recombination, ofthe nonequilibrium quasiparticle population. The dynam-ics of thermalization change suddenly upon crossing fromthe pseudogap regime to the superconducting state.We measured the decay of the DRR at a photon en-ergy of 1.5 eV due to excitation with photons of the sameenergy. The optical pulses are produced by a mode-lockedTi:sapphire laser, and have duration 100 fs, pulse to pulse37001-1 0031-90070288(13)137001(4)$20.00separation 12 ns, and center wavelength 800 nm. Both thepump and probe beams were focused onto the sample witha 20 cm focal length lens, yielding a spot size with 90%of its intensity within a 100 mm diameter. A photoelas-tic modulator varied the pump intensity at 100 kHz and avibrating mirror oscillating at 40 Hz varied the time delaybetween pump and probe. This double modulation pro-vides sensitivity to DRR of 1027.Figure 1a shows DRR due to absorption of a pumppulse of energy 0.07 nJ vs time t, at several temperatures.These reflectivity transients were measured with pump andprobe polarization aligned perpendicular to the chain axis.The amplitude of DRR increases and the decay rate de-creases as the temperature is lowered. Figure 1b showsthe temperature dependence of the maximum amplitudeDRR0. The reflectivity change is smaller when mea-sured with pump and probe parallel to the chains, particu-larly above Tc.FIG. 1. (a) DRR vs t at constant pump intensity for differenttemperatures (pump and probe both polarized perpendicular tochains). (b) Maximum amplitude of DRR vs T for polarizationparallel and perpendicular to the chains.© 2002 The American Physical Society 137001-1VOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 2002The T dependence shown in Fig. 1 is consistent withreports of DRR in underdoped (twinned) thin films ex-cited at 1.5 eV and probed at either near-infrared [1] or far-infrared [4] frequencies. As emphasized in Ref. [4], theincrease of DRR with decreasing T tracks the growth of aspin resonance peak seen by neutron scattering [5,6] and agaplike feature seen in optical conductivity [7,8]. Further-more, DRR shows the same behavior with varying carrierconcentration as do these spectroscopic features, namelyabrupt onset at Tc for near optimal doping [9] and a slowonset above Tc for underdoped materials [1,4]. Such con-siderations suggest that 1.5 eV photons ultimately generatelow-energy excitations, despite the fact that they initiallycreate an electron-hole pair whose energy is much largerthan the maximum gap D0.It is generally agreed that the generation of low-energyquasiparticles occurs via a rapid cascade process, in whichthe parent electron-hole pair creates a large number ofexcitations at much lower energy. What has remainedless clear is the mechanism by which this nonequilibriumpopulation of quasiparticles causes a change in reflectivityin the visible region of the spectrum. However, recentmeasurements [4,10] point to a mechanism for changes inreflectivity at 1.5 eV.Measurements of the change in THz conductivity ofan underdoped YBCO YBa2Cu3O61x film show thatphotoexcitation at 1.5 eV removes spectral weight fromthe condensate d function [10]. Far-IR measurements [4]reveal that this spectral weight reappears at frequenciesabove the maximum superconducting gap, or 100 meV.The Kramers-Kronig relations dictate that this redistribu-tion of spectral weight changes the real part of the dielec-tric function at much higher frequencies v accordingto De1v  28v4S, where S Rdv0 Ds1v0v02and Ds1 is the change in the real part of the opti-cal conductivity. The change in reflectivity at 1.5 eV,DRR  20.225De1, can be obtained from literature[11] values for the dielectric function, e1  1.1 ande2  2.7.The rate of increase of the photoinduced reflectivitywith increasing pump intensity provides a quantitativetest of the link between DRR and S. According to themechanism described above, DR reaches an upper limit,DRsat, when photoexcitation shifts the entire condensatespectral weight to nonzero frequency. Figure 2 showsDRR0 at 15 K vs u  lE4pr20 , the average energydensity deposited by the pump in the volume that isprobed (l  1.3 3 1025 Å is the penetration depth ofthe pump beam, E is the energy of the pump pulse, andr0  42 mm is the 1e radius of the laser intensity).There is a clear tendency toward saturation evident inthe data, which allows us to estimate DRsat. The dashedline shows the best fit to a simple saturation model,DR0DRsat  lu021Rdz1 2 e2uzusat uz, whereuz is the average energy density at a depth z be-low the sample surface. The best fit parameters areDRRsat  1.1 3 1023 and usat  0.43 Jcm3.137001-2FIG. 2. DRR vs excitation density at 15 K. The dashed lineis the best fit to the saturation model described in the text.We now compare the above value of DRsat with thatexpected if all the condensate spectral weight is shiftedaway from v  0. The value of De1 at saturation isv2pv2	v4, where vp is the plasma frequency corre-sponding to the condensate spectral weight and v2	 isthe mean square frequency shift. Using vp  1.5 eV [12]and De1sat  4.9 3 1023, we obtain v2	  130 meV2.That this frequency shift is comparable to that directly ob-served by Kaindl et al. [4] strongly supports our interpre-tation of the photoinduced change in reflectivity.We now turn to the rate of decay of DRR measuredas a function of T and pump intensity I. We have seenin Fig. 1 that the decay of DRR becomes slower as Tdecreases. Figure 3a, a plot of the reflectivity change at15 K created by pulses of varying intensity, shows that thedecay rate also slows as the excitation density decreases.The decays shown in Fig. 3a are nonexponential in thatthe instantaneous rate of decay, gt  2dlnDRdt,decreases as t increases. To characterize the intensity de-pendence of the decay rate in a relatively simple way, wefocus on the initial decay rate, or g0. We estimate g0from the slope of DRtR between 100% and 75% ofDRR0, normalized by the average value of DRtRin that interval. Given our time resolution, this proce-dure provides a good estimate of g0 for rates slower than1 ps21. Figure 3b shows g0 as a function of DRR0,obtained by analysis of the curves similar to the ones inFig. 3a. g0 varies linearly with DRR0 and extrapo-lates to a nonzero intercept as the excitation density ap-proaches zero.The dependence of g0 on excitation density is con-sistent with two-particle kinetics, for example, a processin which a pair of quasiparticles scatter off of each other.For high excitation densities the rate of such scattering isproportional to the nonequilibrium density. As the excita-tion density decreases, becoming smaller than the thermalpopulation, g0 approaches the equilibrium scattering rateat that temperature [13,14].137001-2VOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 2002FIG. 3. (a) Decay of DRR for several pump intensities at15 K. (b) Initial decay rate g0 vs DRR0.Figure 4 presents the temperature dependence of thedecay rate for a range of intensities, in the form of a loga-rithmic plot of g0 vs T . Points with the same (open)symbol show g0 measured at the same excitation density.The data sets coincide at high temperatures but diverge atTc  57 K. This indicates that the dependence of g0on I starts abruptly upon crossing from the pseudogap tothe superconducting state. The solid symbols show thedecay rate in the limit of zero excitation density, gth, asdetermined from the intercept of plots such as in Fig. 3b.The same quantity is plotted on linear axes in the inset. For10 , T , 40 K, gth appears to vary as T 3, although giventhe experimental uncertainty an activated form cannot beexcluded.The decay rates shown in Fig. 4 were measured with theprobe beam polarized perpendicular to the chains. We findthat the rates measured with the probe polarized parallelto the chains are indistinguishable, within the sensitivityof our measurement, for all T and I. The absence of po-larization dependence suggests that the carrier relaxationprocesses probed in this experiment take place in the CuOplane and not in the chain layers. Given this observation,137001-3FIG. 4. Initial decay rate g0 vs T at fixed I (open symbols).Decay rate in low I limit, gth, vs T (solid symbols in main paneland inset).we speculate that the difference in DRR for the orthogo-nal polarizations (Fig. 1b) is due to anisotropy in the spec-tral weight shifted by the nonequilibrium quasiparticles.Several aspects of the decay rate of DRR suggest astrong connection to quasiparticle dynamics and the den-sity of states. For example, the decay rate appears sensitiveto the opening of the pseudogap, decreasing near T in amanner which is remarkably similar to the nuclear spinrelaxation rate in underdoped YBCO [15]. The onset ofsuperconductivity also affects the decay dynamics — thedecay rate depends on excitation density only below Tc.Finally the T 3 dependence of gth is consistent with a pre-diction for the recombination and scattering rate of nodalquasiparticles [16].The simplest interpretation of the connection betweeng0 and quasiparticle dynamics is that DRtR reflectsthe decay of the nonequilibrium quasiparticle density. Ac-cording to this view, g0 is the rate at which quasipar-ticle pairs scatter into the condensate and gth is its valuein thermal equilibrium. However, this description of thedecay of DRR cannot be complete because for quasipar-ticles to scatter into the condensate they must shed theirexcess energy. In the model of Ref. [16] the excess en-ergy appears as a spin fluctuation, which is built fromparticle-hole excitations of the same band of electrons thatform the condensate. Therefore the “recombination” pro-cess essentially scatters one pair into another, with no re-duction in the number or energy density. This is analogousto a problem in the interpretation of transport experiments,where quasiparticle scattering alone cannot reduce the to-tal momentum [17].The actual recombination rate, in the sense of recov-ery of the equilibrium quasiparticle density, would likelybe much slower than the quasiparticle scattering describedabove. Decay of the quasiparticle density requires that ex-cess energy flow irreversibly away from the system of su-perconducting electrons to the lattice vibrations [18]. We137001-3VOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 2002expect such a process to be extremely slow on the timescale of quasiparticle scattering and to exhibit single ratherthan two-particle kinetics. This expectation is based on thephysics of the “phonon bottleneck” in s-wave supercon-ductors [13,14], an effect which may be even more restric-tive in d-wave superconductors.The bottleneck arises because the process in which aquasiparticle pair emits a phonon and scatters into the con-densate is reversible— the emitted phonon can immedi-ately regenerate the quasiparticle pair. The quasiparticledensity relaxes at the rate at which the typical phonon en-ergy decreases below the threshold for pair creation. Notonly is this rate slower than the quasiparticle scatteringrate, it is also approximately independent of the excessquasiparticle density. Experiments with pulsed photoex-citation have provided convincing evidence that the relax-ation of the quasiparticle density in Pb films, for example,is limited by the phonon bottleneck [19,20].The relaxation of the quasiparticle density may be evenslower in the cuprates than in conventional superconduc-tors. In s-wave superconductors the phonons decouplefrom the electrons when their energy becomes less than2D. In the d-wave superconductors, where there is nothreshold for pair creation, the typical phonon energy mustdegrade to kBT in order for the electronic system to reachequilibrium. The extremely weak coupling between nodalquasiparticles and phonons compounds this effect. Thedecay of a quasiparticle pair into an acoustic phonon iskinematically forbidden because the quasiparticle velocityis larger than the sound velocity [18].If relaxation of the nonequilibrium density is extremelyslow, why does DRR decay on a picosecond time scale?The remaining possibility is that the decay correspondsto thermalization, rather than recombination. If DRRis not a direct measure of the quasiparticle density, butproportional instead to S as we have argued previously,it can decrease during thermalization, despite a constant,or even increasing, density of quasiparticles. Microwavemeasurements show that S for nodal particles is small,because their spectral weight is confined to a very nar-row 10 meV Drude peak [21]. The 100 meV spec-tral weight shifts [4], and consequently large values of S,are likely due to the antinodal quasiparticles. These con-siderations suggest that the decay of DRR measured at1.5 eV tracks the conversion of quasiparticles from a non-thermal distribution, which has substantial S, to a qua-sithermal distribution in which S is a factor 108 smaller.Measurements in which the nonequilibrium state is probedin the frequency range of the Drude conductivity [18] showmuch longer decay times (typically milliseconds), consis-137001-4tent with an experiment which selectively probes the nodalquasiparticle density.In summary, we present measurements of the photoin-duced change in reflectivity in an underdoped crystal ofYBCO, and discuss a new perspective on this effect. Weinterpret the decay rate of DRR as the inelastic scatter-ing rate of quasiparticle pairs, which sets the time scalefor thermalization of the nonequilibrium population. Thethermalization rate decreases with the development of thepseudogap, becomes excitation density dependent in thesuperconducting state, and decreases rapidly with decreas-ing T in the low excitation limit. Coordinated measure-ments of photoinduced changes in optical response over abroad spectral range, from terahertz to visible frequencies,are needed to test this perspective.We acknowledge valuable discussions with D. J.Scalapino. This work was supported by NSF-9870258,DOE-DE-AC03-76SF00098, CIAR, and NSERC.[1] V. V. Kabanov et al., Phys. Rev. B 59, 1497 (1999).[2] J. Demsar et al., Phys. Rev. Lett. 83, 800 (1999).[3] D. Mihailovic and J. Demsar, in Spectroscopy of Super-conducting Materials, ACS Symposium Series Vol. 730,edited by E. Faulqes (American Chemical Society, Wash-ington, D.C., 1999).[4] R. Kaindl et al., Science 287, 470 (2000).[5] J. Rossat-Mignod et al., Physica (Amsterdam) 185–189C,86 (1991).[6] H. A. Mook et al., Phys. Rev. Lett. 70, 3490 (1993); H. F.Fong et al., ibid. 75, 316 (1995).[7] J. Orenstein et al., Phys. Rev. B 42, 6342 (1990).[8] L. D. Rotter et al., Phys. Rev. Lett. 67, 2741 (1991).[9] R. D. Averitt et al., Phys. Rev. B 63, 140502 (2001).[10] J. M. Chwalek et al., Appl. Phys. Lett. 57, 980 (1990).[11] S. L. Cooper et al., Phys. Rev. B 47, 8233 (1993).[12] D. N. Basov et al., Phys. Rev. Lett. 74, 598 (1995).[13] A. Rothwarf and B. N. Taylor, Phys. Rev. Lett. 19, 27(1967).[14] For a review see K. E. Gray, in Nonequilibrium Super-conductivity, Phonons, and Kapitza Boundaries, edited byK. E. Gray (Plenum Press, New York, 1981).[15] W. W. Warren et al., Phys. Rev. Lett. 62, 1193 (1989).[16] S. M. Quinlan et al., Phys. Rev. B 49, 1470 (1994).[17] M. B. Walker and M. F. Smith, Phys. Rev. B 61, 11 285(2000).[18] B. J. Feenstra et al., Phys. Rev. Lett. 79, 4890 (1997).[19] C. C. Chi et al., Phys. Rev. B 23, 124 (1981).[20] G. L. Carr et al., Phys. Rev. Lett. 85, 3001 (2000).[21] A. Hosseini et al., Phys. Rev. B 60, 1349 (1999).137001-4

Photoinduced changes of reflectivity in single crystals of YBa2Cu3O6.5 (Ortho II)

eScholarship - University of California

Lawrence Berkeley National LaboratoryLBL PublicationsTitlePhotoinduced changes of reflectivity in single crystals of YBa2Cu3O6.5 (Ortho II)Permalinkhttps://escholarship.org/uc/item/56r576p0JournalPhysical Review Letters, 88(13)AuthorsSegre, Gino P.Gedik, NuhOrenstein, Josephet al.Publication Date2002-03-14eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaVOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 20021Photoinduced Changes of Reflectivity in Single Crystals of YBa2Cu3O6.5 (Ortho II)G. P. Segre, N. Gedik, and J. OrensteinMaterials Sciences Division, Lawrence Berkeley National Laboratory and Physics Department, University of California,Berkeley, California 94720D. A. Bonn, Ruixing Liang, and W. N. HardyUniversity of British Columbia, Vancouver, Canada(Received 15 July 2001; published 14 March 2002)We report measurements of the photoinduced change in reflectivity of an untwinned single crystal ofYBa2Cu3O6.5 in the ortho II structure. The decay rate of the transient change in reflectivity is found todecrease rapidly with decreasing temperature and, below Tc , with decreasing laser intensity. We interpretthe decay as a process of thermalization of antinodal quasiparticles, with a rate determined by inelasticscattering of quasiparticle pairs.DOI: 10.1103/PhysRevLett.88.137001 PACS numbers: 74.25.Gz, 78.47.+pThe desire to understand the pseudogap phenomenoncontinues to dominate research in the high-Tc cuprates.At issue is the nature of the partial gap that onsets wellabove Tc in underdoped materials. The gap is likely to bea manifestation of either fluctuating or long-range order.A key question is whether this order competes with orenhances superconductivity, or is, in fact, a fluctuatingform of the superconducting phase itself.One approach to answering this question is to studythe dynamics of nonequilibrium quasiparticles, which canbe extremely sensitive to a gap [1,2]. A promising tech-nique to study such dynamics is optical pump and probespectroscopy. In this type of experiment a pulse of lightstimulates a nonequilibrium state with excess energy andquasiparticle density. A weaker pulse, which is delayedrelative to the pump, probes the nonequilibrium state bydetecting changes in the absorptance or reflectance. Dy-namics can be measured with subpicosecond time reso-lution while anisotropy can be explored by varying thepolarization of the pump and probe beams.In this paper we report pump and probe measurementsperformed on an untwinned single crystal of YBa2Cu3O6.5(Ortho II). Together with YBa2Cu4O8 it is one of two un-derdoped materials in which doping does not introducedisorder. We find, in contrast with an earlier report [3]on underdoped films, that the decay rate of the photoin-duced change in reflectivity, DRR, depends strongly onthe excitation density and temperature. Because it van-ishes in the limit that both tend to zero, we interpret thedecay rate as an inelastic scattering rate of quasiparticlepairs. We present evidence that the decay corresponds toa process of thermalization, rather than recombination, ofthe nonequilibrium quasiparticle population. The dynam-ics of thermalization change suddenly upon crossing fromthe pseudogap regime to the superconducting state.We measured the decay of the DRR at a photon en-ergy of 1.5 eV due to excitation with photons of the sameenergy. The optical pulses are produced by a mode-lockedTi:sapphire laser, and have duration 100 fs, pulse to pulse37001-1 0031-90070288(13)137001(4)$20.00separation 12 ns, and center wavelength 800 nm. Both thepump and probe beams were focused onto the sample witha 20 cm focal length lens, yielding a spot size with 90%of its intensity within a 100 mm diameter. A photoelas-tic modulator varied the pump intensity at 100 kHz and avibrating mirror oscillating at 40 Hz varied the time delaybetween pump and probe. This double modulation pro-vides sensitivity to DRR of 1027.Figure 1a shows DRR due to absorption of a pumppulse of energy 0.07 nJ vs time t, at several temperatures.These reflectivity transients were measured with pump andprobe polarization aligned perpendicular to the chain axis.The amplitude of DRR increases and the decay rate de-creases as the temperature is lowered. Figure 1b showsthe temperature dependence of the maximum amplitudeDRR0. The reflectivity change is smaller when mea-sured with pump and probe parallel to the chains, particu-larly above Tc.FIG. 1. (a) DRR vs t at constant pump intensity for differenttemperatures (pump and probe both polarized perpendicular tochains). (b) Maximum amplitude of DRR vs T for polarizationparallel and perpendicular to the chains.© 2002 The American Physical Society 137001-1VOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 2002The T dependence shown in Fig. 1 is consistent withreports of DRR in underdoped (twinned) thin films ex-cited at 1.5 eV and probed at either near-infrared [1] or far-infrared [4] frequencies. As emphasized in Ref. [4], theincrease of DRR with decreasing T tracks the growth of aspin resonance peak seen by neutron scattering [5,6] and agaplike feature seen in optical conductivity [7,8]. Further-more, DRR shows the same behavior with varying carrierconcentration as do these spectroscopic features, namelyabrupt onset at Tc for near optimal doping [9] and a slowonset above Tc for underdoped materials [1,4]. Such con-siderations suggest that 1.5 eV photons ultimately generatelow-energy excitations, despite the fact that they initiallycreate an electron-hole pair whose energy is much largerthan the maximum gap D0.It is generally agreed that the generation of low-energyquasiparticles occurs via a rapid cascade process, in whichthe parent electron-hole pair creates a large number ofexcitations at much lower energy. What has remainedless clear is the mechanism by which this nonequilibriumpopulation of quasiparticles causes a change in reflectivityin the visible region of the spectrum. However, recentmeasurements [4,10] point to a mechanism for changes inreflectivity at 1.5 eV.Measurements of the change in THz conductivity ofan underdoped YBCO YBa2Cu3O61x film show thatphotoexcitation at 1.5 eV removes spectral weight fromthe condensate d function [10]. Far-IR measurements [4]reveal that this spectral weight reappears at frequenciesabove the maximum superconducting gap, or 100 meV.The Kramers-Kronig relations dictate that this redistribu-tion of spectral weight changes the real part of the dielec-tric function at much higher frequencies v accordingto De1v  28v4S, where S Rdv0 Ds1v0v02and Ds1 is the change in the real part of the opti-cal conductivity. The change in reflectivity at 1.5 eV,DRR  20.225De1, can be obtained from literature[11] values for the dielectric function, e1  1.1 ande2  2.7.The rate of increase of the photoinduced reflectivitywith increasing pump intensity provides a quantitativetest of the link between DRR and S. According to themechanism described above, DR reaches an upper limit,DRsat, when photoexcitation shifts the entire condensatespectral weight to nonzero frequency. Figure 2 showsDRR0 at 15 K vs u  lE4pr20 , the average energydensity deposited by the pump in the volume that isprobed (l  1.3 3 1025 Å is the penetration depth ofthe pump beam, E is the energy of the pump pulse, andr0  42 mm is the 1e radius of the laser intensity).There is a clear tendency toward saturation evident inthe data, which allows us to estimate DRsat. The dashedline shows the best fit to a simple saturation model,DR0DRsat  lu021Rdz1 2 e2uzusat uz, whereuz is the average energy density at a depth z be-low the sample surface. The best fit parameters areDRRsat  1.1 3 1023 and usat  0.43 Jcm3.137001-2FIG. 2. DRR vs excitation density at 15 K. The dashed lineis the best fit to the saturation model described in the text.We now compare the above value of DRsat with thatexpected if all the condensate spectral weight is shiftedaway from v  0. The value of De1 at saturation isv2pv2	v4, where vp is the plasma frequency corre-sponding to the condensate spectral weight and v2	 isthe mean square frequency shift. Using vp  1.5 eV [12]and De1sat  4.9 3 1023, we obtain v2	  130 meV2.That this frequency shift is comparable to that directly ob-served by Kaindl et al. [4] strongly supports our interpre-tation of the photoinduced change in reflectivity.We now turn to the rate of decay of DRR measuredas a function of T and pump intensity I. We have seenin Fig. 1 that the decay of DRR becomes slower as Tdecreases. Figure 3a, a plot of the reflectivity change at15 K created by pulses of varying intensity, shows that thedecay rate also slows as the excitation density decreases.The decays shown in Fig. 3a are nonexponential in thatthe instantaneous rate of decay, gt  2dlnDRdt,decreases as t increases. To characterize the intensity de-pendence of the decay rate in a relatively simple way, wefocus on the initial decay rate, or g0. We estimate g0from the slope of DRtR between 100% and 75% ofDRR0, normalized by the average value of DRtRin that interval. Given our time resolution, this proce-dure provides a good estimate of g0 for rates slower than1 ps21. Figure 3b shows g0 as a function of DRR0,obtained by analysis of the curves similar to the ones inFig. 3a. g0 varies linearly with DRR0 and extrapo-lates to a nonzero intercept as the excitation density ap-proaches zero.The dependence of g0 on excitation density is con-sistent with two-particle kinetics, for example, a processin which a pair of quasiparticles scatter off of each other.For high excitation densities the rate of such scattering isproportional to the nonequilibrium density. As the excita-tion density decreases, becoming smaller than the thermalpopulation, g0 approaches the equilibrium scattering rateat that temperature [13,14].137001-2VOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 2002FIG. 3. (a) Decay of DRR for several pump intensities at15 K. (b) Initial decay rate g0 vs DRR0.Figure 4 presents the temperature dependence of thedecay rate for a range of intensities, in the form of a loga-rithmic plot of g0 vs T . Points with the same (open)symbol show g0 measured at the same excitation density.The data sets coincide at high temperatures but diverge atTc  57 K. This indicates that the dependence of g0on I starts abruptly upon crossing from the pseudogap tothe superconducting state. The solid symbols show thedecay rate in the limit of zero excitation density, gth, asdetermined from the intercept of plots such as in Fig. 3b.The same quantity is plotted on linear axes in the inset. For10 , T , 40 K, gth appears to vary as T 3, although giventhe experimental uncertainty an activated form cannot beexcluded.The decay rates shown in Fig. 4 were measured with theprobe beam polarized perpendicular to the chains. We findthat the rates measured with the probe polarized parallelto the chains are indistinguishable, within the sensitivityof our measurement, for all T and I. The absence of po-larization dependence suggests that the carrier relaxationprocesses probed in this experiment take place in the CuOplane and not in the chain layers. Given this observation,137001-3FIG. 4. Initial decay rate g0 vs T at fixed I (open symbols).Decay rate in low I limit, gth, vs T (solid symbols in main paneland inset).we speculate that the difference in DRR for the orthogo-nal polarizations (Fig. 1b) is due to anisotropy in the spec-tral weight shifted by the nonequilibrium quasiparticles.Several aspects of the decay rate of DRR suggest astrong connection to quasiparticle dynamics and the den-sity of states. For example, the decay rate appears sensitiveto the opening of the pseudogap, decreasing near T in amanner which is remarkably similar to the nuclear spinrelaxation rate in underdoped YBCO [15]. The onset ofsuperconductivity also affects the decay dynamics — thedecay rate depends on excitation density only below Tc.Finally the T 3 dependence of gth is consistent with a pre-diction for the recombination and scattering rate of nodalquasiparticles [16].The simplest interpretation of the connection betweeng0 and quasiparticle dynamics is that DRtR reflectsthe decay of the nonequilibrium quasiparticle density. Ac-cording to this view, g0 is the rate at which quasipar-ticle pairs scatter into the condensate and gth is its valuein thermal equilibrium. However, this description of thedecay of DRR cannot be complete because for quasipar-ticles to scatter into the condensate they must shed theirexcess energy. In the model of Ref. [16] the excess en-ergy appears as a spin fluctuation, which is built fromparticle-hole excitations of the same band of electrons thatform the condensate. Therefore the “recombination” pro-cess essentially scatters one pair into another, with no re-duction in the number or energy density. This is analogousto a problem in the interpretation of transport experiments,where quasiparticle scattering alone cannot reduce the to-tal momentum [17].The actual recombination rate, in the sense of recov-ery of the equilibrium quasiparticle density, would likelybe much slower than the quasiparticle scattering describedabove. Decay of the quasiparticle density requires that ex-cess energy flow irreversibly away from the system of su-perconducting electrons to the lattice vibrations [18]. We137001-3VOLUME 88, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 1 APRIL 2002expect such a process to be extremely slow on the timescale of quasiparticle scattering and to exhibit single ratherthan two-particle kinetics. This expectation is based on thephysics of the “phonon bottleneck” in s-wave supercon-ductors [13,14], an effect which may be even more restric-tive in d-wave superconductors.The bottleneck arises because the process in which aquasiparticle pair emits a phonon and scatters into the con-densate is reversible— the emitted phonon can immedi-ately regenerate the quasiparticle pair. The quasiparticledensity relaxes at the rate at which the typical phonon en-ergy decreases below the threshold for pair creation. Notonly is this rate slower than the quasiparticle scatteringrate, it is also approximately independent of the excessquasiparticle density. Experiments with pulsed photoex-citation have provided convincing evidence that the relax-ation of the quasiparticle density in Pb films, for example,is limited by the phonon bottleneck [19,20].The relaxation of the quasiparticle density may be evenslower in the cuprates than in conventional superconduc-tors. In s-wave superconductors the phonons decouplefrom the electrons when their energy becomes less than2D. In the d-wave superconductors, where there is nothreshold for pair creation, the typical phonon energy mustdegrade to kBT in order for the electronic system to reachequilibrium. The extremely weak coupling between nodalquasiparticles and phonons compounds this effect. Thedecay of a quasiparticle pair into an acoustic phonon iskinematically forbidden because the quasiparticle velocityis larger than the sound velocity [18].If relaxation of the nonequilibrium density is extremelyslow, why does DRR decay on a picosecond time scale?The remaining possibility is that the decay correspondsto thermalization, rather than recombination. If DRRis not a direct measure of the quasiparticle density, butproportional instead to S as we have argued previously,it can decrease during thermalization, despite a constant,or even increasing, density of quasiparticles. Microwavemeasurements show that S for nodal particles is small,because their spectral weight is confined to a very nar-row 10 meV Drude peak [21]. The 100 meV spec-tral weight shifts [4], and consequently large values of S,are likely due to the antinodal quasiparticles. These con-siderations suggest that the decay of DRR measured at1.5 eV tracks the conversion of quasiparticles from a non-thermal distribution, which has substantial S, to a qua-sithermal distribution in which S is a factor 108 smaller.Measurements in which the nonequilibrium state is probedin the frequency range of the Drude conductivity [18] showmuch longer decay times (typically milliseconds), consis-137001-4tent with an experiment which selectively probes the nodalquasiparticle density.In summary, we present measurements of the photoin-duced change in reflectivity in an underdoped crystal ofYBCO, and discuss a new perspective on this effect. Weinterpret the decay rate of DRR as the inelastic scatter-ing rate of quasiparticle pairs, which sets the time scalefor thermalization of the nonequilibrium population. Thethermalization rate decreases with the development of thepseudogap, becomes excitation density dependent in thesuperconducting state, and decreases rapidly with decreas-ing T in the low excitation limit. Coordinated measure-ments of photoinduced changes in optical response over abroad spectral range, from terahertz to visible frequencies,are needed to test this perspective.We acknowledge valuable discussions with D. J.Scalapino. This work was supported by NSF-9870258,DOE-DE-AC03-76SF00098, CIAR, and NSERC.[1] V. V. Kabanov et al., Phys. Rev. B 59, 1497 (1999).[2] J. Demsar et al., Phys. Rev. Lett. 83, 800 (1999).[3] D. Mihailovic and J. Demsar, in Spectroscopy of Super-conducting Materials, ACS Symposium Series Vol. 730,edited by E. Faulqes (American Chemical Society, Wash-ington, D.C., 1999).[4] R. Kaindl et al., Science 287, 470 (2000).[5] J. Rossat-Mignod et al., Physica (Amsterdam) 185–189C,86 (1991).[6] H. A. Mook et al., Phys. Rev. Lett. 70, 3490 (1993); H. F.Fong et al., ibid. 75, 316 (1995).[7] J. Orenstein et al., Phys. Rev. B 42, 6342 (1990).[8] L. D. Rotter et al., Phys. Rev. Lett. 67, 2741 (1991).[9] R. D. Averitt et al., Phys. Rev. B 63, 140502 (2001).[10] J. M. Chwalek et al., Appl. Phys. Lett. 57, 980 (1990).[11] S. L. Cooper et al., Phys. Rev. B 47, 8233 (1993).[12] D. N. Basov et al., Phys. Rev. Lett. 74, 598 (1995).[13] A. Rothwarf and B. N. Taylor, Phys. Rev. Lett. 19, 27(1967).[14] For a review see K. E. Gray, in Nonequilibrium Super-conductivity, Phonons, and Kapitza Boundaries, edited byK. E. Gray (Plenum Press, New York, 1981).[15] W. W. Warren et al., Phys. Rev. Lett. 62, 1193 (1989).[16] S. M. Quinlan et al., Phys. Rev. B 49, 1470 (1994).[17] M. B. Walker and M. F. Smith, Phys. Rev. B 61, 11 285(2000).[18] B. J. Feenstra et al., Phys. Rev. Lett. 79, 4890 (1997).[19] C. C. Chi et al., Phys. Rev. B 23, 124 (1981).[20] G. L. Carr et al., Phys. Rev. Lett. 85, 3001 (2000).[21] A. Hosseini et al., Phys. Rev. B 60, 1349 (1999).137001-4

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Photoinduced Changes of Reflectivity in Single Crystals of YBa2Cu3O6.5
  (Ortho II)

Photoinduced Changes of Reflectivity in Single Crystals of YBa2Cu3O6.5 (Ortho II)

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