Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.issp.ac.ru/lek/trunin/art47RE.pdf Дата изменения: Thu Oct 1 15:28:21 2015 Дата индексирования: Sun Apr 10 02:15:23 2016 Кодировка: Поисковые слова: m 106

PHYSICAL REVIEW B, VOLUME 65, 132501

Anomalous microwave conductivity due to collective transport in the pseudogap state of cuprate superconductors
C. Kusko, Z. Zhai, N. Hakim, R. S. Markiewicz, and S. Sridhar*
Physics Department, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115

D. Colson, V. Viallet-Guillen, and A. Forget
ґ CEA-Saclay, Service de Physique de l'Etat Condense, 91191 Gif sur Yvette Cedex, France

Yu. A. Nefyodov, M. R. Trunin, and N. N. Kolesnikov
Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russia

A. Maignan and A. Daignere
ґ CRISMAT-ISMRA, 6 Boulevard du Marechal Juin, 14050 Caen Cedex, France

A. Erb
Walther Meissner Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany Received 29 October 2001; published 6 March 2002 The microwave surface impedance Z s R s iX s of HgBa2 Ca2 Cu3 O8 , HgBa2 CuO4 , Tl2 Ba2 CuO6 , and underdoped YBa2 Cu3 O6.5 is found to be anomalous in that R s ( T T c ) X s ( T T c ) in the pseudogap state. This implies plasmonlike response and negative permittivities ( ) 0 at microwave frequencies indicating non-Fermi-liquid transport in the ab plane. The anomalous microwave response is shown to arise from a collective mode characterized by a plasma frequency pC M 0.1 eV and extremely low damping CM 10 5 ­10 4 eV, distinctly different from those observed at optical frequencies. DOI: 10.1103/PhysRevB.65.132501 PACS number s : 74.72.Bk, 74.72.Fq, 74.72.Gr, 74.25.Nf

The ``normal'' state above T c of the high-temperature cuprate superconductors is well known to be extremely abnormal. A wide variety of experimental techniques photoemission, optical conductivity, NMR, tunneling, neutron scattering, infrared, Raman, etc. Ref. 1 have been applied to its study and suggest that there is a common phenomenology for all high-temperature superconductors: the existence of a partial gap or a pseudogap meaning the suppression of the low-energy density of states. An important issue is the nature of the pseudogap, several alternative theoretical models of this having been proposed, such as superconducting fluctuations2 or islands,3 competing order parameter,4 and stripes.5,6 In this paper, we show that low-energy microwave measurements of the surface impedance Z s R s iX s on HgBa2 Ca2 Cu3 O8 ( Hg: 1223) , HgBa2 CuO4 ( Hg: 1201) , Tl2 Ba2 CuO6 ( Tl: 2201) , and underdoped YBa2 Cu3 O6.5 reveal new features of transport in the pseudogap state. The measurements indicate a breakdown of the so-called Hagen, the Rubens limit where the measurement frequency carrier relaxation or dissipation rate , indicating a plasmonlike response characterized by negative microwave dielectric permittivities ( ) 0 , for currents in the ab plane. Such an anomalous conduction in the pseudogap state indicates non-Fermi-liquid NFL behavior rather than a singleparticle Fermi liquid transport mechanism and that the microwave dynamics and the optical response are characterized by different energy scales. A model based upon a collective phason mode arising from the presence of charge fluctuations, such as from stripes or a density wave DW , quantitatively explains the observed temperature dependence of experimental data.
0163-1829/2002/65 13 /132501 4 /$20.00

Single crystals of Hg: 1201 ( T c 94.4 K) , Hg: 1223 ( T c 122 K) , Tl: 2201 ( T c 91K) , and underdoped YBa2 Cu3 O6.5 ( T c 60 K) were prepared by appropriate methods for each material. The high quality of the crystals discussed here has been confirmed by a variety of other techniques.7 The data reported here were confirmed with measurements on several samples of each material. The high-sensitivity microwave measurements of R s and X s were carried out in a Nb superconducting cavity resonant at 10 GHz in the TE011 mode with very high unloaded Q 108 .8 Since Z s R s iX s i 0 / ~ , from R s and X s it is possible to obtain 1 and 2 , the real and imaginary parts of the 2 conductivity, using ~ 1 i 2 i 0 /( R s iX s ) . In all microwave measurements, R s ( T ) can be measured absolutely, while relative changes X s ( T ) X s ( T ) X s (0) are typically measured. We obtain X s (0) 0 ab ( 0 ) from estimates of the low-T penetration depth ab (0):130 nm ( Hg: 1223) , 117 nm ( Hg: 1201) , and 260 nm ( YBCO6.5) . It should be emphasized that because X s ( T T c ) X s (0), the results discussed in this paper are not sensitive to X s (0) or (0). The temperature dependences of X s and R s for Hg: 1223 when the microwave magnetic field H c axis and of X s and R s when H c are shown in Fig 1. In Fig. 1 a H c so that we are probing in-plane charge dynamics, while in Fig. 1 b , H c i.e., H ab ) , the current is flowing in the ab and c directions. In this mixed case, the data are represented as X s because ab c ( 0 ) and hence X s ( 0 ) cannot be easily estimated. At low T T c , ab ( T ) has a power-law depen©2002 The American Physical Society

65 132501-1


BRIEF REPORTS

PHYSICAL REVIEW B 65 132501

FIG. 1. a R s and X s vs T for H c and b R s and X s vs T for H c for HgBa2 Ca2 Cu3 O8 . The violation of the Hagen-Rubens limit in Hg: 1223 is evident since X s R s for T T c and X s ( T c ) R s ( T c ) . Similar anomalous results are also observed in Tl2 Ba2 CuO6 , HgBa2 CuO4 , and underdoped YBa2 Cu3 O6.50 not shown . In contrast such a violation is not observed in optimally doped YBa2 Cu3 O6.95 inset to a .

dence on T, consistent with measurements on other cuprate superconductors.9 Details of the superconducting state will be discussed separately. Two principal features of the data for Hg: 1223 of Fig. 1 are evident. i Above T c the curves of R s vs T and X s vs T are not parallel, so that R s ( T T c ) X s ( T T c ). ii FurtherR s ( T c ) , exactly opposite to that observed more, X s ( T c ) in conventional metals like Nb and Sn, and to within experimental accuracy, in optimally doped YBa2 Cu3 O6.95 see Fig. 1 a , inset and Bi2 Sr2 CaCu2 O8 . Essentially similar data were found for the other materials in this study: Hg: 1201, Tl: 2201, and YBa2 Cu3 O6.5 . The inequality R s ( T T c ) X s ( T T c ) for all four materials is evident from Fig. 2, where we present the data in terms of the anomaly A X s / R s 1 vs T for both H c Fig. 2 a and as c Fig. 2 b . The anomaly A is X s / R s 1 vs T when H clearly finite nonzero for T T c for both orientations. In optimally doped YBa2 Cu3 O6.95 the anomaly A( T T c ) 0 from the data of Fig. 1 a , inset. The influence of the pseudogap temperature scale on the transport is clearly evident in Fig. 2 for Hg: 1223 ( T * 270 K) and Hg: 1201 ( T * 260 K) .10 The onset of the pseudogap greatly enhances the c-axis contribution, as is clearly seen in the data for Hg: 1201 and Hg: 1223 Fig. 2 b ,

although the onset can also be seen in the pure ab -plane data Fig. 2 a albeit more gently. Thus our data are consistent with other findings that the c-axis pseudogap is different from the ab -plane pseudogap.1 For a conventional metal, the electromagnetic response can be expressed in terms of the dynamic conductivity writ2 ) i ), ten as ~ ( ) 1i2 n 0 /(1 i p 0 /( 1 where p is the plasma frequency, is the relaxation or dissipation rate, and n 0 is the zero-frequency dc conductivity. In typical metals like Al, p 15 eV and 0.1 eV, a negative dielectric constant is observed at opti, and cal frequencies ( 1013Hz, 0.1 eV) where 2 / 1 1 , since ~ 1 /( i ) . On the other hand, 2 p microwave frequency ( 1010Hz, 10 4 eV) experiments are , 2/ 1 / 1 , implyin the Hagen-Rubens limit 2 / , and the conventional Ohm's law aping ~ n0 p0 plies. In the Hagen-Rubens limit, R s X s 0 /2 n /2, where the skin depth n (2/ 0 n ) 1/2. Clearly 0 n then our finding that A( T T c ) X s / R s 1 0 shows that these materials violate the Hagen-Rubens condition in the pseudogap state.11 The violation of the Hagen-Rubens limit immediately implies a finite value of the imaginary part 2 ( T T c ) , since 2 2 2 22 2 0 ( X s R s )/( R s X s ) and a corresponding negative microwave dielectric permittivity ( T T c) 2( T T c )/ 0 , for the nonsuperconducting state above T c for these materials. 2 ( T ) is shown in Fig. 3. In Hg: 1223 it achieves rather large values 106 ( m) 1 and decreases with increasing temperature. The corresponding dielectric 2 106 is large and negative. constant 2/ 0 Tl: 2201 also violates the Hagen-Rubens limit, with values of 5 m) 1 leading to 2 105 . Essentially 2 10 ( similar results have been found for Tl: 2201 in other microwave measurements.12 In underdoped YBa2 Cu3 O6.5 the corresponding 2 ( T T c ) values 104 ( m) 1 are significantly lower. Thus the violation of the Hagen-Rubens limit is less severe although unambiguous and is consistent with the trend that in optimum-doped YBa2 Cu3 O6.95 , X s ( T c ) R s ( T c ) and R s ( T T c ) X s ( T T c ) so that 2 ( T T c ) 0( 1 ) within experimental error. The above conclusions concerning finite 2 ( T T c ) 1 ( T T c ) are directly a consequence of the data and not

FIG. 2. a Experimental data dark lines for the anomaly A X s / R s 1 vs T and the model X s / R s 1 vs T light lines when H c . b when H c . The arrows indicate the pseudogap temperature T * .

132501-2


BRIEF REPORTS

PHYSICAL REVIEW B 65 132501
2 weight ( )d and pC M pC M 0 /2 . Thus our results clearly show a disparity in energy p , op t scales between the microwave and optical frequency transport. Using the Drude form 2 M ne 2 / m * 0 , we can extract pC the effective mass m * . For n we use conventional estimates of 0.2 holes per plane, leading to n 1027/ m 3 . The resulting effective masses then are somewhat large, m * 300 ­ 400 for Hg: 1223, 100 ­ 200 for Tl: 2201, 100 for YBa2 Cu3 O6.5 , and 8000 ­ 23 000 for Hg: 1201 in the temperature range of the data. These large masses are comparable with those observed in one-dimensional 1D charge density waves CDW's .15 1 The simultaneous enhancement of CM ( CM ) and m * leaves 1 nearly unchanged, so the microwave anomaly consists of a large value of 2 ( T T c ) . It should be noted that earlier analysis of microwave scattering rates in Bi: 2212 and YBa2 Cu3 O6.95 Ref. 16 assumed an effective mass m * m e no mass enhancement so that the deduced from the microwave conductivity for T T c in those cases is much larger than those deduced here. Massive carriers with m * 103 have been deduced from microwave measurements in nonsuperconducting La2 CuO4 .17 The microwave results are suggestive of a phason mode of a CDW, whose electrodynamic response can be repre2 2 i CM ) . In the sented as ~ CM ( ) CM 0 /(1 pin / unpinned case pin ( 0 ) , the response reduces to the Drude form ~ CM ( ) 0 /(1 i CM ) used above. If the phason has a finite pinning frequency, the model cannot explain the dc conductivity, which is actually enhanced below the pseudogap transition. To approximately describe this residual conductivity, we introduce a second Drude component, which is unaffected by the pseudogap transition. For simplicity, we assume the same marginal Fermi liquid form for the unrenormalized scattering of both components: 1 1 ^ 0 /( MF L i m * ) r c ^ 0 /( MF L i ) , with r c the ratio 2 of the ungapped to gapped contributions, ^ 0 p 0 , and 1 2 2 2 2 ( T T 0 ), T 0 providing a low-temperature MF L cutoff. The CDW effective mass enhancement is m * / m 1 , with a 2( T ) ( T ) is the 0 (1 T / T * ) , where gap, assumed to have a BCS form.18 Figure 2 shows the resulting calculated variation with T of 2 1 1 the measured anomaly A ( X s R s )/ R s compared with the experimental data for the case H c

spectral

FIG. 3. YBCO6.5.

2

( T T c ) for Hg: 1201, Hg: 1223, Tl: 2201, and

obtained from any modeling of the dynamics. In the framework of a Drude relaxation model ~ ( ) 1i2 2 CM 0 /(1 i CM CM ) pC M 0 /( CM i ) valid at microwave frequencies, we can obtain pC M and CM from the 1 ( 10 GHz, T ) and 2 ( 10 GHz, T ) data. The resulting values of pC M 0.1 eV are significantly lower than indicated by optical spectra. More striking are the extremely low dissipation or scattering rates CM 10 5 ­10 4 eV. These low values of CM are to be expected from the finite 2 since 2 / 1 / CM 0.1 ­ 1 . Similar small values of and also p are observed in the heavy fermion materials 0.3 eV, 6 10 5 eV) Ref. 13 and the UPt3 ( p /2 conducting polymer polypyrrole ( 0.007 eV, 1.2 10 4 eV) Ref. 14 from microwave measurements. The temperature dependences of pC M ( T ) and CM ( T ) are shown in Fig. 4. In Hg: 1201 and Hg: 1223, the temperature dependences appear to be tied to the pseudogap temperatures although no consistent trend is apparent. Optical experiments show a Drude peak at much higher frequencies than microwaves, leading to the parameters 2 eV and op t 0.1 eV. These magnitudes also p , op t /2 correspond to ARPES measurements of the quasiparticle scattering rate. It is clear that these high-energy experiments are not able to observe the very low dissipation rates reported in this experiment, since pC M , CM for them, and further the collective mode observed in this work has small

FIG. 4. a Plasma frequency pC M and b in meV vs T for dissipation rate CM Hg: 1201, Hg: 1223, Tl: 2201, and YBCO6.5, for H c.

132501-3


BRIEF REPORTS

PHYSICAL REVIEW B 65 132501

where 2 / 1 . Parameters are ( m * , T * , T 0 / T * , r c ) ( 1000, 400 K,0.3, .85) for Hg: 1201, ( 400, 450 K, 0, 0 ) for Hg: 1223, ( 500, 400 K, 0.5, 0.9 ) for Tl: 2201, and ( 150, 400 K, 0.3, 6) for YBCO6.5 . The model reproduces the temperature dependence of ( X s R s )/ R s found experimentally, decreasing at higher temperatures. The calculated * T * is an onset temperature T on , while the experiment mea* sures a crossover T cr , where X s / R s changes most rapidly. We have compared only the case H c for the pure ab -plane currents, since the mixed case H c requires an an additional c-axis contribution and is the subject of future work. We note that the microwave data do not find any clear indications for pinning of the phason mode i.e., 2 is positive . We have thus demonstrated that a collective mode approach is capable of explaining the anomalous microwave data, while requiring a high-frequency component for explaining the optical data. Since pair fluctuations persist only for a few K above T c , the phenomena discussed here must be associated with pseudogap dynamics, rather than superconducting dynamics.19

In conclusion, we have presented microwave experiments that unambiguously reveal entirely novel transport properties of the nonsuperconducting or pseudogap state of several high-temperature superconductors. The pseudogap state has been probed at microwave time scales in several of these materials. The results show that the low-frequency transport is likely to be collective in nature, consistent with earlier suggestions of NFL above T c Ref. 20 and characterized by extremely low damping distinctly different from optical transport parameters. The results are quantitatively explainable in terms of a collective phason mode. Such a phason mode response can arise from a DW order parameter4 or also from stripe fluctuations, which have CDW-like dynamics.21 The implications of these results both for the pseudogap state, as well as the pseudogap-superconductor transition, are intriguing and of considerable importance. We thank A.H. Castro Neto for valuable discussions. This work was supported by ONR and NATO.

*Electronic address: srinivas@neu.edu
1 2

10 11

3

4

5

6 7

8

9

T. Timusk and B. Statt, Rep. Prog. Phys. 62, 61 1999 . Q. Chen, I. Kosztin, B. Janko, and K. Levin, Phys. Rev. Lett. 81, 4708 1998 . Yu.N. Ovchinnikov, S.A. Wolf, and V.Z. Kresin, Phys. Rev. B 63, 064524 2001 . S. Chakravarty, R.B. Laughlin, and C. Nayak, cond-mat/005433 unpublished . V.J. Emery, S.A. Kivelson, and J.M. Tranquada, Proc. Natl. Acad. Sci. U.S.A. 96, 8814 1999 . R.S. Markiewicz, Phys. Rev. B 62, 1252 2000 . Representative references are provided below, from which further details can be obtained: J.R. Kirtley, K.A. Moler, G. Villard, and A. Maignan, Phys. Rev. Lett. 81, 2140 1998 ; A.V. Puckov, P. Fournier, T. Timusk, and N.N. Kolesnikov, ibid. 77, 1853 1996 ; M. Kang, G. Blumberg, M.V. Klein, and N.N. Kolesnikov, ibid. 77, 4434 1996 ; M.H. Julien, P. Carretta, M. Horvatic, ґ C. Berthier, Y. Berthier, P. Segransan, A. Carrington, and D. Colson, ibid. 76, 4238 1996 ; M. Grueninger, D. van der Marel, A.A. Tsvetkov, and A. Erb, ibid. 84, 1575 2000 . Z. Zhai, C. Kusko, N. Hakim, and S. Sridhar, Rev. Sci. Instrum. 71, 3151 2000 . J.D. Kokales, P. Fournier, L.V. Mercaldo, V.V. Talanov, R.L. Greene, and S.M. Anlage, Phys. Rev. Lett. 85, 3696 2000 .

12 13 14 15 16 17 18 19 20 21

J. Bobroff, H. Alloul, P. Mendels, V. Viallet, J.-F. Marucco, and D. Colson, Phys. Rev. Lett. 78, 3757 1997 . We emphasize that the anomaly R s X s is not due to a size effect, since n d for H c , the sample size, and is also not due to nonlocal electrodynamics since n l , the mean free path. J.R. Waldram, D.M. Broun, D.C. Morgan, R. Ormeno, and A. Porch, Phys. Rev. B 59, 1528 1999 . S. Donovan, A. Schwartz, and G. Gruner, Phys. Rev. Lett. 79, 1401 1997 . R.S. Kohlman, J. Joo, Y.Z. Wang, J.P. Pouget, H. Kaneko, T. Ishiguro, and A.J. Epstein, Phys. Rev. Lett. 74, 773 1995 . S. Sridhar, D. Reagor, and G. Gruner, Phys. Rev. Lett. 55, 1196 1985 . H. Srikanth, B.A. Willemsen, T. Jacobs, S. Sridhar, A. Erb, E. Ё Walker, and R. Fluautkiger, Phys. Rev. B 55, R14 733 1997 . D.W. Reagor, E. Ahrens, S.W. Cheong, A. Migliori, and Z. Fisk, Phys. Rev. Lett. 62, 2048 1989 . G. Gruner, Density Waves in Solids Addison-Wesley, Reading, MA, 1994 . J. Demsar, B. Podobnik, V.V. Kabanov, Th. Wolf, and D. Mihailovic, Phys. Rev. Lett. 82, 4918 1999 . P. W. Anderson, The Theory of Superconductivity in the High T c Cuprates Princeton University Press, Princeton, 1997 . N. Hasselmann, A.H. Castro Neto, C. Morais Smith, and Y. Dimashko, Phys. Rev. Lett. 82, 2135 1999 .

132501-4