The temperature dependence of the real part of the microwave complex
conductivity at 17.9 GHz obtained from surface impedance measurements of two
c-axis oriented MgB2 thin films reveals a pronounced maximum at a temperature
around 0.6 times the critical temperature. Calculations in the frame of a
two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that
this maximum corresponds to an anomalous coherence peak resembling the two-gap
nature of MgB2. Our model assumes there is no interband impurity scattering and
a weak interband pairing interaction, as suggested by bandstructure
calculations. In addition, the observation of a coherence peak indicates that
the pi-band is in the dirty limit and dominates the total conductivity of our
filmsComment: 10 pages, 4 figures, to be published in Phys. Rev. Let

A. I. Gubin

A. I. Posazhennikova

B. B. Jin

Eun-Mi Choi

Hyun Jung Kim

M. Tinkham

N. Klein

Sung-IK Lee

T. Dahm

W. N. Kang

English

arXiv

Crossref

Anomalous Coherence Peak in the Microwave Conductivity of
                    
                      c

Jin BB, Dahm T, Gubin AI, et al. Anomalous coherence peak in the microwave conductivity of c-axis oriented MgB(2) thin films. Physical Review Letters. 2003;91(12): 127006.The temperature dependence of the real part of the microwave complex conductivity at 17.9 GHz obtained from surface impedance measurements of two c-axis oriented MgB(2) thin films reveals a pronounced maximum at a temperature around 0.6 times the critical temperature. Calculations in the frame of a two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that this maximum corresponds to an anomalous coherence peak resembling the two-gap nature of MgB(2). Our model assumes there is no interband impurity scattering and a weak interband pairing interaction, as suggested by band structure calculations. In addition, the observation of a coherence peak indicates that the pi band is in the dirty limit and dominates the total conductivity of our films

Jin, BB

Dahm, Thomas

Gubin, AI

Choi, EM

Kim, HJ

Lee, SI

Kang, WN

Klein, N

Publications at Bielefeld University

Anomalous coherence peak in the microwave conductivity of c-axis oriented MgB(2) thin films

The temperature dependence of the real part of the microwave complex conductivity at 17.9 GHz obtained from surface impedance measurements of two c-axis oriented MgB2 thin films reveals a pronounced maximum at a temperature around 0.6 times the critical temperature. Calculations in the frame of a two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that this maximum corresponds to an anomalous coherence peak resembling the two-gap nature of MgB2. Our model assumes there is no interband impurity scattering and a weak interband pairing interaction, as suggested by band structure calculations. In addition, the observation of a coherence peak indicates that the pi band is in the dirty limit and dominates the total conductivity of our films

Jin, B. B.

Dahm, T.

Gubin, A. I.

Choi, H. D.

Kim, H.-J.

Lee, S.-I.

Kang, W. N.

Klein, N.

Juelich Shared Electronic Resources

P H Y S I C A L R E V I E W L E T T E R S week ending19 SEPTEMBER 2003VOLUME 91, NUMBER 12Anomalous Coherence Peak in the Microwave Conductivityof c-Axis Oriented MgB2 Thin FilmsB. B. Jin,1 T. Dahm,2 A. I. Gubin,3 Eun-Mi Choi,4 Hyun Jung Kim,4 Sung-IK Lee,4 W. N. Kang,5 and N. Klein11Forschungszentrum Ju¨lich GmbH, Institute of Thin Films and Interfaces, D-52425 Ju¨lich, Germany2Universita¨t Tu¨bingen, Institut fu¨r Theoretische Physik, Auf der Morgenstelle 14, 72076 Tu¨bingen, Germany3Usikov Institute of Radiophysics and Electronics, NAS of Ukraine, 12 Acad. Proskura Str., 61085 Kharkov, Ukraine4National Creative Research Initiative Center for Superconductivity, Department of Physics,Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea5Department of Physics, Pukyung National University, Pusan, 608-737, Korea(Received 31 March 2003; published 19 September 2003)127006-1The temperature dependence of the real part of the microwave complex conductivity at 17.9 GHzobtained from surface impedance measurements of two c-axis oriented MgB2 thin films reveals apronounced maximum at a temperature around 0.6 times the critical temperature. Calculations in theframe of a two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that thismaximum corresponds to an anomalous coherence peak resembling the two-gap nature of MgB2.Our model assumes there is no interband impurity scattering and a weak interband pairing interaction,as suggested by band structure calculations. In addition, the observation of a coherence peak indicatesthat the  band is in the dirty limit and dominates the total conductivity of our films.DOI: 10.1103/PhysRevLett.91.127006 PACS numbers: 74.25.Fy, 74.25.Nf, 74.70.Adand gradually disappears when the mean free path be- resistance Rs and reactance Xs can be calculated bySuperconductivity in magnesium diboride (MgB2) witha remarkable high critical temperature Tc of 39 K hasattracted a great deal of attention both regarding itsfundamental physics as well as its practical applications[1–14]. Many theoretical calculations and experimentalresults have demonstrated its phonon-mediated pairingmechanism and s-wave pair symmetry. However, unlikeconventional superconductors it displays a two energy gapstructure. Combining a simple crystal structure and ahigh Tc [15,16], it provides a real system to study thevarious fundamental properties related to two-bandsuperconductivity [13,14].In the present work we report on experimental resultsfor the microwave conductivity of c-axis oriented thinfilms. For conventional superconductors this quantity dis-plays a peak close to Tc in its temperature dependence,which is called the ‘‘coherence peak’’ [17,18]. The obser-vation of its analog — the Hebel-Slichter peak — in thenuclear magnetic resonance (NMR) relaxation rate andits natural occurrence within the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity are re-garded as one of the key triumphs of BCS theory [19].Within BCS theory the peak arises due to the density ofstates (DOS) singularity which develops below Tc whenthe superconducting gap opens. At lower temperatures anexponential decrease of the conductivity and the NMRrelaxation rate sets in due to the condensation of quasi-particles. Usually the peak occurs at a normalized tem-perature around t  T=Tc  0:8–0:9 and can be observedboth in the NMR relaxation rate and in the microwaveconductivity, because both quantities possess the samecoherence factors. However, the peak in the microwaveconductivity is visible most clearly only in the dirty limit0031-9007=03=91(12)=127006(4)$20.00 comes longer than the coherence length [20]. In thehigh-Tc cuprates the behavior of these two quantities isquite different. In the NMR relaxation rate no Hebel-Slichter peak has been observed, while in microwaveconductivity experiments a exceptionally high maximumoccurs at temperatures much below Tc [21,22] with itsposition being strongly dependent on frequency [23]. Theabsence of the Hebel-Slichter peak in NMR experimentswas attributed to the d-wave nature of the superconduct-ing order parameter in the cuprates [24,25]. The largepeak in the conductivity has been interpreted as occur-ring due to an unusual rapid drop of the inelastic quasi-particle scattering rate below Tc which one expects, ifinelastic scattering is dominated by electron-electronscattering (e.g., spin fluctuations) [26]. Since the NMRrelaxation rate is much less sensitive to the quasiparticlescattering rate, this scenario can explain the difference ofNMR and microwave conductivity in the cuprates.In this Letter we report on the observation of an un-usual conductivity maximum in microwave absorptionmeasurements on MgB2 and on a comparison with theo-retical calculations based on a two-gap BCS model. Thetemperature dependence of the effective surface imped-ance Zeffs  Reffs  j!eff of two c-axis oriented MgB2films (samples S1210 and S1211) was measured at afrequency !=2 of 17.9 GHz employing a sapphire reso-nator technique [7]. The films were fabricated using atwo-step method by pulsed laser deposition. The detailedprocess is described in Ref. [27]. In our previous work thezero temperature gap ratio 0=kTc and penetrationdepth 0 were extracted using the clean limit BCSmodel with a 0=kTc value being much lower thanthe BCS prediction of 1.76. Subsequently, the surface2003 The American Physical Society 127006-1P H Y S I C A L R E V I E W L E T T E R S week ending19 SEPTEMBER 2003VOLUME 91, NUMBER 12impedance transformations [28]. Since the coherencelength in our samples is much smaller than the penetra-tion depth, the local limit applies and the real part of thecomplex microwave conductivity 1 can be derived fromRs and Xs using the formula 1  2!RsXs=R2s  X2s 2.At Tc we determined normal-state conductivities of0:137= cm (sample S1210) and 0:049= cm(sample S1211). We can get a rough estimate of thescattering rates  in our films using the relation  "0!2p h=, where a plasma frequency of !p  5:9 eV isused as suggested by band structure calculations [11].According to this procedure we find   34 meV(S1210) and   95 meV (S1211). These values are big-ger than the larger of the two gaps   7 meV, whichsuggests an analysis of our data within the dirty limit. Inaddition, many of the experiments and calculations men-tioned above showed that MgB2 appears to be a two-gapsuperconductor. Therefore, in the present work we ex-tracted 0=kTc and 0 values using the two-gapmodel and the dirty limit. In this case the temperaturedependence of the penetration depth is given by [29–31]202T n;T tanhT2kBT  n;T tanhT2kBTn;0  n;0 :(1)Here, n; and n; are the partial normal-state conduc-tivities of the  and  band, respectively. The tempera-ture dependences of the two gaps T and T areobtained from a solution of the two-by-two gap equation,as pointed out below.Figure 1 shows the measured eff (symbols) andfits based on Eq. (1) (lines). We found 0=kTc  0:69and 0  82 nm for sample S1210, and 0=kTc  0:79 and 0  118 nm for sample S1211. Thevalues for the small gap are fairly consistent with obser-1 2 3 4 5 6 7100101102103 S1210 δλδλ δλδλeff (nm)Tc/T10-1100101102103δλδλ δλδλeff (nm) S1211 Simulation FIG. 1. logeff vs Tc=T representation of the penetrationdepth data for two MgB2 samples. The solid lines are calcu-lated within the two-gap model in the dirty limit with parame-ters as described in the text. Note the different scale ranges forthe two samples.127006-2vations from tunneling experiments [2,3]. Using thesevalues, 1 was obtained by the procedure mentionedabove. In Fig. 2 we show the temperature dependence of1 normalized to its value at Tc. A distinct feature of thetemperature dependence of 1 is a maximum appearingaround t  0:6 rather than close to Tc, as one wouldexpect from a BCS coherence peak.In order to verify our measurement and extrac-tion procedure, we also measured a 200-nm-thickniobium film. The film was deposited on a silicon sub-strate at room temperature by dc magnetron sputteringin argon atmosphere. Tc 9:2 K and normal-state resis-tivity  ( 4:4 cm at 10 K) were measured withstandard four-probe method [32]. From the Tc and values we can obtain the intrinsic coherence length0  40 nm and mean free path l  10 nm. This re-sult shows that the dirty limit is a good approximationfor our Nb thin film. Therefore, the same procedurewas used to fit the measured change of penetrationdepth. Good agreement was obtained for 0=kTc 1:90 and 0  91 nm. Then, 1, as shown in Fig. 2(triangles), was extracted using the same procedures asabove. A pronounced coherence peak appears close to Tc,as one expects for a conventional superconductor. Thisresult is reproduced very well by a calculation based onthe BCS model and Mattis-Bardeen conductivity with theparameters above, as shown in Fig. 2 (solid line) [33].Since the observation of the coherence peak in the mi-crowave region needs highly accurate measurement of Rsand Xs, results were reported only recently for the con-ventional superconductors Nb and Pb [17,18]. The successof our technique for the Nb thin film is a strict testbecause eff and Rs for MgB2 are larger than for theNb thin film.0.0 0.2 0.4 0.6 0.8 1.00.00.51.01.52.02.53.03.5 S1210 S1211 Nb Simulationσσ σσ1/ σσ σσnt=T/TcFIG. 2. Temperature dependence of 1 at 17.9 GHz for MgB2samples S1210 (squares), S1211 (circles), and a Nb thin film(triangles). The lines show the calculations described in thetext. The data for S1210 and S1211 are shifted by 1 and 0.5units for clarity.127006-20.0 0.2 0.4 0.6 0.8 1.00.00.51.01.52.0∆ π ∆ σ∆ ∆ /kTct=T/TcFIG. 3. Calculated temperature dependence of the two energygaps within the two band model and parameters as described inthe text. The dashed line represents T  kT. The arrowpoints to the intersection of the dashed line and T, atwhich the coherence peak appears.P H Y S I C A L R E V I E W L E T T E R S week ending19 SEPTEMBER 2003VOLUME 91, NUMBER 12Now, we turn back to the question about the nature ofthe maximum observed in our measurement on the MgB2samples. As discussed before, in the high-Tc cuprates amuch larger maximum below Tc was attributed to a rapiddrop of the scattering rate. Therefore one might betempted to look for the same reason in this case.However, we do not expect a rapid drop of the scatteringrate below Tc in MgB2. Measurements of the dc resistancecan be well fitted by the Bloch-Gru¨neisen formula, whichsuggests that the normal-state transport properties arewell described by an electron-phonon interaction [8]. AtTc the dc resistance is already in the saturation regime,where impurity scattering dominates. Therefore, we can-not expect an important contribution of electron-electronscattering below Tc. Also, band structure calculationshave shown that electron-phonon interaction and impu-rity scattering are sufficient to understand the propertiesof MgB2 [10,11,14]. For these reasons the scenario of arapid drop of the scattering rate in MgB2 is rather un-likely as an explanation of the observed conductivitymaximum.If the maximum is related to coherence effects weshould explain it does not appear close to Tc. For thisreason we have calculated the temperature dependence of1 within the two-band BCS model using the two-bandgap equation [10] and the dirty limit Mattis-Bardeenformula for the conductivity [33]. In the two-band modelthe two superconducting gap values on the two Fermisurfaces ( band and  band) have to be calculatedfrom the following two by two matrix equation: XZ !c0dEtanhE22p2TE2  2q ; (2)where  and  run over the two bands, !c is a character-istic phonon frequency,   VN is a two-by-twocoupling matrix, N is the partial density of states ofband , and V is the symmetric matrix of the pairinginteractions. From this equation we calculate the tem-perature dependence of the two gaps  and  numeri-cally using !c  56 meV and N=N  1:35 as given inRef. [10]. In order to further reduce the number of freeparameters, the pairing matrix is adjusted to give theexperimental Tc and the value of 0=kTc of the smallgap at zero temperature obtained from the fit to thepenetration depth data in each sample. With these con-straints given, there is only one free parameter left inEq. (2): the interband pairing interaction V. In Fig. 3we show the temperature dependence of the two gapscalculated this way using a ratio r  V=V of 0.25.The temperature dependence of the energy gaps re-sembles the experimental results by Gonnelli et al. [2].Once the temperature dependences of the two gapsare known, the partial conductivities of the two bandscan be calculated using the dirty limit Mattis-Bardeen127006-3formula [33]:!n; 12!Z 11dtanh!2T tanh2T 	NN!MM!; (3)whereNRe(jj22p)and MRe(sgn22p)are the normal and anomalous densities of states forthe two bands. In Ref. [11] it has been shown thatinterband impurity scattering is expected to be smallin MgB2, because the two bands possess different sym-metries, which strongly reduces the scattering matrixelement for interband impurity scattering. In this casethe total conductivity 1! is just the sum of the par-tial conductivities ! and !. In order to calculatethe temperature dependence of 1 for our measure-ment frequencies we need to know the ratio of the par-tial conductivities in the normal state. This ratio dependson the plasma frequencies !p; and the scattering rates in the two bands n;=n;  !2p;=!2p;. Fromthe analysis in Ref. [11] we know that !2p;=!2p;  2,however, the ratio of the scattering rates will depend onthe impurities and imperfections present in our film andremains unknown. We will show in the following that wecan obtain a coherence peak appearing significantly be-low Tc, if we assume that the total conductivity is domi-nated by the partial conductivity of the  band, i.e.,n;  n;. In the other limiting case that the  banddominates the total conductivity we find a conventional127006-3P H Y S I C A L R E V I E W L E T T E R S week ending19 SEPTEMBER 2003VOLUME 91, NUMBER 12coherence peak appearing close to Tc, which does not fitour observation.Assuming 1!  ! we show the temperaturedependence of 1 at 17.9 GHz obtained from Eq. (2) inFig. 2 (solid lines) for both samples. The best fit was foundfor r  0:25 for both samples. This value is in fair agree-ment with the value of r  0:17 from band structurecalculations in Ref. [10].We can obtain an intuitive understanding of the peakposition, if we remember that the coherence peak appearswhen the condensation of quasiparticles sets in, whichroughly appears when T  kBT. In Fig. 3 this criterionis satisfied when the dashed line intersects the small gap(arrow). From this picture it becomes clear that the down-ward shift of the coherence peak is directly related to thesmallness of the gap.To summarize, we have presented experimental resultsof the temperature dependence of the microwave conduc-tivity in c-axis oriented MgB2 thin films. We find ananomalous peak around t  T=Tc  0:6 far below thetemperature at which one would expect to see the BCScoherence peak. We argue that this peak is not related to arapid drop in the quasiparticle scattering rate below Tc, asfor the high-Tc cuprates. Instead, we provide argumentsthat this anomalous peak in MgB2 is related to the two-gap nature of its superconducting state, particularly to thesmaller gap. Furthermore, our results imply that the band is in the dirty limit and dominates the total con-ductivity of our films.One of the authors (A. I. G.) is funded in part withinthe INTAS program by the European Union, which sup-ports his research stay in Ju¨lich. The work at Postech wassupported by the Ministry of Science and Technology ofKorea through the Creative Research Initiative Program.1270[1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani,and J. Akimitsu, Nature (London) 410, 63 (2001).[2] R. S. Gonnelli et al., Phys. Rev. Lett. 89, 247004(2002).[3] H. Schmidt, J. F. Zasadzinski, K. E. Gray, and D. G. Link,Phys. Rev. Lett. 88, 127002 (2002).[4] S. Souma et al., Nature (London) 423, 65 (2003).06-4[5] F. Bouquet, R. A. Fisher, N. E. Phillips, D. G. Hinks, andJ. D. Jorgensen, Phys. Rev. Lett. 87, 047001 (2001).[6] H. D. Yang et al., Phys. Rev. Lett. 87, 167003 (2001).[7] B. B. Jin et al., Phys. Rev. B 66, 104521 (2002).[8] Kijoon H. P. Kim et al., Phys. Rev. B 65, 100510(R)(2002).[9] J. Kortus, I. I. Mazin, K. D. Belashchenko,V. P. Antropov,and L. L. Boyer, Phys. Rev. Lett. 86, 4656 (2001).[10] A.Y. Liu, I. I. 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Anomalous coherence peak in the microwave conductivity of c-axis oriented MgB2 thin films

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