Quasiparticle and Cooper Pair Tunneling in the Vortex State of Bi-2212

a r X i v :c o n d -m a t /0005393v 1 [c o n d -m a t .s u p r -c o n ] 23 M a y 2000

Quasiparticle and Cooper Pair Tunneling in the Vortex State of Bi 2Sr 2CaCu 2O 8+δ

N.Morozov 1,L.N.Bulaevskii 1,M.P.Maley 1,https://www.sodocs.net/doc/041314382.html,tyshev 2?,and T.Yamashita 2

1

Los Alamos National Laboratory,Los Alamos,NM 87545

2

Research Institute of Electrical Communication,Tohoku University,2-1-1,Katahira,Aoba-ku,Sendai 980-8577,Japan

(February 1,2008)

From measurements of the c -axis I-V characteristics of intrinsic Josephson junctions in Bi 2Sr 2CaCu 2O 8+δ(Bi-2212)mesas we obtain the ?eld dependence (H c )of the quasiparticle (QP)conductivity,σq (H,T ),and of the Josephson critical current density,J c (H,T ).σq (H )in-creases sharply with H and reaches a plateau at 0.05T

Important information regarding pairing symmetry in cuprate superconductors has been obtained from the quasiparticle (QP)spectrum.Strong evidence in favor of d -wave symmetry of the superconducting order parame-ter has come from ARPES and STM experiments [1,2].The e?ect of a magnetic ?eld on QP properties becomes particularly interesting because,in the nodal regions of a d-wave gap,it probes ?ne details of the low-energy QP spectrum and its alteration by supercurrents surround-ing vortices.An increase of QP density of states (DOS)produced by the Doppler shift of near-nodal QP ener-gies by the vortex supercurrents is predicted to lead to an increasing QP DOS with magnetic ?eld [3,4].This e?ect was apparently observed in calorimetric measure-ments in HTS [5].In-plane thermal conductivity mea-surements however have indicated a more complex mag-netic ?eld dependence.At low temperatures κab (H )was seen to increase sublinearly with ?eld in agreement with predictions of the Volovik mechanism [8].At higher tem-peratures,T >2–5K.κab (H )was observed in Bi-2212to ?rst decrease with increasing magnetic ?eld and then reach a plateau and remain constant up to ?elds of several tesla [6].A similar behavior was observed also in YBCO [7].Franz [9]attempted to explain the high temperature plateau behavior as resulting from a compensating e?ect of QP scattering from in-plane vortex disorder.While this provides a qualitative description of the high tem-perature behavior,it fails to account for the fact that the low temperature sublinear increase with H shows no e?ect of a compensating scattering from vortex disor-der.Thus,the thermal measurements have presented an ambiguous picture of the competing contributions of vor-tices,increasing DOS and scattering,to QP transport.More direct information on QP properties can be ob-tained by study of the charge transport,namely,the c -axis conductivity σc (H ),in Josephson-coupled lay-ered HTS.Recent measurements on micron-sized mesas of Bi-2212have demonstrated that QP conductivity in the superconducting state can be accessed by exceeding the Josephson critical current,switching the interlayer

Josephson junctions into the resistive state and return-ing to low currents on the resistive branch [10].Recent theoretical development has shown that c -axis QP con-ductivity is determined by the QP DOS and the e?ective scattering rate for interlayer tunneling [11].In this Letter we provide an unambiguous determination of the e?ects of vortices on the QP DOS and on the e?ective scattering rate for c -axis tunneling.

We study the e?ect of vortices on the c -axis QP con-ductivity,σq (H,T ),by measuring the I-V characteristics in the resistive state of small Bi-2212mesas as a func-tion of the magnetic ?eld 0

TABLE I.Bi-2212mesa samples;S ≈4μm 2,T c ≈73K.R n is the resistance at T =300K,N is the number of intrinsic junctions,J c is the maximum critical current density (H =0),γis the in-plane e?ective scattering rate,and σq (0,0)is the QP conductivity at H =0,T →0.

mesa R n ,k?N J c @4K,A /cm 2γ,K σq (0,0),(k?cm)?

1

Focused Ion Beam technique

[10].In this Letter we present data obtained on 4typical samples (See Table I).We performed measurements of I-V characteristics at di?erent magnetic ?elds and temperatures in a standard He-?ow cryostat,which provided temperature stabiliza-tion better than ±10mK.Magnetic ?elds up to 9T were applied along the c -axis of the mesa by a super-conducting solenoid.The intrinsic Josephson junctions in high quality mesas have a small shunting conductance due to QP tunneling and thus behave as underdamped junctions with highly hysteretic I-V dependence.Typi-cal multibranching I-V curves in zero-?eld-cooled (ZFC)mode at T =4K are shown in Fig.1.The increasing current branch provides information on the critical cur-rent,whereas the decreasing current branch corresponds to the resistive state,where current is due to QP tunnel-ing.Direct comparison of I-V curves at H =0T,0.05T,and 0.15T (Fig.1)shows that a)critical currents drop with H ,and thus all branches collapse to that of the resistive state,and b)variation of critical current for dif-ferent junctions increases with H in comparison with that at H =0.

FIG.1.I-V curves for Bi-2212mesa m3at H =0,H =0.05T,and H =0.15T.For this sample all 17branches are resolved.

It is important that the branch of I-V curves for de-creasing current,when all junctions are in the resistive state,is the same for all current sweeps for both ?eld cool-ing (FC),and ZFC (Fig.2).This observation allows us to study the ?eld dependence of QP conductivity,σq (H,T ),measured in ZFC.The value of average QP resistivity, ρq ,was obtained from the all-junction resistive-state I-V curve at low currents as described in Ref.[10],and σq =1/ ρq was calculated.

In contrast to the behavior of σq (H ),the distribution of critical current over junctions is di?erent for FC and ZFC modes.The distribution of J c (B,T )over junctions in small-area mesas arises because a)at T →0and H =0junctions are inequivalent with respect to J c at least due to their geometrical position in the mesa,b)at nonzero ?eld J c (B,0)for a junction between layers n and n +1

depends on vortex positions in the layers,which vary randomly with n in the case of uncorrelated pinning [13],and c)at nonzero T ,jumps from the superconducting

FIG.2.I-V curves for H =0.03T,FC (?)and ZFC ( )modes.In the FC mode vortices initially are better correlated,providing larger J c .Switching the junctions in the resistive state suppresses c -axis pancake correlations,and the system becomes similar for both FC and ZFC.Inset:the distribution of J c in junctions for ZFC (dash)and FC (line)modes.

state to a resistive one occur at di?erent J due to thermal ?uctuations [14].We can ?nd the distribution function of the critical current density,f (J ),from our data as f (J )=d (V ↑/V ↓)/d J ,where V ↑(J )[V ↓(J )]are voltages on increasing [decreasing]currents.The inset in Fig 2shows smoothed distribution functions f (J )for FC and ZFC modes.We note that average critical current den-sity, J c (H =0.03T) ,obtained in the FC mode at 4K is larger by the factor ≈2than that in the ZFC mode.This result is in agreement with measurements [15]of the Josephson plasma resonance (JPR)frequency.Below the irreversibility line (in the vortex glass phase)the JPR

FIG.3.For mesa m1σq (V →0)is plotted vs.H for three di?erent temperatures.

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frequency in the FC mode was found to be larger than in the ZFC mode.A very important new observation is that curves obtained in the second and subsequent cur-

rent sweeps in the FC mode are similar,and they prac-tically coincide with those observed in the ZFC mode. This shows that in our thin plate-like mesas suppres-sion of Josephson coupling by switching into the resistive state irreversibly produces pancake disorder comparable to that produced by ramping the magnetic?eld,i.e.vor-tices do not change their positions when one goes from the

resistive state back into the superconducting state. In Fig.3we present our principal result showing a typical dependence of QP conductivity as a function of magnetic?eld.The conductivity rises steeply with mag-netic?eld,reaches a distinct plateau,and then rises more gradually with?eld at higher?elds.Below we explain our experimental data using theoretical results[11]forσq(B) and an estimate for J c(B,T)in small mesas.

Let us outline the main theoretical predictions[11]for QP conductivityσq(B)in the mixed state.QP tunneling in a d-wave layered superconductor in the presence of vor-tices is determined by two competing mechanisms:σq is proportional to the QP DOS and inversely proportional to the e?ective scattering rate for interlayer tunneling,γc.In-plane supercurrents around vortices lead to a DOS increase near gap nodes proportional to the averaged Doppler shift in the QP spectrum,E H≈v F(B/Φ0)1/2 atγ?E H??0,whereγis the impurity induced e?ec-tive in-plane scattering rate and?0is the gap amplitude. In the framework of the specular tunneling model,when in-plane momentum is conserved at tunneling,σq will in-crease strongly with B due to DOS enhancement when vortices are correlated along the c-axis.If c-axis corre-lation of pancakes is absent,the e?ective scattering rate γc increases with B due to di?erent Doppler shifts at equivalent points in adjacent layers,suppressing tunnel-ing.There is a characteristic?eld,Bγ=Φ0γ2/ 2v2F,es-timated as Bγ～0.2?0.6T,which corresponds roughly to the?eld at which the variation of Doppler shift be-comes comparable to the scattering rateγ.The lat-ter may be estimated from the temperature dependence σq(0,T)=σq(0,0)(1+cT2),where c=π2/18γ2.Values ofγfor mesas studied are presented in the Table I.It was predicted that in the quasiclassical approach,valid at E H??0,when one accounts for Doppler shifts only, one getsγc≈E H in?elds B≥Bγ.In this?eld range increase in scattering caused by Doppler shift variation in adjacent layers compensates inσq(H)the increase in DOS,providing a nearly?eld independentσq(H).Cor-rections to this approach lead to a weak linear increase of QP conductivity at Bγ?B?B0,

σq(B)/σq(0)=C1+B/B0,(1) where B0≈20T.Here C1depends on in-plane pan-cake ordering.The values of C1between1.07and1.22

were calculated for a2D vortex liquid depending on the e?ective temperature of vortex disorder T eff[11].

FIG.4.For mesas[m1( ),m2(?)and m3(▽)]the nor-malizedσq(top)and J c (bottom)are plotted vs.H.Three di?erent regimes with respect to H are marked by verti-cal dotted lines.The theoretical curves ofσq(B)for cor-related(dashed)and c-axis-uncorrelated(dash-dotted)vor-tex systems are shown for Bγ=0.6T,?0=25meV,and T ef f=0.06(Φ20s/8π2λ2ab)[11].

The?eld dependence of the Josephson critical current in the vortex glass state for H c comes from the depen-dence of J c(B,T)=J c(0,T) cos?n,n+1(r) on the gauge-invariant phase di?erence?n,n+1(r)induced by pancakes when they are misaligned in the layers n and n+1due to random pinning.Correlations of pancakes in neighboring layers,leading to lower energy,are induced by magnetic coupling of pancakes and by Josephson interlayer cou-pling;both tend to align vortices along the c-axis.Maxi-mum J c in the vortex glass phase may be achieved by ad-justment of pancake positions to minimize both Joseph-son and pinning energy[16].This e?ect is negligible for the ZFC mode and,as shown above,for the FC mode after switching from the resistive state where Josephson coupling is absent.For the critical current J c(B,0)in mesas with the size L?λ2J/a,the relations

J2c(B,0)

L4

exp[i?n,n+1(r)?i?n,n+1(r′)] ,(2)?n,n+1(r)= iφv(r?r ni)?φv(r?r n+1,i)

hold[13].Here a=(Φ0/B)1/2is the intervortex distance,λJ is the Josephson length,～1μm in typical mesas,φv(r)is the polar angle of the point r,and r ni is the co-ordinate of pancake i in the layer n.In Eq.(2)the inte-grand, exp[i?n,n+1(r)?i?n,n+1(r′)] ,drops with|r?r′|

3

on the scale a at a?L.Then we estimate J c(B,0) < J2c(B,0) 1/2≈J c(0,0)(Φ0/BL2)1/2.Thermal?uctua-tions cause jumps into the resistive state at J

Now we explain our experimental results using these theoretical results.In Fig.4we plot the low-?eld part of theσq(H)dependence together with extracted J c,max(H) for three di?erent samples.Shown here are also theo-retical curves calculated forσq(B)in the case of c-axis-correlated and uncorrelated vortex states[11],indicating clearly that c-axis disorder is responsible for strong sup-pression ofσq at high?elds.The experimentally observed σq(H)can be divided into three segments as magnetic ?eld increases as shown in Fig.4.These segments cor-respond to appropriate parts of the?eld dependence of the critical current density,J c,max,obtained in the ZFC mode,presented in the lower part of Fig.4.At very low?elds,H 5mT,(Segment I)there is practically no change inσq and in J c,max.This regime corresponds to the Meissner state of the sample.Note that,despite the suppression of supercurrent along the c-axis by ap-plied transport current in the resistive state,the in-plane Meissner currents persist,preventing pancake vortex en-trance into the sample.Only when the magnetic?eld H exceeds～5mT do pancakes enter into the sample. In the intermediate?eld range,5≤H<40mT,(seg-ment II)the experimental results forσq(H)lay slightly above the curve for uncorrelated vortices but well below the curve for the c-axis-correlated vortex state.This in-dicates that weak c-axis vortex correlations are present in this?eld range.Weakly correlated pancakes a?ect J c much more strongly thanσq,because increase in B leads to decrease of J c(the?uctuations of the phase di?erence increase and cos?n,n+1(r) drops),while forσq the in-crease of DOS is compensated partly by an increase of γc.As the?eld continues to increase above40mT(seg-ment III)increase ofσq with H is slowing down due to a stronger decrease of c-axis correlations and,respectively, stronger increase ofγc.This leads to formation of the plateau(or even dip)in the range40

We thank A.M.Nikitina for providing us with Bi-2212 single crystal whiskers,Ch.Helm,A.E.Koshelev,and I.B.Vekhter for useful discussions,and J.Y.Coulter for the technical assistance.This work was supported by the Los Alamos National Laboratory under the auspices of the U.S.Department of Energy,CREST,the Japan Science and Technology Corporation,and the Russian State Program on HTS under grant No.99016.