Quasiparticle Tunnelling and Field-Dependent Critical Current in 2212-BSCCO

a r X i v :c o n d -m a t /0002246v 1 [c o n d -m a t .s u p r -c o n ] 16 F e

b 2000

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Intrinsic C-Axis Tunnelling in BSCCO Crystals

C.E.Gough,P.J.Thomas,J.C.Fenton and G.Yang

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Superconductivity Research Group,University of Birmingham,Edgbaston,Birmingham B152TT,United Kingdom

Intrinsic c-axis tunnelling in the superconducting state has been measured in zero and ?nite ?elds in small mesa structures fabricated on the surface of 2212-BSCCO single crystals.The temperature dependence of the zero-?eld critical current and quasi-particle conductance is related to microscopic d-wave models in the presence of impurity scattering.The strong ?eld dependence of the c-axis critical current provides information on the correlation of ?ux pancakes across adjacent superconducting bi-layers.An instability in the IV characteristics is observed below 20K,which accounts for the apparent drop in critical current at low temperatures previously reported.

1.Introduction

Measurements of c-axis tunnelling across ad-jacent superconducti-+ng bi-layers in highly anisotropic cuprate superconductors,such as 2212-BSCCO,provide important information about the tunnelling of superconducting pairs and thermally excited quasi-particles.In a ?eld,the decrease in critical current can be related to the misalignment of ?ux pancakes across adjacent su-perconducting bi-layers.In this paper,we con-sider both the quasiparticle conductance and the ?eld dependence of the critical current.2.Measurements

Measurements have been made on small mesa structures,typically,shown schematically in the inset of ?gure 1,20×20μm and ～10nm in height corresponding to a linear array of intrin-sic Josephson junctions [1].Measurements have been made on a number of mesas on slightly un-derdoped (#1),near optimally doped (#2)and slightly overdoped (#3)2212-BSCCO crystals,as described along with experimental details in [2]In zero-?eld we observe the familiar multi-branched IV-characteristics ?rst reported and ex-plained by Kleiner et al [1]and con?rmed by many other groups.Yurgens et al [3]have already pub-lished measurements at relatively large ?elds[4],

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suitably scaled 11th branch can be superimposed on the 1st branch.Such characteristics are dom-inated by quasi-particle tunnelling,since the Mc-Cumber parameter βc ? 1.The temperature-corrected characteristics are considerably more linear than any previously reported.Addi-tional short-pulse measurements con?rm heating to be the major source of non-linearity and back-bending [2].Using the voltage at which the dy-namic conductance becomes in?nite[6]is there-fore unlikely to provide a meaningful measure-ment of the energy gap.

For a d-wave superconductor with incoherent quasi-particle tunnelling,the tunnel current at low temperatures is expected to vary as V 3.In contrast,the conductance is almost linear over an extended energy range,with I =αV +βV 3as in-dicated in ?gure 1.Figure 2illustrates the tem-perature dependence of the derived ohmic con-ductivity in the low-bias limit for our three sam-ples.Also included are normal state values,ex-tended somewhat below T c by the application of a large ?eld (6.6T)parallel to the c-direction.Interestingly,there is no signi?cant change in the conductance nor its temperature depen-dence at T c .On decreasing temperature,the

low-bias conductance falls continuously from its high temperature normal state value to a doping-dependent limiting value at low temperatures (see inset).

Similar results have also been reported by Latyshev et al [7]for measurements on ion-beam milled,2212-BSCCO,c-axis microbridges fabri-cated from single-crystal whiskers.They inter-pret their measurements in terms of additional impurity-induced states close to the nodes of the d-wave superconductor gap.For coherent inter-layer tunnelling,such states would contribute a low bias,ohmic,tunnel current ～Γ

τis the impurity scattering limited energy scale,in contrast to the V 3dependence in the clean limit[7].For coherent tunnelling,the con-ductivity would be reduced by an additional fac-tor ～Γ

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4.Field dependence of critical current For magnetic?elds along the c-direction,the ?eld penetrates as a series of?ux pancakes with induced currents largely con?ned to the CuO planes.In a defect free crystal at low temper-atures,the?ux pancakes would align to form a uniform lattice of?ux lines along the c-direction. However,thermal?uctuations and crystal de-fects disturb the alignment of the pancakes,de-stroying the phase coherence across the planes, hence reducing the critical current by an amount ,whereθij(r)is the local phase di?er-ence across adjacent superconducting planes and <>represents the thermally averaged spatial av-erage.

Typical measurements of the?eld dependence of the critical current are shown in?gures3and4 for modest?elds up to0.1T and for larger?elds up to7T.Measurements were taken on cooling and subsequent warming in the applied?eld,to ensure a nearly uniform distribution of?ux.

increasing temperature,though with a di?erent temperature dependence from BCS.The linear temperature dependence at low temperatures is inconsistent with the higher power-dependence of the c-axis penetration depth and theoretical mod-

heating,which was not monitored in these earlier measurements.

Figures3and4suggest changes in both?eld and temperature dependences of the critical cur-rent as we pass from the solid to liquid vortex states,particularly at the higher?elds.The po-sition of the melting line T(B m),inferred from μSR and ac susceptibility measurements(see ref.

[8])on similar crystals,is indicated by the large open circles.The correlation of?ux pancakes across adjacent superconducting planes therefore depends on the nature of the magnetic state.

At low temperatures(<20K)we also observe an instability in the IV characteristics,illustrated in Figure5.Provided measurements are con?ned to the?rst one or two phase-slip transitions,the critical current remains high,increasing mono-tonically on decreasing temperature with no sig-ni?cant change in form of the IV-characteristics. However,once a critical voltage has been ex-ceeded,there is an immediate irreversible transi-tion to an entirely new dynamic state,indicated by the lower set of characteristics in?gure5,with critical currents given by the open circles in?g-ures3and4.The original characteristics can only be recovered by annealing the mesa above～25K. Almost identical behaviour has been observed for mesas on all three samples.This change in phase-slip dynamics is not understood,but almost cer-

4

tainly accounts for the decrease in critical cur-rents at low temperatures reported previously[4].

A similar bimodal behaviour has been reported

8.3K19.7K

V #3

#3

Small transverse misalignment of the pancakes vortices d(<γs)results in a reversed Joseph-son coupling energy over an area～d2per?ux line,whereγis the anisotropy factor and s the bilayer spacing.For small?elds,this will lead to a fractional decrease in critical current?I c

φ0)d2=B B?

dependence shown in?gure6,where B?～725 gauss and190gauss for the glassy lattice state at10K and liquid state at75K.This corresponds to displacements d～165nm and～330nm,～γs assuming an anisotropy factor of～300.

At higher?elds,a simple model of?ux pan-cakes of e?ective areaφ0

B cosθij

2Bk B T

,

where?J=J cφ0

BμT

,withμ=1for random disor-der and<1for increased in-plane correlation. In the solid state at low temperatures the?eld dependence approaches B?2

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