Intrinsic c-axis tunnelling in the superconducting state has been measured in zero and finite fields in small mesa structures fabricated on the surface of 2212-BSCCO single crystals. The temperature dependence of the zero-field critical current and quasi-particle conductance is related to microscopic d-wave models in the presence of impurity scattering. The strong field dependence of the c-axis critical current provides information on the correlation of flux 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

Fenton, JC

Gough, CE

Thomas, PJ

Yang, G

English

arXiv

Gough, Colin

Thomas, Philip

Fenton, Jonathan

Yang, Guang

University of Birmingham Research Portal

Quasiparticle tunnelling and field-dependent critical current in 2212-BSCCO

UCL Discovery

Quasiparticle Tunnelling and Field-Dependent Critical Current in 2212-BSCCO  C. E. Gough, P.J. Thomas, J.C. Fenton and G. Yang Superconductivity Research Group, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom  This article was published as Physica C 341-348 (2000) 1539 http://dx.doi.org/10.1016/S0921-4534(00)01327-7   Intrinsic c-axis tunnelling in the superconducting state has been measured in zero and finite fields in small mesa structures fabricated on the surface of 2212-BSCCO single crystals. The temperature dependence of the zero-field critical current and quasi-particle conductance is related to microscopic d-wave  models in the presence of impurity scattering. The strong field dependence of the c-axis critical  current  provides  information  on  the  correlation  of  flux  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 adjacent superconducting 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 field, the decrease in critical current can be related to the misalignment of flux pancakes across adjacent superconducting bilayers. In this paper, we consider both the quasiparticle conductance and the field dependence of the critical current.  2. Measurements Measurements have been made on small mesa structures, typically, shown schematically in the inset of figure 1, 20 × 20 m and ~10 nm in height corresponding to a linear array of intrinsic Josephson junctions [1]. Measurements have been made on a number of mesas on slightly underdoped (#1), near optimally doped (#2) and slightly overdoped (#3) 2212-BSCCO crystals, as described along with experimental details in [2] In zero-field we observe the familiar multibranched IV-characteristics first reported and explained by Kleiner et al. [1] and confirmed by many other groups. Yurgens et al. [3] have already published measurements at relatively large fields[4], which we extend to smaller fields.  In our structures, the first critical current is smaller than all subsequent transitions, indicating a slight degradation of the uppermost intrinsic junction either below the metal-HTS interface or at the milled surface between the current and voltage contacts (see ref. [2]). When considering the temperature- and field-  dependence  of  Jc(T,B),  we  therefore  take  the  largest  critical  current  in  the  multibranched characteristics as representative of the bulk properties.  Measurements  inevitably  involve  a  significant  amount  of  self-heating,  ~  Ic  x  20mV  per  intrinsic junction, heating the mesa above the measured base temperature. To circumvent this problem, we determine the mesa temperature directly, by monitoring the temperature dependent contact resistance between two separate contacts on the top of each mesa [5], which varies approximately as 1/T. The IV-measurements can then be corrected for the measured temperature rise, which can be as large as a few tens of degrees at the lowest temperatures for large amplitude voltage measurements.  3. Quasi-particle conductance Figure 1 shows a typical set of corrected IV characteristics, obtained quasistatically, for the 1st and 11th phase-slip branches of a mesa on sample #2. Once corrected for heating [2], the suitably scaled 11th branch can be superimposed on the 1st branch. Such characteristics are dominated by quasi-particle tunnelling, since the McCumber parameter  c>>1. The temperature-corrected characteristics are  considerably  more  linear  than  any  previously  reported.  Additional  short-pulse  measurements confirm heating to be the major source of non-linearity and backbending [2]. Using the voltage at which the dynamic conductance becomes infinite [6] is therefore unlikely to provide a meaningful measurement 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 V3. In contrast, the conductance is almost linear over an extended energy range, with I= V+ V3 as indicated in figure 1. Figure 2 illustrates the temperature dependence of the derived ohmic conductivity in the low-bias limit for our three samples. Also included are normal state values, extended somewhat below Tc by the application of a large field (6.6T) parallel to the c-direction.  Figure 1 (left). Measured IV characteristics and corrected for heating for 1st and 11th branch of #2. Figure 2 (right).  c(T) for mesas on three crystals  Interestingly, there is no significant change in the conductance nor its temperature dependence at Tc. 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  fabricated  from  single-crystal  whiskers.  They  interpret  their measurements  in  terms  of  additional  impurity-induced  states  close  to  the  nodes  of  the  d-wave superconductor  gap.  For  coherent  interlayer  tunnelling,  such  states  would  contribute  a  low  bias, ohmic, tunnel current .~ ( ) nV, where  h  is the impurity-scattering-limited energy scale, in contrast to the V3 dependence in the clean limit [7]. For coherent tunnelling, the conductivity would be reduced by an additional factor ~ /EF [7]. We therefore expect a crossover from an impurity-limited V-dependence to intrinsic V3 tunnelling, when kBT*~  or when eV~ kBT*.  The only significant difference between our results and those of Latyshev et al are the somewhat smaller values of  c derived for samples of similar expected doping.  4. Field dependence of critical current For magnetic fields along the c-direction, the field penetrates as a series of flux pancakes with induced currents largely confined to the CuO planes. In a defect-free crystal at low temperatures, the flux pancakes would align to form a uniform lattice of flux lines along the c-direction. However, thermal fluctuations and crystal defects disturb the alignment of the pancakes, destroying the phase coherence across the planes, hence reducing the critical current by an amount <cos  ij> , where  ij(r) is the local phase difference across adjacent superconducting planes and <> represents the thermally averaged spatial average. Typical measurements of the field dependence of the critical current are shown in figures 3 and 4 for modest fields up to 0.1 T and for larger fields up to 7T. Measurements were taken on cooling and subsequent warming in the applied field, to ensure a nearly uniform distribution of flux.  In  zero  field,  the  critical  current  decreases  with  increasing  temperature,  though  with  a  different 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 models. This  may,  in  part,  be  associated  with  self-heating,  which  was  not  monitored  in  these  earlier measurements.  Figures 3 and 4 suggest changes in both field and temperature dependences of the critical current as we pass from the solid to liquid vortex states, particularly at the higher fields. The position of the melting line T(Bm), inferred from  SR and ac susceptibility measurements (see ref. [8]) on similar crystals,  is  indicated  by  the  large  open  circles.  The  correlation  of  flux  pancakes  across  adjacent superconducting planes therefore depends on the nature of the magnetic state.   Figure 3 (left). Ic(T) at low fields for sample #3. Figure 4 (right). Ic (T) at high fields for sample #3  At low temperatures (< 20K) we also observe an instability in the IV characteristics, illustrated in Figure 5. Provided measurements are confined to the first one or two phase-slip transitions, the critical current remains high, increasing monotonically on decreasing temperature with no significant change in form of the IV-characteristics. However, once a critical voltage has been exceeded, there is an immediate irreversible  transition to an  entirely  new  dynamic  state,  indicated by  the  lower  set  of characteristics in figure 5, with critical currents given by the open circles in figures 3 and 4. 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 certainly accounts for the decrease in critical currents at low temperatures reported previously [4].   Figure 5. Measured characteristics illustrating bimodal behaviour at low temperatures, and stable characteristics at a higher temperature for sample #3.  Small  transverse  misalignment  of  the  pancakes  vortices  d  (< s)  results  in  a  reversed  Josephson coupling energy over an area ~d2 per flux line, where   is the anisotropy factor and s the bilayer spacing.  For  small  fields,  this  will  lead  to  a  fractional  decrease  in  critical  current Ic/Ic~(B/ 0)d2=B/B*, consistent with the low-field exp(-B/B*) dependence shown in figure 6, where B*~725  gauss  and  190  gauss  for  the  glassy  lattice  state  at  10K  and  liquid  state  at  75K.  This corresponds to displacements d~165nm and ~330nm, ~ s assuming an anisotropy factor of ~300.   Figure 6. Field dependence of the critical current for sample # 3 in the solid and liquid flux pancake states  At higher fields, a simple model of flux pancakes of effective area  0/B, randomly distributed such that <cos  ij>spatial=0, would give a fractional reduction in Josephson current  <cos ij exp ( -(EJ 0/B)(cos ij /kBT) > = EJ/2BkBT,  where EJ = Jc 0/2  is the Josephson coupling energy per unit area. This result was derived more rigorously by Koshelev for pancakes in the liquid state [10] . A similar result is also expected for flux lines thermally diffusing in the solid [11] with Jc~1/B T with  =1 for random disorder and <1 for increased in-plane correlation. In the solid state at low temperatures, the field dependence approaches B-2/3 at large fields and 1/B in the liquid state at high temperatures, as illustrated by the solid lines in figure 5.  5. Acknowledgments This work is supported by EPSRC. We thank Peter Andrews and Gary Walsh for technical support. PJT gratefully acknowledges financial support from EPSRC.  References 1. R. Kleiner et al, Phys. Rev. Lett. 68 (1992) 2394 2. P.J. Thomas, J.C. Fenton, G. Yang and C.E. Go'ugh, cond-mat/0001365 3. A. Yurgens et al, Physica C 235-240 (1994) 3269 4. A. Yurgens et al, Phys. Rev. B 59 (1999) 7196 5. P.J. Thomas, J.C. Fenton, G. Yang and C. E. Gough, Physica B 280, (2000) to be published 6. A. Yurgens et al, Phys. Rev. B 53 (1996) R8887 7. Yu. I. Latyshev et al, Phys. Rev. Lett. 82 (1999) 5345 8. S.L. Lee et al, Phys. Rev. Lett. 71 (1993) 3862 9. M.Suzuki, T. Watanabe and A. Matsuda, Phys. Rev. Lett. 81 (1998) 4248 10. A.E. Koshelev, Phys.Rev.B 77 (1996) 3901 11. A.E.Koshelev, Phys.Rev.B 76 (1996)1340    

Quasiparticle tunnelling and field-dependent critical current in 2212-BSCCO

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