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Normal-superconducting tunneling in bulk high Tc superconductors: Charging effects and effect of energy gap asymmetries
Physica B 165&166 (1990) 1595-1596 North-Holland
Normal-Superconducting tunneling in bulk high Tc superconductors: Charging effects and effect of energy gap asymmetries. R. Medina, J. Aponte and M. Octavio, Centro de Ffsica, Instituto Venezolano de Investigaciones Cientfficas, Apartado 21827, Caracas 1020 A, Venezuela. We present experimental data for normal-superconducting (N-S) contacts using both La-Sr-Cu-O and Y-SaCu-O as superconductor. We find that the I-V characteristics can be explained with a simple model incorporating charging effects,which can explain the increasing differential resistance at voltages well above the gap voltage and the variation on the observed gap voltages on nominally equal samples. We also note the relationship between asymmetries in the I-V characteristics and the energy dependence of the gap. While the I-V characteristics of (N-S) contacts made with the high-Tc superconductors can vary widely from sample to sample and even within the same sample(1), a number of consistent features are observed. Among these, one can mention the continuous rise of the differential resistance up to voltages well above those of the gap, asymmetries with voltage polarity above and below T62) and difficulties in observing sharp gap features. In experiments with tunneling microscopes most of these features disappear, suggesting that the large normal point contact plays a role. In this paper we present experimental data for tunneling between a normal metal and with both La-Sr-Cu-O and Y-SaCu-O as superconductors. We show that some of these features mentioned earlier are consistently observed and can be explained taking into account charging effects, due to the large point being embedded in the superconductor, and asymmetries in the energy gap of the new high Tc superconductors. We calculate some of these effects and compare them to experimental data. Fig. 1 shows the temperature dependence of the derivative dl/dV as a function of the voltage for a normal superconducting contact made with Y1Sa2Cu3~ -d' This is typical of what is observed in this material. Note that the derivative curve is asymmetric with voltage and that, up to the highest voltages, the derivative does not reach an asymptotic value. Furthermore, for all the curves there is an asymmetry of the order of 8 mV around the zero voltage point where dl/dV is a minimum. In addition the gap structure is not sharply defined. 0921-4526/90/$03.50
© 1990 -
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Figure 1. dl/dV vs. V for Y-Sa-CuO as a function of temperature. The observed asymmetry is not related to superconductivity as it can be observed below and above the critical temperature of the ceramic. In fact, the asymmetry is intrinsic to the high-Tc ceramic and not to the contact as we have observed it in (N-S) contacts made of copper, indium and tungsten.lnstead, it appears that the asymmetry is due to the oxygen deficient phase formed at the surface of the Y-Sa-Cu-O compound, which is semiconducting. This interpretation can be confirmed by looking at the same curve for the La-Sr-Cu-O material which does not develop an oxygen deficiency. As shown in Fig. 2 this curve does not exhibit, above Tc the same asymmetry as the yttrium compound. In contrast, as the sample is cooled below its Tc, as shown in Fig. 3, the derivative curve develops a small asymmetry in voltage although the magnitude
Elsevier Science Publishers B.V. (North-Holland)
1596
R. Medina, J. Aponte, M. Octavia
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V (mV) Figure 2. dl/dV vs. V for the La-Sr-CuO compound above its critical temperature (T=62K) of this asymmetry is smaller than that observed in the yttrium compound. We believe that the continuous rise of the derivative with voltage up to values well above the gap (>1 OOmV) can only be explained in terms of charging effects and not as a rectifying effect which which varies quadratically with voltage(3). If one considers a large normal point contact (compared to the size of the grains) at voltage V embedded in a granular superconductor, charging effects will be of importance if the tunneling time is less than the repetition time. Then, the effective potential of an electron going from N to S will be V efF V+e/2C while that in the opposite direction is VeW V-e/2C, where C is the capacitance between the two, Then, to calculate the tunneling current one needs to include there effective potentials: I t =-eAT 2 dEPs(E) [Pn(E+eV+eV c )x
f (E+eV+eVc) (l-f (E) ) -P n (E+eV-eVc) (l-f(E+eV-eVc ))f(E) ]
x
(1)
where Vc=e I 2C. Assuming that only particles within a certain distance contribute to the current and that there is a broad distribution of particle sizes such that the probability of having a certain particle size is p(V c)=p(O)=V m-1, then it can be shown from Eq.(1) that above Tc the derivative of the current with respect to the voltage is given by:
~=G dV
0.4
~--------------
nn
V V
1
eV m tanh(2kT)
(2)
Figure 2 shows our experimental data for T=62K for a La-Sr-Cu-O sample. The points are the
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V (mV) Figure 3. dl/dV vs. V for the La-Sr-CuO compound below its critical temperature. experimental data and the continuous curve is the result of adjusting Eq.(2) with an added constant to account for the observed zero voltage conductance which is probably due to the presence of metallic contacts between the grains. In contrast with the good fit shown in Fig. 2, any form of a quadratic fit attempted, only yielded fair results at low voltages. The presence of charging effects would also provide an explanation for the observation of different values of the gap since the main effect of the effective potential in Eq.(1) is to shift the gaps by an amount of the order of the charging voltage Vc which depends crucially on the size of the grains. Finally, we believe that the asymmetry observed below Tc in the La-Sr-Cu-O compound can be explained assuming an energy dependent gap(4), If such a dependence were present, the minimum in the quasiparticle dispersion curve would be shifted since dE/dEk=O would occur for Ek=~-l1dMdEkThis implies that the divergence in the density of states would move into the hole or electron-like branch of the curve, leading to two different gap values. In fact, such a dependence is present in the model of Medina et al(4) and other models(5).we will report on such effects in a separate publication This work supported in part by CONICIT S1-1828 and the EEC Cooperation program. 1.-A.P.Fein et aL, Phys. Rev. B.3Z,9738 (1988) 2.-J. Takadaet aL, Phys. Rev ~,4478 (1989) 3.-R.S. Gonnelli et aL, Phys. Rev, ~,2261 (1989) 4.-R. Medina et ai, Phys. Rev. aaa,4277 (1989) 5.-F. Marsiglio and J.E.Hirsch, Physica Cill(1989)
Normal-Superconducting tunneling in bulk high Tc superconductors: Charging effects and effect of energy gap asymmetries. R. Medina, J. Aponte and M. Octavio, Centro de Ffsica, Instituto Venezolano de Investigaciones Cientfficas, Apartado 21827, Caracas 1020 A, Venezuela. We present experimental data for normal-superconducting (N-S) contacts using both La-Sr-Cu-O and Y-SaCu-O as superconductor. We find that the I-V characteristics can be explained with a simple model incorporating charging effects,which can explain the increasing differential resistance at voltages well above the gap voltage and the variation on the observed gap voltages on nominally equal samples. We also note the relationship between asymmetries in the I-V characteristics and the energy dependence of the gap. While the I-V characteristics of (N-S) contacts made with the high-Tc superconductors can vary widely from sample to sample and even within the same sample(1), a number of consistent features are observed. Among these, one can mention the continuous rise of the differential resistance up to voltages well above those of the gap, asymmetries with voltage polarity above and below T62) and difficulties in observing sharp gap features. In experiments with tunneling microscopes most of these features disappear, suggesting that the large normal point contact plays a role. In this paper we present experimental data for tunneling between a normal metal and with both La-Sr-Cu-O and Y-SaCu-O as superconductors. We show that some of these features mentioned earlier are consistently observed and can be explained taking into account charging effects, due to the large point being embedded in the superconductor, and asymmetries in the energy gap of the new high Tc superconductors. We calculate some of these effects and compare them to experimental data. Fig. 1 shows the temperature dependence of the derivative dl/dV as a function of the voltage for a normal superconducting contact made with Y1Sa2Cu3~ -d' This is typical of what is observed in this material. Note that the derivative curve is asymmetric with voltage and that, up to the highest voltages, the derivative does not reach an asymptotic value. Furthermore, for all the curves there is an asymmetry of the order of 8 mV around the zero voltage point where dl/dV is a minimum. In addition the gap structure is not sharply defined. 0921-4526/90/$03.50
© 1990 -
::i 0.21
ci
> '1J
~ '1J
o 7K o 52 K .97
A
24 K
• 86 K
I(
0.16
O. 11 ,--~_~_---,-_~_~_-,--_-,------l -80 -60 -40 -20 0 20 40 60 80 V (mV)
Figure 1. dl/dV vs. V for Y-Sa-CuO as a function of temperature. The observed asymmetry is not related to superconductivity as it can be observed below and above the critical temperature of the ceramic. In fact, the asymmetry is intrinsic to the high-Tc ceramic and not to the contact as we have observed it in (N-S) contacts made of copper, indium and tungsten.lnstead, it appears that the asymmetry is due to the oxygen deficient phase formed at the surface of the Y-Sa-Cu-O compound, which is semiconducting. This interpretation can be confirmed by looking at the same curve for the La-Sr-Cu-O material which does not develop an oxygen deficiency. As shown in Fig. 2 this curve does not exhibit, above Tc the same asymmetry as the yttrium compound. In contrast, as the sample is cooled below its Tc, as shown in Fig. 3, the derivative curve develops a small asymmetry in voltage although the magnitude
Elsevier Science Publishers B.V. (North-Holland)
1596
R. Medina, J. Aponte, M. Octavia
0.16 '":' 0.15
'":' 0.3
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:J
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C
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0.1 2 l------'_--'-_----'-_--'--_"'--_'"-------'_--' -80 -60 -40 -20 0 20 40 60 80
V (mV) Figure 2. dl/dV vs. V for the La-Sr-CuO compound above its critical temperature (T=62K) of this asymmetry is smaller than that observed in the yttrium compound. We believe that the continuous rise of the derivative with voltage up to values well above the gap (>1 OOmV) can only be explained in terms of charging effects and not as a rectifying effect which which varies quadratically with voltage(3). If one considers a large normal point contact (compared to the size of the grains) at voltage V embedded in a granular superconductor, charging effects will be of importance if the tunneling time is less than the repetition time. Then, the effective potential of an electron going from N to S will be V efF V+e/2C while that in the opposite direction is VeW V-e/2C, where C is the capacitance between the two, Then, to calculate the tunneling current one needs to include there effective potentials: I t =-eAT 2 dEPs(E) [Pn(E+eV+eV c )x
f (E+eV+eVc) (l-f (E) ) -P n (E+eV-eVc) (l-f(E+eV-eVc ))f(E) ]
x
(1)
where Vc=e I 2C. Assuming that only particles within a certain distance contribute to the current and that there is a broad distribution of particle sizes such that the probability of having a certain particle size is p(V c)=p(O)=V m-1, then it can be shown from Eq.(1) that above Tc the derivative of the current with respect to the voltage is given by:
~=G dV
0.4
~--------------
nn
V V
1
eV m tanh(2kT)
(2)
Figure 2 shows our experimental data for T=62K for a La-Sr-Cu-O sample. The points are the
0.2 0.1
/~
o
'v~
0.0 l-------'_--'--_-'-_-'--_-'-------'_--'--_--' -80 -60 -40 -20 0 20 40 60 80
V (mV) Figure 3. dl/dV vs. V for the La-Sr-CuO compound below its critical temperature. experimental data and the continuous curve is the result of adjusting Eq.(2) with an added constant to account for the observed zero voltage conductance which is probably due to the presence of metallic contacts between the grains. In contrast with the good fit shown in Fig. 2, any form of a quadratic fit attempted, only yielded fair results at low voltages. The presence of charging effects would also provide an explanation for the observation of different values of the gap since the main effect of the effective potential in Eq.(1) is to shift the gaps by an amount of the order of the charging voltage Vc which depends crucially on the size of the grains. Finally, we believe that the asymmetry observed below Tc in the La-Sr-Cu-O compound can be explained assuming an energy dependent gap(4), If such a dependence were present, the minimum in the quasiparticle dispersion curve would be shifted since dE/dEk=O would occur for Ek=~-l1dMdEkThis implies that the divergence in the density of states would move into the hole or electron-like branch of the curve, leading to two different gap values. In fact, such a dependence is present in the model of Medina et al(4) and other models(5).we will report on such effects in a separate publication This work supported in part by CONICIT S1-1828 and the EEC Cooperation program. 1.-A.P.Fein et aL, Phys. Rev. B.3Z,9738 (1988) 2.-J. Takadaet aL, Phys. Rev ~,4478 (1989) 3.-R.S. Gonnelli et aL, Phys. Rev, ~,2261 (1989) 4.-R. Medina et ai, Phys. Rev. aaa,4277 (1989) 5.-F. Marsiglio and J.E.Hirsch, Physica Cill(1989)