Proximity effect and high Tc superconductivity

Proximity effect and high Tc superconductivity V. Z. Kresin Materials and Chemical Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, USA

Received 27 January 1988 A proximity system containing a high T~ superconductor can be used to strengthen the field effect. The use of the proximity contact Sh-Nb in the Josephson junction Sh-Nb-lnAs Nb Sh (Sh is a high Tc film) is promising from the point of view of making a three-terminal device. The proximity effect can also be used to increase the values of the parameters of a conventional superconductor, such as, Tc, critical field and critical current.

Keywords: low temperature electronics; high T~ superconductivity; superconductors This Paper is concerned with the properties of proximity systems containing new high T~ superconductors l'z. The recent progress in high T~ films preparation (see, for example, References 3-5) makes this problem of definite interest. As is shown, the proximity effect allows the superconducting state to be induced in materials which are not superconductors by themselves. For example, the S-Sm system (S is a superconductor and Sm is a semiconductor) lets one take advantage of both superconducting and semiconducting properties. Another interesting proximity system is S,-Sp, consisting of two superconductors. If S= -= Sh, where Sh is a high Tc superconducting film, and Sa is a conventional superconductor, then T ) > T¢ > Tfl (see, for example, References 6 and 7), where T~ and T~ are the critical temperatures of isolated ~ and fl films. Such a system allows one (see below) to take advantage of the large values of T~ and HCh2of the high T¢ film and the large values of pinning forces in the fl film (if the/~ film is an A-15 or B1 compound). This Paper contains an analysis of two problems. First, we are going to study the field effect in the presence of a high T¢ film. This effect is important from the point of view of making a three-terminal device. Secondly, the transport properties of the proximity system Sh-S~ Sh, where SBis an A-15 or B I superconductor, will be studied.

High Tc and the field effect Reference 5, in which the field effect has been used to bring about a change in the amplitude of the Josephson current, has attracted a lot of interest. The system Nb- InAs Nb has been studied; the value of the Josephson current can be controlled by an applied electric field. A detailed theoretical analysis has been carried out by the present author in References 9 and 10. The noticeable field effect is due to the presence of an inversion layer in InAs; the reduced dimensionality of the barrier plays an important role. The origin of the field effect is connected 0011-2275/88/060409-03 $03.00 ~) 1988 Butterworth & Co (Publishers) Ltd

with the exponential dependence Ofjm (maximum value of the Josephson current) on the surface carrier concentration, N~. An applied electric field affects the value of N~ and, as a result, noticeably changes the current. According to Reference 9, the sharpness of the field effect, that is, the relative current change at fixed voltage, depends strongly on several parameters, such as temperature, Z thickness of the semiconductor film, L N, effective mass, mN, etc. For example, in the region T ~ To, the Josephson current is described by the dependence Jmax~ exp[ -- F~(c)] where Fd and Fc correspond to the 'dirty' (/<< CN, where I is the mean free path and IN is the coherence length in the normal film 1~) and the 'clean' limits, respectively. One can show 9 that F d ,~ (T/Ns/~)~LN

where/~ is the mobility, and F c ~ ~ N ~ ~L N It has also been shown that the use of a one-dimensional channel will lead to an even stronger field effect. We would like to stress the strong dependence of the current on temperature. An increase in T leads to a decrease in the absolute value of the Josephson current but at the same time it leads to an increase of the field effect, that is, the dependence jm(Ns) is getting sharper. That is why the use of the system NbN-InAs-NbN has been suggested in Reference 9 (T~IN~N> T~INb). Such a dependence of the field effect on temperature makes use of the high T~ oxides very promising. In principle, there are two possibilities: one approach is the replacement Nb --, Sh, giving the system Sh-InAs-S h. This will increase the temperature of the contact. The coherence length in high T~ oxides is small but the density of states is large (see References 12 and 13); as a result there will be a noticeable manifestation of the field effect. However, preparation of such a contact is difficult because of the

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Proximity effect. V.Z. Kresin undesirable effect of the Sh-S m interface on the oxide, etc. A more realistic approach is the use of another structure: Sh-Nb-InAs-Nb-Sh. The proximity system Sh-Nb will permit observation of the field effect at higher temperatures. The values of T are restricted by the critical temperature of the proximity system (for example, the Nb-InAs-Nb system studied in Reference 8 has T¢ ~ 6 K), and the latter is related to the T¢ of superconductors. Consider the following example. Assume that the electron surface concentration changes from N1 = 5 x 1011 c m - 2 t o N 2 = 10 x2 cm-2. I f T = 4 K , L N = 2 X 10 -s cm, m# = 0.025me,#(N 0 = 3.3 x 103 cm 2 ( V s ) - 1 , / / ( N 2 ) = 6 x 103 cm 2 (Vs)-1 (these values are realistic for InAs), we obtain, with the use of equations (19) and (24) of Reference 9, 3 = - j m ( N 2 ) / j m ( N 1 ) . , ~ 1.8. If T ~ 1 5 K we obtain 6 ~ 6, if T ~ 20 K then 6 ~ 11 (such high values of T can be obtained in the Sh Nb-InAs-Nb-Sh system; note that in this case the coherence length in the N film is smaller 11 and we are dealing with a 'clean' case, see the discussion in Reference 9). Hence, the use of a high T~ superconductor in a proximity system leads to an increase of the field effect.

Proximity effect and critical current Consider the proximity system Sh-St~-Sh (see Figure 1), where Sh is a high T~ oxide, and Sa is a conventional superconductor. The most interesting case in when S# is an A-15 or BI compound; in this case S e is characterized (in the isolated state) by high values ofjc, Ho2, etc. The critical temperature, T~, of the system of interest will be lower than T h but, which is most important, higher than T~ (the critical temperature of an isolated fl film). Hence, as a consequence of the proximity effect, we have obtained and A-15 or BI superconductor with a high T~. If the system is placed in an external magnetic field (see Figure 1; we assume that the field is perpendicular to the boundary), then one can observe vortex penetration (up to H = He2 ). In the region T~ < T < T~, the system can be treated as an S-N-S proximity contact (see, for example, Reference 14). It is important that the new high T~ materials are characterized by high values ofH~2. As a result, the critical

field, H¢2 , for the proximity system of interest, Sh-Sa-Sh,

will be larger than H~2 (the critical field of Sa in the isolated state). The value of He2 can be obtained from the expression for an S-N-S system (see Reference 14)

Hc2 = Hh2(1 + 00-1(1 -- txr) where O~ ~ o'#db,(O'hdh)- i

where tri and d i are the normal conductivities and thicknesses of the films (i = r, h), respectively, and r depends on T/Tic and the diffusion coefficients. One can see that indeed Hc2 < Hc2. h There is a lot of flexibility in changing Hc2 in the desired direction. Note that the case of licE > HcO2is perfectly realistic (a more detailed numerical analysis will be given elsewhere). Of course, the possibility of obtaining Hc2 > He#2 does not violate any thermodynamic restrictions because the fl film is not an isolated system and the increase in H~2 relative to Hc#2 is at the expense of the high T~ film. Consider now the flow of the transport current through the system; assume that the current is perpendicular to the magnetic field. We are interested in the current density in the fl film (see Figure 1; on the whole, we are dealing with some space distribution of the current; a more detailed analysis will be given elsewhere). As is known, the critical value of the current, j¢, is determined by the pinning force, Fp, and can be evaluated from the expression j~B -- Fp. The pinning force is determined by many factors (see, for example, the review Reference 15), such as Hc2 , fl, the nature and scale of inhomogeneities, and the parameters of the vortex lattice. Its value strongly depends on the pinning mechanism. The interesting case of the penetration of Josephson vortices in a parallel field will be considered separately. According to Reference 15 (see also Reference 16), Fp can be written in the form Fp = ~ncn2f(r/) where rI = H / H ~ 2

and -- constant

t7

B

The value of ~ as well as the value of n (usually n = 2) and the dependence f(q) are determined by the properties of the sample. It is important that an increase in H~2 leads to an increase in the value of j~. Since Hc2 > He02 (see above), the pinning force can be increased by a proximity contact with a high T~ material. As a result, one can obtain an effective increase in j~ in the fl film. However, most importantly, because of the proximity effect, the conventional fl film is able to carry a high critical current at temperature T > T¢a. It would be interesting to study the properties of the proximity system Sh-Sa-Sm, where Sa is an Nb, NbN, A-15 or other conventional superconducting film.

Conclusions I

Figure 1 Schematic diagram of S h Sff-S h proximity system

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In this Paper we studied a proximity system consisting of a high T~ superconductor and a conventional

Proximity effect: V.Z. Kresin superconductor. The main results are summarized as follows. The use of the proximity system Sh-K-Sh, where Sh is a high Tc film and K is an S f S m - S ~ contact (where Sm is a semiconductor and S~ is a conventional superconductor), for example, the Sh N b I n A s - N b - S h (or Sh N b N I n A s - N b N - S 0 system, is promising from the point of view of making a three-terminal device. An analysis of the system Sh-S/~-Sh,where Sp is an A-15 or BI superconductor, shows that such a system is characterized by high values of He2 (the magnetic field is perpendicular to the boundary) and the critical current. The transport current is perpendicular to the magnetic field. The proximity effect can be used to increase the pinning force and the values of the parameters (Tc, H~2, Jc) of the conventional material.

Acknowledgements The a u t h o r is grateful to J. Clem, P. Chaikin, V. Kogan, M. Nisenoff, I. Schuller and S. Wolf for valuable discussions. This work was supported by the US Office of N a v a l Research under Contract No. N00014-86-F0015

and carried out at the Lawrence Berkeley L a b o r a t o r y under C o n t r a c t No. DE-AC03-76SF00098.

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