《量子力学》THE DISCOVERY OF TUNNELLING SUPERCURRENTS

THE DISCOVERY OF TUNNELLING SUPERCURRENTS Nobel Lecture, December 12, 1973 Cavendish Laborate ambridge, England The events leading to the discovery of tunnelling supercurrents took place while I was working as a research student at the Royal Society Mond Labo- ratory, Cambridge, under the supervision of Professor Brian Pippard. During my second year as a research student, in 1961-2, we were fortunate to have as a visitor to the laboratory Professor Phil Anderson, who has made numerous contributions to the subject of tunnelling supercurrents, including a number lf. His lecture Cambridge introduced the new concept of 'broken symmetry' in supercon- ductors, (1)which was already inherent in his 1958 pseudospin formulation of superconductivity theory, (2 which I shall now describe As discussed by Cooper in his Nobel lecture last year (3)according to the Bardeen-Cooper-Schrieffer theory there is a strong positive correlation in a uperconductor between the occupation of two electron states of equal and opposite momentum and spin. Anderson showed that in the idealized case where the correlation is perfect the system can be represented by a set of inter acting pseudospin, with one pseudospin for each pair of electron states The situation in which both states are unoccupied is represented by a pseude spin in the positive z direction, while occupation of both states is represented in the negative z direction; other pseudospin orientations orrespond to a superposition of the two possibilities The effective Hamiltonian for the system is given by H=-2∑(ek-)5-∑vk(skx5kx+ysty) (1) the first term being the kinetic energy and the second term the interaction energy. In this equation Skrnky and Skz are the three components of the k seudospin. E k is the single-particle kinetic energy, u the chemical potential and Vkk the matrix element for the scattering of a pair of electrons of equal and opposite momentum and spin. The k"pseudospin sees an effective field H=2(Ek-1)+2∑Vksk⊥ where z is a unit vector in the z direction and indicates the component of the pseudospin in the xy plane One possible configuration of pseudospin consistent with(2)is shown in Fig. 1(a). All the pseudospin lie in the positive or negative z direction, and

THE DISCOVERY OF TUNNELLING SUPERCURRENTS Nobel Lecture, December 12, 1973 by B RIAN D. J OSEPHSON Cavendish Laboratory, Cambridge, England The events leading to the discovery of tunnelling supercurrents took place while I was working as a research student at the Royal Society Mond Labo￾ratory, Cambridge, under the supervision of Professor Brian Pippard. During my second year as a research student, in 1961-2, we were fortunate to have as a visitor to the laboratory Professor Phil Anderson, who has made numerous contributions to the subject of tunnelling supercurrents, including a number of unpublished results derived independently of myself. His lecture course in Cambridge introduced the new concept of ‘broken symmetry’ in supercon￾ductors, (1) which was already inherent in his 1958 pseudospin formulation of superconductivity theory, (2) which I shall now describe. As discussed by Cooper in his Nobel lecture last year (3) according to the Bardeen-Cooper-Schrieffer theory there is a strong positive correlation in a superconductor between the occupation of two electron states of equal and opposite momentum and spin. Anderson showed that in the idealized case where the correlation is perfect the system can be represented by a set of inter￾acting ‘pseudospins’, with one pseudospin for each pair of electron states. The situation in which both states are unoccupied is represented by a pseudo￾spin in the positive z direction, while occupation of both states is represented by a pseudospin in the negative z direction; other pseudospin orientations correspond to a superposition of the two possibilities. The effective Hamiltonian for the system is given by the first term being the kinetic energy and the second term the interaction energy. In this equation skr,sli. and sliz are the three components of the kth pseudospinck is the single-particle kinetic energy, µ the chemical potential and Vlilz’ the matrix element for the scattering of a pair of electrons of equal and opposite momentum and spin. The kth pseudospin sees an effective field where i is a unit vector in the z direction and 1 indicates the component of the pseudospin in the xy plane. One possible configuration of pseudospins consistent with (2) is shown in Fig. 1 (a). All the pseudospins lie in the positive or negative z direction, and

Physics 1973 Fig. 1. Pseudospin cor ns in (a)a normal metal(b)a superconductor. k, i the Fermi momentum the direction reverses as one goes through the Fermi surface, since akp changes sign there. If the interaction is attractive, however(corresponding to negative Vkk), a configuration of lower energy exists, in which the pseudo- spins are tilted out of the z direction into a plane containing the z axis, and the pseudospin direction changes continuously as one goes through the Fermi surface, as in Fig. 1(b) The ground state of Fig. 1(b)breaks the symmetry of the pseudospin Hamiltonian(1)with respect to rotation about the z axis, which is itself a con- sequence of conservation of number of electrons in the original Hamiltonian. Because of this symmetry a degenerate set of ground states exists, in which t pseudospin can lie in any plane through the z axis. The angle a which this plane makes with the Oxz plane will play an important role in what follows Anderson made the observation that with a suitable interpretation of the Gor'kov theory,(4)a is also the phase of the complex quantity F which occurs in that theory I was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally. The existence of th original symmetry implies that the absolute phase angle a would be unobserv- able, but the possibility of observing phase differences between the F functions in two separate superconductors was not ruled out. However, consideration of the number-phase uncertainty relation suggested that the phase difference Ag be if the twe trons. When I learnt of observations suggesting that a supercurrent could flow through a sufficiently thin normal region between two superconductors(5, 6), I realized that such a supercurrent should be a function of 4. I could see in principle how to calculate the supercurrent, but considered the calculation te be too difficult to be worth attempting I then learnt of the tunnelling experiments of Giaever, (7)described in th

2 Fig. 1. Pseudospin configurations in (a) a normal metal (b) a superconductor. kF is the Fermi momentum. the direction reverses as one goes through the Fermi surface, since F li-~ changes sign there. If the interaction is attractive, however (corresponding to negative V,,.), a configuration of lower energy exists, in which the pseudo￾spins are tilted out of the z direction into a plane containing the z axis, and the pseudospin direction changes continuously as one goes through the Fermi surface, as in Fig. 1 (b) . The ground state of Fig. 1 (b) breaks the symmetry of the pseudospin Hamiltonian (1) with respect to rotation about the z axis, which is itself a con￾sequence of conservation of number of electrons in the original Hamiltonian. Because of this symmetry a degenerate set of ground states exists, in which the pseudospins can lie in any plane through the z axis. The angle F which this plane makes with the Oxz plane will play an important role in what follows. Anderson made the observation that with a suitable interpretation of the Gor'kov theory, (4) F is also the phase of the complex quantity F which occurs in that theory. I was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally. The existence of the original symmetry implies that the absolute phase angle F would be unobserv￾able, but the possibility of observing phase differences between the F functions in two separate superconductors was not ruled out. However, consideration of the number-phase uncertainty relation suggested that the phase difference d@ could be observed only if the two superconductors were able to exchange elec￾trons. When I learnt of observations suggesting that a supercurrent could flow through a sufficiently thin normal region between two superconductors (5, 6), I realized that such a supercurrent should be a function of d@. I could see in principle how to calculate the supercurrent, but considered the calculation to be too difficult to be worth attempting. I then learnt of the tunnelling experiments of Giaever, (7) described in the

B. D. Josephson preceding lecture( 8). Pippard(9) hadconsidered the possibility that a Coo- per pair could tunnel through an insulating barrier such as that which Giaever used, but argued that the probability of two electrons tunnelling si- multaneously would be very small, so that any effects might be unobservable This plausible argument is now known not to be valid. However, in view of it I turned my attention to a different possiblity, that the normal currents through the barrier might be modified by the phase difference. An argument in favour of the existence of such an effect was the fact that matrix elements for processes in a superconductor are modified from those for the corres ing processes in a normal metal by the so-called coherence factors, (3 are in turn dependent on 49(through the uks and uks of the BCs theory At this time there was no theory available to calculate the tunnelling current. part from the heuristic formula of Giaever, (7)which was in agreement with experiment but could not be derived from basic theory. I was able however, to make a qualitative prediction concerning the time dependence of the current. Gor'kov(4) had noted that the F function in his theory should be time-dependent, being proportional to e-2ijge, where u is the chemical potential as before. (10) The phase a should thus obey the relation a中t=-21h while in a two-superconductor system the phase difference obeys the relation (4)=2eh here V is the potential difference between the two superconducting regions so tha Ad=2evt/h+const. Since nothing changes physically if Ag is changed by a multiple of 2, I was led to expect a periodically varying current at a frequency 2e v/h The problem of how to calculate the barrier current was resolved when one day Anderson showed me a preprint he had just received from Chicago, (11)in which Cohen, Falicov and Phillips calculated the current flowing in a super conductor-barrier-normal metal system, confirming Giaever's formula. They introduced a new and very simple way to calculate the barrier current-they simply used conservation of charge to equate it to the time derivative of the mount of charge on one side of the barrier. They evaluated this time deriva- tive by perturbation theory, treating the tunnelling of electrons through the barrier as a perturbation on a syste In consI isting of two isolated subsystems between which tunnelling does not take place I immediately set to work to extend the calculation to a situation in which both sides of the barrier were superconducting. The expression obtained was

preceding lecture (8). Pippard (9) ha considered the possibility that a Coo- d per pair could tunnel through an insulating barrier such as that which Giaever used, but argued that the probability of two electrons tunnelling si￾multaneously would be very small, so that any effects might be unobservable. This plausible argument is now known not to be valid. However, in view of it I turned my attention to a different possiblity, that the normal currents through the barrier might be modified by the phase difference. An argument in favour of the existence of such an effect was the fact that matrix elements for processes in a superconductor are modified from those for the correspond￾ing processes in a normal metal by the so-called coherence factors, (3) which are in turn dependent on A@ (through the U/~‘S and u,,.‘s of the BCS theory). At this time there was no theory available to calculate the tunnelling current. apart from the heuristic formula of Giaever, (7) which was in agreement with experiment but could not be derived from basic theory. I was able. however, to make a qualitative prediction concerning the time dependence of the current. Gor'kov (4) had noted that the F function in his theory should be time-dependent, being proportional to e-2ip”/h, where µ is the chemical potential as before. (10) The phase F should thus obey the relation (3) while in a two-superconductor system the phase difference obeys the relation where V is the potential difference between the two superconducting regions. so that Since nothing changes physically if A@ is changed by a multiple of 2p, I was led to expect a periodically varying current at a frequency 2eV/h . The problem of how to calculate the barrier current was resolved when one day Anderson showed me a preprint he had just received from Chicago, (11) in which Cohen, Falicov and Phillips calculated the current flowing in a super￾conductor-barrier-normal metal system, confirming Giaever’s formula. They introduced a new and very simple way to calculate the barrier current-they simply used conservation of charge to equate it to the time derivative of the amount of charge on one side of the barrier. They evaluated this time deriva￾tive by perturbation theory, treating the tunnelling of electrons through the barrier as a perturbation on a system consisting of two isolated subsystems between which tunnelling does not take place. I immediately set to work to extend the calculation to a situation in which both sides of the barrier were superconducting. The expression obtained was of the form

Physics 1973 =l6(V)+l"(V)cos(4)+l1(r)sin(4) [6] At finite voltages the linear increase with time of 4d implies that the only contribution to the dc current comes from the first term, which is the same as Giaever's prediction, thus extending the results of Cohen et al. to the two- superconductor case. The second term had a form consistent with my expecta tions of a Ag dependence of the current due to tunnelling of quasi-particles The third term, however, was completely unexpected, as the coefficient 11(v), unlike L(V, was an even function of V and would not be expected to vanish when V was put equal to zero. The 4g dependent current at zero voltage had the obvious interpretation of a supercurrent, but in view of the qualitative argument mentioned earlier I had not expected a contribution to appear to the same order of magnitude as the quasiparticle current, and it w days before I was able to convince myself that I had not made an error in the calculation Since sin(4)can take any value from-I to 1, the theory predicted a value of the critical supercurrent of I,(0). At a finite voltage V an ac supercurrent of amplitude {[4()2+[P frequency 2ev/h was expected. As mentioned earlier, the only contribu n to the dc current in this situation (V* 0)comes from the Io(v) term, so that a two-section current-voltage relation of the form indicated in Fig. 2 is expec I next considered the effect of superimposing an oscillatory voltage at fre- quency v on to a steady voltage V. By assuming the eff voltage to be to modulate the frequency of the ac supercurrent 1 concluded that constant-voltage steps would appear at voltages V for which the frequency of the unmodulated ac supercurrent was an integral multiple of v, i.e. when V=nhu/ge for some integer n The embarrassing feature of the theory at this point was that the effects order of magnitude as the jump in current occurring as the voltage through that at which production of pairs of quasi-particles becomes possible. xamination of the literature showed that possibly dc supercurrents of this magnitude had been observed, for example in the first published observation of tunnelling between two evaporated-film superconductors by Nicol, Shapiro and Smith(12)(fig. 3). Giaever(13)had made a similar observation, but ascribed the supercurrents seen to conduction through metallic shorts through the barrier layer. As supercurrents were not always seen, it seeme lanation in terms of shorts might be the correct one, and the whole theory might have been of mathematical interest only (as was indeed suggested in the literature soon after)

160 Physics 1973 (6) At finite voltages the linear increase with time of ,LI@ implies that the only contribution to the dc current comes from the first term, which is the same as Giaever’s prediction, thus extending the results of Cohen et al. to the two￾superconductor case. The second term had a form consistent with my expecta￾tions of a A@ dependence of the current due to tunnelling of quasi-particles. The third term, however, was completely unexpected, as the coefficient 11 (V), unlike IO (V) , was an even function of V and would not be expected to vanish when V was put equal to zero. The A@ dependent current at zero voltage had the obvious interpretation of a supercurrent, but in view of the qualitative argument mentioned earlier I had not expected a contribution to appear to the same order of magnitude as the quasiparticle current, and it was some days before I was able to convince myself that I had not made an error in the calculation. Since sin (A(@) can take any value from e-1 to + 1, the theory predicted a value of the critical supercurrent of I 1 (0). At a finite voltage V an `ac supercurrent’ of amplitude and frequency 2eV/h was expected. As mentioned earlier, the only contribu￾tion to the dc current in this situation (V ¹ 0) comes from the IO (V) term, so that a two-section current-voltage relation of the form indicated in Fig. 2 is expected. I next considered the effect of superimposing an oscillatory voltage at fre￾quency v on to a steady voltage V. By assuming the effect of the oscillatory voltage to be to modulate the frequency of the ac supercurrent 1 concluded that constant-voltage steps would appear at voltages V for which the frequency of the unmodulated ac supercurrent was an integral multiple of V, i.e. when V = nhv/2e for some integer n. The embarrassing feature of the theory at this point was that the effects predicted were too large! The magnitude of the predicted supercurrent was proportional to the normal state conductivity of the barrier, and of the same order of magnitude as the jump in current occurring as the voltage passes through that at which production of pairs of quasi-particles becomes possible. Examination of the literature showed that possibly dc supercurrents of this magnitude had been observed, for example in the first published observation of tunnelling between two evaporated-film superconductors by Nicol, Shapiro and Smith (12) (fig. 3). Giaever (13) had made a similar observation, but ascribed the supercurrents seen to conduction through metallic shorts through the barrier layer. As supercurrents were not always seen, it seemed that the explanation in terms of shorts might be the correct one, and the whole theory might have been of mathematical interest only (as was indeed suggested in the literature soon after)

B. I). Josephs Current Fig. 2. Predicted two-part current-voltage characteristic of a superconducting tunnel missing supercurrents, which was sufficiently convincing for me to decide to alculation, (14)although it turned out lat the critical supercurrent and the normal state resistivity depended on the assumption of time-reversal symmetry, which would be violated if a magnetic field were present. I was able to calculate the magnitude of the effect by using the Ginzburg- Landau theory to find the effect of the field on the phase of the f functions, and concluded that the earth's field could have a drastic effect on the supercurrents Brian Pippard then suggested that I should try to observe tunneling super currents myself, by measuring the characteristics of a junction in a compe sated field. The result was negative-a current less than a thousandth of the predicted critical current was sufficient to produce a detectable voltage across the junction. This experiment was at one time to be written up in a chapter of my thesis entitled'Two Unsuccessful Experiments in Electron Tunnelling between Superconduct Eventually Anderson realized that the reason for the non-observation of dc supercurrents in some specimens was that electrical noise transmitted down the measuring leads to the specimen could be sufficient in high-resistance

161 : Current Fig. 2. Predicted two-part current-voltage characteristic of a superconducting tunnel junction. Then a few days later Phil Anderson walked in with an explanation for the missing supercurrents, which was sufficiently convincing for me to decide to go ahead and publish my calculation, (14) although it turned out later not to have been the correct explanation. He pointed out that my relation between the critical supercurrent and the normal state resistivity depended on the assumption of time-reversal symmetry, which would be violated if a magnetic field were present. I was able to calculate the magnitude of the effect by using the Ginzburg-Landau theory to find the effect of the field on the phase of the F functions, and concluded that the Earth’s field could have a drastic effect on the supercurrents. Brian Pippard then suggested that I should try to observe tunneling super￾currents myself, by measuring the characteristics of a junction in a compen￾sated field. The result was negative-a current less than a thousandth of the predicted critical current was sufficient to produce a detectable voltage across the junction. This experiment was at one time to be written up in a chapter of my thesis entitled ‘Two Unsuccessful Experiments in Electron Tunnelling between Superconductors’. Eventually Anderson realized that the reason for the non-observation of dc supercurrents in some specimens was that electrical noise transmitted down the measuring leads to the specimen could be sufficient in high-resistance