Recent Work on Superconductivity*

W. Meissner, Munich

1. The Emergence of Superconductivity

Keesom discovered that at very low temperatures, which can be obtained by boiling liquid helium under reduced pressure, certain metals become superconducting. Thus, for example, in aluminum superconductivity sets in at \(1.14^\circ\ \mathrm{K}\), in zinc—at \(0.79^\circ\ \mathrm{K}\). In contrast to this, according to the data of the same Keesom, gold at \(0.73\), silver, magnesium, and tungsten at \(0.74\), bismuth, iron, and nickel at \(0.75\), and platinum at \(0.77^\circ\ \mathrm{K}\) still do not exhibit superconductivity. Likewise, phosphor bronze at a temperature of \(0.75^\circ\ \mathrm{K}\) still has normal resistance, from which Keesom concludes that copper as well, through which the current in a phosphor-bronze conductor undoubtedly flows, does not acquire the properties of a superconductor at this temperature.

Simon and Kurti established that cadmium becomes superconducting at a temperature of about \(0.6^\circ\ \mathrm{K}\). These investigators obtained such a low temperature by demagnetizing magnesium ammonium sulfate.

Altogether, up to the present time, 14 pure metals are known that exhibit superconductivity. Whether a superconducting state exists also for other metallic elements, in particular for monovalent metals, may be expected to be clarified soon—when still lower temperatures, not yet attained at present, are obtained. The attainment of these low temperatures will probably prove possible by means of the magnetocaloric method.

The question of whether the transition point into the superconducting state changes when direct current is replaced by high-frequency current has been answered in the negative by new measurements of Burton, Wilhelm, Pitt, and Young (in Toronto, USA): up to frequencies of \(3 \cdot 10^7\) hertz the transition point remains unchanged. Consequently, all conclusions drawn on the basis of the earlier work of these investigators, which had yielded opposite results, fall away.

* From reports read at the Tenth German Physico-Mathematical Congress in Bad Pyrmont (10–15 September 1934), Phys. Z. 35, 931–938, 1934; translated by N. Khlebnikov.

Burton, Wilhelm, and Meissner (Toronto, USA) investigated the superconductivity of thin layers of tin deposited electrolytically on wires made of metals that do not exhibit superconductivity. The results of these experiments are shown in Fig. 1. The data refer to layers with thicknesses from 2 to 3, from 6 to 8, and of \(10\cdot 10^{-8}\) cm at various current strengths. The thinner the layer, the lower the temperature corresponding to the transition point, and the stronger the dependence on the current strength. Layers having a thickness of less than approximately \(2\cdot 10^{-5}\) cm, down to \(2^\circ\) K, do not exhibit superconductivity. It is significant that these layers have a very high residual resistance,

Fig. 1. Superconductivity of thin layers of tin (after Burton, Wilhelm, and Meissner)

a resistance which, in the case of the thinnest layer, is only 6% less than the resistance at room temperature. Thus the layers with which these investigators worked proved to no longer have the properties of a continuous metal, despite the fact that, for example, in R. Schulze’s elegant experiments it was possible, by means of cathodic sputtering—at least for gold—to obtain much thinner layers that had the properties of a continuous metal.

Of considerable interest are experiments by the same investigators in Toronto, in which they covered a layer of tin with a layer of a metal that does not exhibit superconductivity. If the tin layer had a thickness of about \(90\cdot 10^{-8}\) cm, then no influence of the covering layer on the superconductivity was observed. This result is in agreement with the author’s experiments, which showed that the presence of a free surface between the superconducting metal

and an insulator is not essential for the occurrence of superconductivity.

Something quite different was found in the case of the thinnest of the tin layers investigated: despite the fact that a jump in resistance exists, the residual resistance has a considerable magnitude. From this the authors of the cited work draw the conclusion that the interface between the superconductor and the insulator plays an essential role in the phenomenon of superconductivity. They assume, moreover, that between the tin layer and the layer of the covering metal, which was likewise deposited electrolytically, no appreciable diffusion could have arisen and, consequently, no alloy formation could have occurred. However, taking into account the large magnitude of the residual resistance observed for thin layers and indicating that these layers can no longer be regarded as continuous, one may suppose just the opposite—namely, that atoms of the covering layer penetrate into the interparticle gaps of the tin layer, and that this is precisely what causes the appearance of the residual resistance. This supposition is all the more plausible since it is known from the earlier experiments of Holst and the author that points of contact between superconductors do not exhibit resistance. From this it follows in an obvious way that even a not entirely continuous layer of tin must be superconducting, provided only that the gaps between the individual particles of tin are not filled with a non-superconducting substance.

The cited investigators also studied the coating of tin layers with films of insulators. Superconductivity was thereby preserved. However, with the method by which the coating with the nonconductor was carried out, one cannot be certain that its particles penetrated into the gaps between the tin particles.

Recently in Toronto, detailed investigations of the superconductivity of alloys have also been carried out (by Allen). The results of these investigations are in general agreement with those obtained earlier in the Charlottenburg low-temperature laboratory: the curve expressing the dependence of the transition temperature into the superconducting state on the content of the constituent parts of the alloy makes it possible to draw quite definite conclusions concerning its composition. A known discrepancy in the results exists only for the alloy of thallium with tin. This discrepancy, however, can be explained by a difference in the preliminary treatment of the material: in our experiments annealing was always more prolonged.

How substantial the influence of the preliminary treatment is may be judged from Fig. 2, which gives the results of Allen’s experiments on the eutectic alloy of thallium with tin containing 45% of the former. This alloy is distinguished by the remarkable feature that the transition curve becomes the steeper the more strongly the alloy has been subjected to rolling. Usually, especially in the case of pure metals, the opposite is true: the transition curves for harder specimens are flatter than the curves for softer ones,

annealed. It is possible that during the rolling of eutectic alloys the components responsible for superconductivity come into closer contact with one another.

On the question of the superconductivity of chemical compounds, nothing substantially new has been published recently.

2. Magnetic phenomena connected with superconductivity. Number of superconductivity electrons. Theory

If, without changing the temperature of a superconductor, it is subjected to the action of a gradually increasing external magnetic field, then at some definite (“critical”) value of the field strength superconductivity disappears. Using a long cylindrical wire and measuring the field strength at a sufficient distance from it, one can observe (according to data from earlier investigations of the Leiden laboratory) the following: the critical strength in the case of a field perpendicular to the axis of the wire is approximately half the strength of the critical field parallel to the axis. This fact was explained about two years ago by Laué, who applied (following Lippmann’s method) Maxwell’s theory to an ideal conductor with a constant magnetic permeability equal to unity. The explanation reduced to the following: essential for the destruction of superconductivity is the tangential component of the magnetic field, which in the case of a transverse field is twice as large as in the case of a longitudinal one, since in the first of these cases the lines of force (which, according to Maxwell’s theory, cannot penetrate into the interior of the superconductor) are crowded together at the surface of the wire.

Fig. 2. Transition curves for a eutectic alloy of tin with thallium, containing 45% thallium (according to Allen)

The conclusions of Laué were confirmed by experiments of de Haas, Voogd, and Casimir-Jonker in Leiden. In the case of a wire of circular cross section, the critical value of the strength $H$ of a transverse magnetic field proved to be equal to 58% of the critical strength for a longitudinal field. For wires with an elliptical cross section the data are given in Table 1.

Thus, qualitatively, Laue’s results are confirmed. In detail there are discrepancies, which can be explained by the fact that, as follows from the most recent experiments of de Haas and Casimir-Jonker, the results of which were not known to Laue, the magnetic field penetrates into a superconductor only gradually. Therefore the presence of resistance is detected only at field strengths greater than those corresponding to the disappearance of superconductivity in the surface layer.

TABLE 1

Wire with an elliptical cross-section

Before turning to these measurements, it is necessary to dwell on phenomena of a hysteretic character. Recording, at an unchanged external magnetic field, the curves of transition into the superconducting state, de Haas, Voogd, and Casimir-Jonker obtained the hysteresis loop shown in Fig. 3. It should be noted that, in recording each point, in order to avoid interference from thermoelectromotive forces, the measuring current was commutated. The work was carried out with a compensation circuit.

Fig. 3. Curves, revealing hysteresis, of the transition for a single crystal of tin in a constant transverse magnetic field (after de Haas, Voogd, and Jonker)

The author also had occasion to observe, in working with single crystals of tin in a weak magnetic field (in the Earth’s field), hysteresis loops (Fig. 4). In this case, however, the measuring current was not commutated, and the resistance was determined simply from the deflection of a galvanometer to which the potential difference from the ends of the superconductor under investigation was applied. As is easy to see, in the absence of commutation of the measuring current the hysteresis phenomena are expressed more sharply. This is undoubtedly connected with a change in the magnetic permeability of the superconductor, occurring upon the onset of superconductivity—a phenomenon discovered by the author in collaboration with Ochsenfeld. It was precisely the hysteresis phenomena that first led the author to the idea of the possibility of a change in magnetic permeability. In the event that, upon the appearance of superconduc-

conductivity there occurred no change in the distribution of the measuring current and of its magnetic field, there would be no basis for the occurrence of hysteresis phenomena.

Fig. 4. Curves revealing hysteresis of the transition—for a single crystal of tin in the absence of a magnetic field and without switching the measuring current (after Meissner)

Fig. 5. Change in the distribution of the magnetic field upon the transition of the specimen into the superconducting state (after Meissner)

a
In the absence of superconductivity.

b
In the superconducting state.

The author had already reported on the change in magnetic permeability that occurs upon the onset of superconductivity at last year’s Physical Congress. During the interval in which the measurements, in which Dr. Heidenreich took part, have been refined since February 1934, a somewhat more complete article on this question has been printed (in Z. f. Ges. Kälteind.). Therefore the author would now like to dwell only on a few main points.

If the temperature is lowered as far as possible for a long conductor of cylindrical cross section, placed in a weak magnetic field perpendicular to its axis, then, when the conductor passes into the superconducting state, the lines of force of the field appear as though expelled from inside the conductor and are arranged approximately as is shown in Fig. 5b. The field distribution was investigated with the aid of a small search coil connected to a ballistic galvanometer and capable of being rotated through 180°. In this way it was possible to determine the field strength both after the onset of superconductivity and before the moment when it

had a value of about 5 gauss. The initial position of the plane of the coil could be changed. This made it possible to determine the direction of greatest field intensity. In the most recent measurements the coil could be moved around the superconductor along two different circumferences, which made it possible to obtain the distribution of the field in all the space surrounding the superconductor. In Fig. 6 the positions of the plane of the coil are shown by small strokes, corresponding to the greatest ballistic deflection when the coil was placed at various points of both circumferences (whose diameters were equal to 12 and 20 mm, respectively). The directions perpendicular to these strokes will evidently represent the directions of the lines of force of the magnetic field. The points at which the coils were placed are marked by the values of the angle \(\alpha\), the diameter for the ends of which \(\alpha = 0^\circ\) and \(\alpha = 180^\circ\) corresponding to the initial direction of the homogeneous magnetic field. The fact that at the positions \(\alpha = 90^\circ\), \(180^\circ\), and \(270^\circ\) the directions of the plane of the coil are not perpendicular and, correspondingly, not parallel to the direction of this plane at \(\alpha = 0^\circ\), is due in part to the fact that the centers of the two circumferences do not exactly coincide with the axis of the crystal. It is possible, moreover, that this is a consequence of defects in the crystal structure, as well as of incomplete homogeneity of the initial field.

Fig. 6. Direction of the magnetic lines of force near a superconductor (according to Meissner and Heidenreich)

In Fig. 7 the positions of the coil corresponding to those shown in Fig. 6 are given once again, now on a diagram of the magnetic field, calculated and constructed for a value of the magnetic permeability \(\mu\) equal to zero. Here the density of the lines depicts, on an arbitrary scale, the field strength at the given point. The number of lines crossing the small stroke representing the coil corresponds, on the same scale, to the number of lines actually passing through the coil.

In Fig. 8 curves are plotted showing the dependence of the greatest ballistic deflection on the positions of the coil (i.e., on the angle \(\alpha\)) for all the investigated points of both circumferences. The fact that for \(\alpha = 0^\circ\) and \(\alpha = 180^\circ\) the deflections for the circumference 12 mm in diameter do not go to zero should be explained by the fact that here the field strength is measured not on the very surface of the superconductor, but at a distance of 1 mm from it. For the circumference with a diameter of 20 mm the deviations of the field from homogeneity

turn out to be already much smaller, and at still greater distances we would naturally find an even closer approximation to a homogeneous field. The indicated field distribution does not change with time. In checking this fact it was established that after 2 hours the field, both in magnitude and in direction, remained exactly the same.

Fig. 7. Magnitude of the magnetic-field strength computed for the case \(\mu = 0\) and found experimentally near a superconductor (according to Meissner and Heidenreich)

In Table 2 the values of the field strength found experimentally are compared with those obtained by calculation on the assumption that \(\mu = 0\). The agreement between the two sets of values may be regarded as very good, and therefore we have the right to say that, with the onset of superconductivity, the field distribution proves to be very close to that corresponding to the magnetic permeability \(\mu\) of the superconductor becoming zero.

Quite different results are obtained when measuring the field strength inside a tubular superconductor. The first experiments in this direction were carried out with a polycrystalline lead tube.

TABLE 2

Computed and observed values of the field strength after the transition to the superconducting state

It turned out that upon transition to the superconducting state the field strength inside the tube does not fall to zero, as might have been expected. The average field strength, which alone could be measured, even increased by 5%. When the external field was switched off, the field inside the tube did not change appreciably. At the same time, on the outer surface of the tube at the points \(\alpha = 0\) and \(\alpha = 180^\circ\) the field was preserved. The strength of this residual field amounted to about 10% of the strength of the initial homogeneous field.

Fig. 8. Magnetic-field strength near a superconductor (after Meissner and Heidenreich)

Analogous experiments carried out with a tube made from a single crystal of tin gave somewhat different results. In this case as well there was a certain increase in the field strength inside the tube upon transition to the superconducting state. However, after the external field was switched off, the field inside the tube weakened considerably.

Fig. 9. Magnetic-field strength inside a channel in a single crystal of tin

The results of these observations are shown in Fig. 9, where the solid horizontal line corresponds to the homogeneous field before the onset of superconductivity, and the curves to the field after its onset, measured on circumferences of 2 and 4 mm in diameter; \(\alpha\) as before indicates the point at which the measurement was made. The larger circumference was located near the inner surface of the cylinder, but in such a way that, when the coil was rotated, it did not touch this surface.

It is evident from the figure, first of all, that the field has different strengths at different points of the circumference and, secondly, that this field is on average approximately 10% stronger than the initial homogeneous field. When the external field was switched off, a residual field remained inside the tube, represented by the curves in the lower part of the same Fig. 9. In this case as well the residual field did not change—

decreased with time, retaining its magnitude for 2 hours, even when the temperature was lowered.

If the external field was switched on again, the field distribution outside proved to correspond to a permeability equal to zero. Inside the tube, however, the field did not return to the state shown in the upper part of Fig. 9, but increased by only 3–4% in comparison with the residual field. When the external field was switched off again, the former value of the residual field inside the tube was established. This process of switching the external field on and off could be repeated any number of times without changing the magnitude of the residual field. In any case, it retained its magnitude after a hundred switchings on and off.

To go into the details of the explanation of this remarkable phenomenon—the preservation of a magnetic field inside superconductors—seems inconvenient to the author at the present time. It can only be pointed out that, for the phenomenon, the circumstance must be essential that the magnetic energy located inside the tube is not able to pass outward through the superconducting layer. In addition, attention should be drawn to the difference between the phenomena in the case of a single crystal and of a polycrystal. It may be assumed that for an ideal single crystal the residual field is completely absent.

Fig. 10. Scheme of the experiments of de Haas and Casimir-Jonker

Here it is not possible to dwell in detail on analogous experiments with two parallel cylindrical superconductors through which a current could be passed. We note only that the results of these experiments correspond to what was set forth above also with respect to the magnetic field of the current flowing through them.

The change in magnetic permeability upon the transition of a substance into the superconducting state was confirmed by experiments conducted in Leiden, Toronto, Oxford, and Kharkov. De Haas and Casimir-Jonker used in their experiments a single crystal of tin having three parallel channel axes (Fig. 10), one of which was at the center of the crystal, and the other two at a distance of 1 mm from the edges. The field strength in these three channels was determined from the resistance of bismuth wires. The experiments of these investigators also showed that the field strength (after the external field was switched off) in the outer channels fell almost to zero, whereas in the central one it increased somewhat.

De Haas and his collaborators used their apparatus also in the following way. Having cooled the superconductor to a temperature below the transition point, they switched on a transverse magnetic field and gradually increased it to a value greater than the critical one. In this case it proved possible to establish that, after the critical value of the field strength had been crossed, the magnetic field penetrated into the crystal only gradually. This explains, as we have already indicated above,

discrepancies between Laue’s experimental data and the results of calculations.

Burton, as well as Tarr and Wilhelm, used in their investigations the apparatus shown in Fig. 11. A tube of polycrystalline tin was wound with wire in the manner clear from the drawing. With the aid of a fluxmeter the change in magnetic flux occurring upon the onset of superconductivity was measured. In these measurements it was found that the field in the external space proves to be very close to coinciding with that which should be expected if the magnetic permeability of superconducting tin is taken to be zero. The internal field, however, increases, according to Burton’s data, by 35%.

Mendelssohn and Babbitt used solid and also hollow spheres of tin and measured the magnetic moments of these spheres after the external magnetic field had been switched off. In the case of a solid—

Fig. 11. Diagram of the experiments of Tarr and Wilhelm

sphere the magnetic moment had a value approximately equal to \(1/6\) of that which it should have had if the magnetic field inside had been completely preserved. But it also did not prove equal to zero, which should have occurred in the case of the magnetic permeability being reduced to zero inside the whole sphere. It should, however, be borne in mind that in the investigations described, in contrast to the author’s experiments, strong magnetic fields were used. In the case of the hollow sphere the magnetic moment was 2–3 times greater than for the solid sphere, evidently on account of the magnetic energy remaining inside the sphere. In this respect, therefore, the experiments of Mendelssohn and Babbitt agree with the data obtained in Berlin, Leiden, and Toronto.

The indicated changes in magnetic permeability must be taken into account in almost all experiments on superconductivity. It was already pointed out above that only in this way can one explain the appearance of a hysteresis loop when plotting the transition curve at constant current strength. Keesom and Kok indicated that this phenomenon must also be taken into account in investigations of the change in specific heat accompanying the transition to the superconducting state. Gor

ter and Casimir attempted to give a thermodynamic theory of this heat effect, associated with the transition into the superconducting state, taking into account the change in magnetic permeability. The course of their reasoning is, in general outline, as follows.

First of all, it is assumed that in the superconducting state the magnetic permeability is always equal to zero. They explain the existence of a magnetic field inside a hollow cylinder after the external field has been switched off by the fact that part of the walls of the tube has not passed into the superconducting state because of the magnetic field existing there, whose intensity has a value greater than the critical one, and whose lines can close outside the tube. This assumption seems to us incompatible with the results obtained in the investigation of a hollow single crystal of tin. Further, Gorter and Casimir apply both principles of thermodynamics to the process of magnetization, in which the transition from the superconducting to the nonsuperconducting state takes place. In doing so they make use either of consideration of a cyclic process, or they carry out calculations with the free enthalpy; both paths give one and the same result. In this way one obtains the formula, already derived earlier by Rutgers, which makes it possible to calculate the dependence of the critical intensity of the magnetic field on temperature from the change in the specific heat upon transition into the superconducting state. In agreement with the experiments of Haas and his collaborators, Gorter and Casimir come to the conclusion that when superconductivity is destroyed by the action of a magnetic field, the latter penetrates into the substance only gradually, so that at the beginning of this process there still exists inside the body a superconducting “core.” Such a conception encounters a difficulty consisting in the fact that the field intensity at the surface of the conductor would then have to fall so much that superconductivity would have to arise there again. In view of this, Gorter and Casimir are compelled to admit the existence inside the conductor of threadlike regions not possessing superconductivity.

The change in magnetic permeability is not the only deviation from the properties of an ideal conductor predicted by classical electromagnetic theory. Becker, Heller, and Sauter, as well as Braunbek, have shown that, as a consequence of the inertia of the electrons, the currents arising when the magnetic field is switched off, etc., cannot be regarded as purely surface currents. They flow in a surface layer approximately \(10^{-6}\) cm thick. Braunbek has also proposed an experiment by means of which it may perhaps be possible to determine the lower limit of the number of electrons producing superconductivity per unit volume. This experiment is to consist in measuring the penetration of a magnetic field, switched on in the external space, into a volume bounded by a shell consisting of a thin layer of superconductor. It should be noted, however, that the effect to be measured lies, in all probability, at the limit of sensitivity of the methods of measurement.

The number of superconductivity electrons can, according to the results of Becker, Heller, and Sauter, be determined from measurements of the current arising when a superconducting sphere is rotated.

A case similar to the one indicated—that of a rotating and instantaneously stopped ring—was considered by Meissner and Grossmann. In the first approximation, i.e., for the case in which the thickness of the ring is small in comparison with its diameter, the following expression is obtained for the final value of the current:

\[ I_{\infty}=-v_{0}\,\frac{1}{\dfrac{U}{Ne}+\dfrac{Le}{mU}}, \]

where \(v_{0}\) is the initial velocity of motion of the circumference of the ring, \(N\) is the total number of superconductivity electrons in the ring, \(U\) and \(L\) are the circumference and self-inductance of the ring, and \(e\) and \(m\) are the charge and mass of the electron. Unfortunately, as an approximate numerical calculation shows, this effect also lies at the limit of measurability. This occurs because the second term in the denominator is always large in comparison with the first.

London is planning experiments to determine the number of superconductivity electrons, based on the following considerations: when a superconductor is acted upon by a high-frequency current, one may expect the appearance (as a result of the inertia of the electrons) of an electric field inside the superconductor. The motion of electrons not belonging to the number of superconductivity electrons, caused by this field, must give rise to the liberation of Joule heat. Experiments of this kind also will not belong to the simple ones.

Up to the present time, the wave-mechanical theory of superconductivity has not yet achieved serious successes. Brillouin attempted to give a wave-mechanical explanation of superconductivity without paying particular attention to details. From Brillouin’s work it follows that superconductivity should set in gradually. Thus, for the principal feature of this phenomenon—the jump in resistance—his theory can give no explanation.

One may think that, upon the onset of superconductivity, randomly oriented closed currents are formed inside the superconductor, encompassing a comparatively large number of atoms. With the aid of this assumption it is possible to explain the observed change in magnetic permeability. For the formation of these currents only a small fraction of the available conduction electrons is necessary, which is in agreement with the change in thermal conductivity upon transition into the superconducting state. When an external electric field is applied, some of these small closed currents (which continuously disappear and arise again) may merge, forming macroscopic superconductivity currents. Of course, these assumptions represent no more than a hypothesis, the admissibility of which is subject to theoretical and experimental verification.

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