ABSTRACTS

SUPERCONDUCTIVITY OF METALS*

The classic experiment of Dewar and Fleming (1898) on measuring the electrical conductivity of metals cooled with liquid air and liquid hydrogen led them to the conclusion that the electrical resistance of all pure metals should vanish at absolute zero. Later experiments by Kamerlingh Onnes (1911) with liquid helium showed that mercury becomes such a superconductor of electricity already at \(4^\circ.2\ \mathrm{K}\). If a strong current is induced in a ring made of a metal cooled in this way, then that current evidently retains its intensity until the temperature of the metal begins to rise. For example, in a lead ring placed in liquid helium, a current of 200 A could be maintained for many hours.

With sufficient cooling, other metals also exhibit such superconductivity, and the temperature of transition from the state of ordinary conductivity to superconductivity differs for different metals. As an example, the following table may be given:

The property of superconductivity is exhibited not only by pure metals, but also by their alloys and by certain chemical compounds. As an example one may cite cuprous oxide, which possesses this property although not one of the conductors entering into its composition is a superconductor. The same is observed in a whole series of other salts, for example in the nitrogen-carbon-boron and silicic-acid salts of molybdenum, tungsten, tantalum, zirconium, and niobium.

The indicated transition temperature, generally speaking, rises in those metals to which metals of the bismuth group have been added. For example, bismuth raises this temperature for lead from \(7^\circ.2\ \mathrm{K}\) to \(8^\circ.8\ \mathrm{K}\), and carbon raises the temperature for niobium from \(8^\circ.2\) to \(10^\circ.5\ \mathrm{K}\). Further, although neither pure gold nor pure bismuth possesses the property of superconductivity even at the very lowest temperatures, their alloy becomes superconducting at \(1^\circ.94\ \mathrm{K}\).

The transition from the normal state to the superconducting state for pure metals takes place within an interval of several hundredths of a degree. For alloys or chemical compounds this interval is usually wider.

* The present article is an abridged presentation of McLennan’s report (McLennan, Nature 130, 878, 1932) on the discussion on the electrical superconductivity of metals. The discussion, in which Salte-Gaz, B. Meissner, and O. V. Richardson took part, was held at the Conference of the British Association in York on September 2, 1932.

Recent investigations of various alloys Ag—Sn, Au—Sn, and Au—Pb have led to the following results. First, in alloys with superconducting elements, gold preserves its own transition temperature, i.e., it behaves in the opposite manner to bismuth, antimony, and arsenic. Secondly, binary alloys of a superconductor and a non-superconductor do not always have only a single transition temperature. Thirdly, for the three alloy systems indicated above, the transition temperatures prove to be higher for eutectic mixtures than for the chemical compounds of the given two metals.

Mechanical effects, for example twisting and stretching, raise the transition temperature. The coefficient of expansion, as observations on lead have shown, does not exhibit a discontinuity when passing through the transition temperature, i.e., \(7.2\ \mathrm{K}\).

Under the action of a magnetic field, superconductivity arises at a lower temperature than under normal conditions. In order to return a metal from the superconducting state to the normal one, a certain critical value of the field strength is required; for example, for an alloy of bismuth with lead at \(1.2\ \mathrm{K}\) a field of \(20{,}000\) gauss is required, while for pure thallium at the same temperature the field is about 15 gauss.

Since, owing to the absence of resistance in superconducting metals, no heat is released when current passes, very large currents can be passed through thin wires, for example more than \(1000\ \mathrm{A}\). The greatest permissible current is determined by that magnetic field which it produces at the axis of the current itself and which affects the restoration of resistance.

Recently MacLennan and his co-workers observed the current strength in various superconductors of identical dimensions. The currents in metal rings were induced by means of the magnetic field of a coil placed near the superconducting rings. It turned out that in weak magnetic fields (from zero to 25 gauss) identical changes of flux produce currents of the same magnitude in Ta, Pb, and Sn. From this it follows that the current strength in a superconductor depends not on the nature of the metal, but only on its dimensions and on the form and magnitude of the magnetic field. This is also understandable, since the induced current for a given flux is determined only by the magnitude of the self-inductance, which, owing to the identical dimensions of the rings, was one and the same, and by the magnitude of the resistance, which in all three cases was, of course, vanishingly small. Above 25 gauss, the curve for tin begins to deviate from the general straight line, while at 43 gauss the current strength in tin begins to drop rapidly. This is explained by the fact that the magnetic field for tin exceeds the above-mentioned critical value, and the resistance is thereby restored. For tantalum and lead, the point \((130\ \text{gauss},\ 245\ \mathrm{A})\) still lies on the former straight line.

To explain the phenomena of superconductivity, theories were proposed (J. J. Thomson, O. W. Richardson, and others), according to which the superconducting state depends on some orientation. If this conjecture were correct, then in the case of high-frequency currents one could expect the appearance of some new phenomena. It is clear that any such phenomena could arise only if the period of oscillation of the field were less than the so-called “relaxation period,” i.e., the time required for the establishment of such an orientation. An example of this kind may be the rapid decrease of the dielectric constant for dielectric fields of high frequency, and for ice at \(0^\circ\ \mathrm{C}\) high-frequency measurements make it possible to establish that the “relaxation period” is of the order of \(10^{-6}\) sec. Analogous experiments, carried out recently by MacLennan and co-workers, led to the discovery in Pb, Sn, and Ta in the superconducting state of certain characteristic phenomena which allow one to conclude that the “relaxation period” in this case is of the order of \(10^{-7}\)—\(10^{-8}\) sec.

As one of these phenomena, they took the absorption by superconductors of \(\beta\)-rays (from mesothorium) by a thin layer of lead at temperatures slightly above and slightly below the critical transition temperature, \(7.2\ \mathrm{K}\). In this case no jump was found in the absorption coefficient over this entire

interval of temperatures. Fast electrons from a mesothorium source apparently encounter in superconducting lead the same resistance as in lead with normal conductivity. It follows from this that, whereas in a superconducting metal the resistance is zero for a current of slow electrons, in the case of fast electrons it retains its normal value. If this result is interpreted on the basis of wave mechanics, it turns out that at the very lowest temperatures lead will not exhibit superconductivity in the case of electric fields with a frequency on the order of \(10^{21}\) periods.

Another series of experiments was carried out with photoelectrons, the thin lead films being placed on glass or quartz plates. The temperature interval here was approximately the same as in the first series of experiments. Measurements showed that here, too, there is no discontinuity in the photoelectric effect or in the coefficient of light absorption upon passing through the transition temperature \(7.2\ \mathrm{K}\). Theory here shows that superconductivity of lead can be detected when the frequency of the alternating electric field is equal to or greater than \(10^{14}\) periods. It must be supposed, however, that if superconductivity exists for a constant electric field, i.e., for a field of zero frequency, then there must exist some critical field that will have a frequency between zero and \(10^{14}\) periods, and at which superconductivity will just disappear.

Further experiments were also carried out with electric fields of radio frequencies, and it turned out that at a frequency of \(1.1 \cdot 10^{7}\) periods a lead wire shows a sharp loss of resistance at a temperature somewhat lower than the critical temperature \(7.2\ \mathrm{K}\) characterizing the transition to superconductivity of the same wire under a constant current. In the case when this transition under a constant current begins at a temperature of \(3.76\ \mathrm{K}\) and ends at \(3.70\ \mathrm{K}\), the corresponding temperatures at high frequency are lowered to \(3.67\ \mathrm{K}\) and \(3.61\ \mathrm{K}\). Further experiments with high frequency made it possible to establish the dependence of this lowering of the temperature on frequency. Extrapolation of this curve, which runs almost linearly, gives for \(0^\circ \mathrm{K}\) a frequency of \(10^{9}\) periods per second. Analogous results were obtained also with wires of a Bi—Pb alloy. It is very interesting that the observed lowering of the critical temperature does not depend on the strength of the high-frequency currents; therefore this lowering cannot be ascribed either to heating of the wire above the temperature of the surrounding helium or to the influence of the magnetic field of the currents. Experiments with wires of different dimensions at one and the same frequency show that the lowering of the transition temperature is not a direct function of the “skin effect,” so that the phenomenon of the current frequency in the metal itself must be regarded as beyond doubt.

From the point of view of explaining the phenomena of superconductivity, experiments with the simultaneous passage through a superconductor of a direct current and an alternating current of high frequency are of very great interest. One such experiment was carried out with tantalum. It turns out that, if one measures the resistance to direct current, the curves of the dependence of this resistance on temperature in the presence of an alternating current show a lag in the appearance of superconductivity. However, the presence of a high-frequency current in the wire does not affect the temperature at which the transition to the superconducting state ends. Undoubtedly it is precisely the “skin effect” that plays a role here, since the destructive action of high-frequency currents at wire temperatures low enough for it to be a superconductor in measurements of direct-current conductivity is limited only to the outer layers of the wire.

Therefore, in another experiment a constantan wire of diameter \(0.16\ \mathrm{mm}\), “rubbed” with tin, the layer of which, with an average thickness of \(0.002\ \mathrm{mm}\), reduced the resistance of the wire at room temperature by approximately \(7\%\), was taken. At a temperature somewhat higher than the critical temperature, the resistance of the constantan, according to calculations, was approximately thirty times greater than that of the tin layer. Here, as in the preceding case, the resistance

layer of lead by the direct current changed in such a way that the curve, in the presence of high-frequency currents, shifted toward lower temperatures. When the ratio of the high-frequency current strength to the direct-current strength was increased, this shift became greater. With the same lead shell, observations were made of the resistance of the shell to high-frequency currents. Here, conversely, it turns out that if a direct current is added to a high-frequency current, the resistance to high-frequency currents partially or completely disappears. All these experiments with alternating high-frequency currents apparently confirm the conclusion that the emergence of the superconducting state in metals is connected with certain phenomena of polarization or orientation.

To explain the phenomena of superconductivity, de Haas assumes that when metals pass into the superconducting state, the electrons pass into a new phase. This view is supported by certain experiments on the conductivity of single crystals. De Haas finds that the temperature range over whose extent the transition to the superconducting state occurs does not exceed 0°.0005. Further, alloys of gold with bismuth become superconductors, although neither pure gold nor pure bismuth becomes superconducting; X-ray investigations show that these alloys have their own crystal lattice. Form has the same influence in the case of gray and white tin, of which only the latter is a superconductor.

Investigations of the thermal conductivity of superconductors point to existing connections between this property and superconductivity. For example, indium shows a sudden increase in thermal conductivity near the critical point. The same is also observed in the case of tin.

The similarity between superconductivity and ferromagnetism led to a search for anomalies in the specific heat of superconductors near the critical point. It is true that the expected anomaly could not be detected here, but this is explained by the fact that the number of electrons with which the existence of superconductivity is connected is, in comparison with their total number or with the number of atoms, too small for them to exert a noticeable influence on the specific heat. It is also possible that there is some compensating influence of the atoms, which balances out any changes in the specific heat arising from changes in the energy of the electrons.

Finally, the determination of the specific heat of electricity (the Thomson effect) on the basis of thermoelectric measurements on lead and gold indicates the existence of an anomaly, though one covering a somewhat broader temperature interval than the transition to the state of superconductivity. This anomaly is quite similar to the corresponding anomaly in the case of ferromagnetic substances near the Curie point, so that, if one considers it to be truly connected with the onset of superconductivity, the natural conclusion will be that we are dealing with a change in the energy of the electron when it passes from the nonsuperconducting state to the superconducting one. On the basis of the magnitudes of the magnetic field and the frequency required to destroy the superconducting state, this change in electronic energy can be approximately calculated.

Experiments of this kind have led to the creation of a theory according to which superconducting electrons in a metal form their own crystalline lattice in addition to the lattice formed by the atomic ions of the metal; moreover, the motion of this electronic lattice through the lattice of the metal can occur without scattering of energy even when the metal lattice is in a state of thermal motion. The temperature of transition of a metal from the superconducting state to the ordinary state may be regarded as the melting point of the electronic lattice. With the aid of this theory it is possible to explain many phenomena connected with superconductivity in metals. Final confirmation of the theory may probably be expected after the study of the superconductivity of single crystals of metals, in which direction the corresponding investigations have now begun.

N. A. Shishakov