## I. The electromagnetic equations of the supraconductor. Offprint from: Proceedings of the Royal Society of London A, Vol. 149, No. 866, March 1935. [With:] II. Supraleitung und Diamagnetismus, Offprint from: Physica, Vol. II, 1935.

London; Haag: Harrison & Sons for the Royal Society; Martinus Nijhoff, 1935; 1935.

First edition, very rare offprints, of the first successful macroscopic theory of superconductivity, the vanishing of electrical resistance in some materials at very low temperatures. This is embodied in the ‘London equations’, the analogue for a superconductor of Ohm’s law for a normal conductor. ‘In 1933 shortly before Heinz London joined his brother at Oxford, W. Meissner and R. Ochsenfeld made a startling discovery. It was well known that currents in superconductors flow in such a way as to shield points inside the material from changes in the external magnetic field … But a superconductor does more. Whereas a zero resistance medium only counteracts changes in the field, it actually tends to expel the field present in its interior before cooling” (DSB). “In 1935, the brothers Fritz London and Heinz London developed the first phenomenological theory of superconductivity [II]. The London equations provide a theoretical description of the electrodynamics of superconductors, including the Meissner effect. In a thin surface layer, just inside the superconductor, screening currents flow without resistance, which cancel the applied magnetic field in the interior of the superconductor. The thickness of this layer, known as the ‘London penetration depth’, is a characteristic of the superconductor in question. In addition, London recognized that superconductivity is an example of a macroscopic quantum phenomenon. The behavior of a superconductor is governed by the laws of quantum mechanics like that of a single atom, but on a macroscopic scale” (‘A brief history of superconductivity,’ in: *Discovering Superconductivity*: *An Investigative Approach* (Ireson, ed.), 2012). “In 1934 two brothers, Fritz and Heinz London, both refugees from Nazi Germany, were working in an upstairs room in a rented house in Oxford. There they solved what was then one of the biggest problems in superconductivity, a phenomenon discovered 23 years earlier. The moment of discovery seems to have been sudden: Fritz shouted down to his wife ‘Edith, Edith come, we have it! Come up, we have it!’ She later recalled, “I left everything, ran up and then the door was opened into my face. On my forehead I had a bruise for a week.’ As Edith recovered from her knock, Fritz told her with delight ‘The equations are established – we have the solution. We can explain it’ … In formulating their theory, the London brothers made the most significant progress in our understanding of superconductors in the first half of the 20th century … John Bardeen, who won his second Nobel prize in 1972 for co-developing the Bardeen–Cooper–Schrieffer (BCS) theory that provided a coherent framework for understanding superconductivity, regarded the achievement of the London brothers as pivotal. ‘By far the most important step towards understanding the phenomena’, Bardeen once wrote, ‘was the recognition by Fritz London that both superconductors and superfluid helium are macroscopic quantum systems.’ Before then, quantum theory had only been thought to account for the properties of atoms and molecules at the microscopic level. As Bardeen explained, ‘It was Fritz London who first recognized that superconductivity and superfluidity result from manifestations of quantum phenomena on the scale of large objects’” (Blundell, ‘The forgotten brothers,’ *Physics World*, April 2011, pp. 26-29).

“Fritz London was born in 1900 in the German city of Breslau (now Wroclaw, Poland) and nearly became a philosopher. However, he switched to physics and became immersed in the heady intellectual atmosphere of the 1920s that surrounded the new quantum theory. London’s early career saw him travelling around Germany, taking positions with some of the great quantum pioneers of the time: Max Born in Göttingen; Arnold Sommerfeld in Munich; and Paul Ewald in Stuttgart. London worked on matrix mechanics and studied how the newly discovered operators of quantum mechanics behave under certain mathematical transformations, but he really made his name after moving again to Zurich in 1927. The lure of Zurich had been to work with Erwin Schrödinger, but almost immediately Schrödinger moved to Berlin and London teamed up with Walter Heitler instead. Together they produced the Heitler–London theory of molecular hydrogen – a bold and innovative step that essentially founded the discipline of quantum chemistry.

“The following year London moved to Berlin, where he worked on intermolecular attraction and originated the concept of what are now known as London dispersion forces. He also succumbed to the interpersonal attraction of Edith Caspary, whom he married in 1929. By now the name ‘Fritz London’ was becoming well known – he was fast gaining a reputation as a creative and productive theorist. However, with Hitler becoming German chancellor in 1933, the Nazis began a process of eliminating the many Jewish intellectuals from the country’s academic system, putting both London and his younger brother Heinz at risk. Born in Bonn in 1907, Heinz had followed in his older brother’s footsteps, studying physics, but became an experimentalist instead, obtaining his PhD under the famous low-temperature physicist Franz Simon.

“A possible way out from the Nazi threat was provided by an unlikely source. Frederick Lindemann, later to become Winston Churchill’s wartime chief scientific adviser and to finish his days as Viscount Cherwell, was then the head of the Clarendon Laboratory. Lindemann was half-German and had received his PhD in Berlin, so was well aware of the political situation in Germany. He decided to do what he could to provide a safe haven in Oxford for refugee scientists. His motives were not entirely altruistic, however: Oxford’s physics department was then a bit of an intellectual backwater and this strategy would effect an instantaneous invigoration of its academic firepower in both theoretical and experimental terms. Later that year Lindemann persuaded the chemical company ICI to come up with funds to support his endeavour.

“Lindemann initially lured both Schrödinger and Albert Einstein to Oxford, although Einstein quickly moved on to Princeton University in the US. Simon also came, bringing with him Heinz London as his assistant as well as Nicholas Kurti. But Lindemann also wanted a theorist and admired Fritz London as a no-nonsense, practical sort of person who was able to work on down-to-earth problems. Thus both London brothers ended up in Oxford, Heinz sharing a rented house with his brother and sister-in-law. Fritz was the superior theorist but Heinz had deep insight into, and a great love for, thermodynamics, something that he had picked up from Simon. He frequently quipped ‘For the second law, I will burn at the stake.’ With Simon’s arrival in Oxford, and the installation there of the first helium liquefier in Britain, experimental research began on low-temperature physics, leading Fritz London to work on superconductivity.

“The discovery of superconductivity in April 1911 by Heike Kamerlingh Onnes and Gilles Holst was the inevitable consequence of Onnes devoting many years to the development of the cryogenic technology needed to achieve low temperatures. With Onnes’s laboratory in Leiden being the first to liquefy helium came the first chance to explore how materials behave in such extreme low-temperature conditions. The disappearance of electrical resistance in a sample of mercury was an unexpected shock, but in retrospect it was an inevitable consequence of having developed a far-reaching new technology that opened up an unexplored world.

“But nobody knew how this new effect worked. For decades theorists tried and failed to come up with an explanation. Felix Bloch is remembered for his eponymous theorem about waves in periodic potentials, but his failure to make progress with understanding superconductivity reduced him to formulate a tongue-in-cheek statement that also became known at the time as Bloch’s theorem: ‘the only theorem about superconductivity that can be proved is that any theory of superconductivity is refutable’ or, more succinctly, ‘superconductivity is impossible’.

“The crucial clue came from the famous 1933 experiment of Walther Meissner and Robert Ochsenfeld. They showed that a superconductor cooled to below its transition temperature in an applied magnetic field suddenly expels that magnetic field. In this ‘Meissner effect’, surface superconducting electrical currents (supercurrents) flow around the superconductor in such a way as to shield the interior from the applied magnetic field. These circulating supercurrents oppose the applied magnetic field, so that deep within the superconductor the magnetic field is close to zero – an effect known as perfect diamagnetism. Fritz London realized that this perfect diamagnetism is even more central to the behaviour of a superconductor than perfect conductivity. Until then perfect conductivity had been thought of as the superconductor’s defining quality – hence the name – but London realized that it is more of a by-product. While others had been trying to figure out how to formulate a new Ohm’s law for a superconductor, in other words to find a relationship between electric current and electric field, London saw that what was needed was a new relation between electric current and magnetic field.

“Existing theories had postulated some sort of acceleration equation: an electric field might not drive a current (as it does in a conventional metal) but it might cause one to accelerate. The perfect conductivity in a superconductor meant that there could be no electric field, but this absence of an electric field could be consistent with an already accelerated current of carriers. However, the equations that described this situation only led to a screening of time-varying magnetic fields and not time-independent ones, as evidently screened in the Meissner–Ochsenfeld experiment, and so did not account for the observations.

“The London brothers instead insisted that the fundamental principle of superconductivity is the expulsion of magnetic fields. It was their conviction in this line of thought that led to their 1934 eureka moment – the one that caused Edith London’s bruised forehead. They postulated an equation that links the magnetic field to the electric current density and produces the required screening of static magnetic fields and hence the Meissner effect. This equation and the brothers’ modified version of an acceleration equation became known as the ‘London equations’, which they published in 1935 [I]. Their theory also predicted a length scale over which a magnetic field can penetrate through the surface of a superconductor, which became known as the ‘London penetration depth’” (Blundell).

“In 1935 Fritz and Heinz London [I, II] proposed that the electrodynamics of superconducting electrons, or superelectrons, should be described by the following pair of equations:

∂(Λ** J**)/∂

*t*=

**, curl(Λ**

*E***) = –**

*J***,**

*B*where Λ is the ‘London parameter’. The first equation shows how the superelectrons accelerate under the influence of an electric field, while the second in effect explains the Meissner effect: it is straightforward to deduce from the second equation that the magnetic field ** B** can only penetrate into a superconductor by a small penetration depth of order 10

^{-6}m in most superconductors.

“These two equations [the ‘London equations’] proved very successful, and the London brothers pointed out that they could be understood if the electronic many-body wave function [behaves] like a single particle wave function but is nevertheless guiding the behaviour of many electrons. It was a mystery how this could come about for the wave function of a strongly interacting many-body system, especially for fermions, which cannot accommodate more than one particle in a given one particle state” (Longair, *Maxwell’s Enduring Legacy* (2016), p. 239).

“The goal for a microscopic theory of superconductivity was then to find the mechanism for cooperative behavior of the electrons. This was achieved by H. Fröhlich; J. Bardeen, L. N. Cooper, and J. R. Schrieffer; and N. Bogoliubov in the years immediately after London’s death” (DSB).

Two offprints. I. 8vo (254 x 177 mm), pp. 71-88; II. 8vo (244 x 161 mm), pp. [241], 242-354, [2, blank]. Original printed wrappers.

Item #5972

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Price:
$1,500.00
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