Professor Sir Brian Pippard (1920 – 2008)

Brian Pippard will be remembered particularly as the first experimenter to map a Fermi surface, for his non-local theories of electromagnetic response in normal metals and superconductors, and as dynamic Head of Physics in Cambridge from 1971 to 1982. But these were the highlights: his range of achievement was remarkable.

He grew up in Bristol, and at Clifton College considered for a time a career in music: his piano-playing was of concert standard. However, in 1938 he entered Clare College to read Natural Sciences, and, doubting his mathematical ability, chose at first to study chemistry, before switching to physics to make himself more useful in the war effort.

He worked at Great Malvern on a radar device for tracking mortar projectiles, returning to Cambridge for his Ph. D. in 1945, in the Royal Society Mond Laboratory, financed by a Stokes Studentship at Pembroke College (which he won partly because he was willing to organise the Chapel music).

Brian was already familiar from his war work with the skin effect, the restriction to a thin surface layer of microwave fields applied to a metal, and his supervisor David Shoenberg encouraged him to follow up some 1940 work of Heinz London by studying it in superconductors—materials that lost all electrical resistance below a sharply defined transition temperature near absolute zero.

At that time, superconductivity was still a mystery, though in 1935 Heinz and his brother Fritz had already hinted that a superconductor might be a quantum fluid, a system of many electrons all governed by an effective wave function dependent on a single position variable.

If this function were sufficiently rigid (unperturbed by an applied magnetic field) one would expect the superconductor to show a local relation between the current density and the magnetic vector potential , analogous to Ohm’s law in the normal metal, with a limited penetration depth for magnetic field analogous to the microwave skin depth.

By measuring the bandwidths of microwave resonators made of tin and mercury, Brian successfully observed a dramatic reduction in microwave absorption when he cooled them through their transitions.

His experimental design was a model of effective simplicity. For instance, the frequency of his klystron source had to be stable to one part in a million, which he achieved using no more than draught protection, a micrometer tuner with weight and pulley to eliminate backlash, and a stack of carefully aged high-tension batteries as power supply.

As well as confirming and expanding the current models of microwave response in superconductors, his doctoral work carried the seeds of two further developments. He noticed that, by combining his bandwidth measurements with extra measurements of the shift in resonant frequency between the normal and superconducting states, he could obtain complete information on the surface impedance, and hence an unambiguous value for the complex conductivity of his samples. This gave full information on the density of superelectrons (in the two-fluid language of the time), and also showed that at microwave frequencies lossy processes continued amongst the normal electrons, even in the superconducting state.

Secondly, following Heinz London’s 1940 observation that in normal metals the surface resistance did not continue to decrease with falling temperature as the dc resistance did, but reached a limit, Brian realised that this anomalous skin effect occurred when the electron free path became greater than the skin depth, and was able to explain it in essentials on the simple basis that under these conditions only those electrons moving parallel to the sample surface remained effective. He joined with Ernst Sondheimer, a theoretician friend, in formulating the problem precisely, and the full theory of the anomalous skin effect was published by Reuter and Sondheimer in 1948. Brian’s simple ineffectiveness concept was later applied to many other phenomena, such as cyclotron resonance and ultrasonic attenuation in metals.

In 1947, he was appointed a University Demonstrator, and returned to Clare as a Fellow.

After his doctorate he became interested in the geometry and dynamics of normal–superconducting boundaries, and introduced the important idea that their stability was determined by whether the magnetic penetration depth was larger or smaller than a characteristic coherence length, which, like the penetration depth, diverged at the transition temperature. This length was later found to be identical with the coherence length of Ginzburg–Landau theory, and proved crucially important in understanding type II superconductors, which can contain quantised flux lines. (Type II materials are used in building practical superconducting magnets, because they can carry heavy currents in very large magnetic fields, when the flux lines are suitably pinned.)

At the same time, Brian began investigating the surface impedance of tin that had been alloyed with indium to reduce the electron free path. He observed that the alloying not only increased the normal state skin depth as expected, but also, and in much the same way, increased the superconducting penetration depth. However, it had little effect on the transition temperature or the condensation energy, suggesting that the density of superelectrons was not much altered. Brian drew the startling conclusion that he must be observing a non-local effect: just as in normal metals the current at a point depended on the electric field at neighbouring points through which the electrons had travelled since last being scattered, so perhaps in a superconductor the London relation ought to be replaced by a non-local relationship in which the supercurrent depended on distant values of the vector potential, the range being limited by an electromagnetic coherence length . In the dirty limit, he assumed that must be essentially the free path, but in pure materials he decided that could not be unbounded, but must be limited by a new length , which unlike the Ginzburg–Landau coherence length was approximately independent of temperature. In 1953 he proposed a precise model of this non-local effect.

What was the new length ? Brian reasoned that the superconducting wave function could not be completely rigid, as the London brothers had assumed. The magnetic field would surely perturb the wave function to some extent, and this perturbation would be expected to spread through the system, carrying supercurrent with it. But the superconducting condensation occurred only below the transition temperature , suggesting that it must be a weak affair, involving only those electrons within of the Fermi surface. Such a group of electrons would be expected to get out of phase with each other at distances greater than , and Brian suggested that was probably of this order, typically 1 ?m.

In early 1957 Brian made a short visit to Moscow, where Landau noisily rejected his ideas of non-locality (probably because no such effect was apparent in Ginzburg–Landau theory, by then proving successful), and was not persuaded by Brian’s arguments that the experimental results demanded it. However, Brian’s model fitted the experimental data very well, and later that year, when Bardeen, Cooper and Schrieffer published their revolutionary pairing theory of superconductivity, they were at pains to demonstrate that it confirmed Brian’s model almost exactly—and once the Moscow theoreticians had taken time to study BCS, they generously sent Brian a private message conceding that he had been right.

In 1952, Onsager had given an interpretation of the de Haas–van Alphen effect (oscillations in the magnetic moment of a metal as a function of magnetic field) in terms of the Fermi surface, a theoretical boundary in momentum-space within which the conduction electrons of a metal were thought to reside, and in 1954 Brian first showed that in the extreme anomalous limit the surface impedance of a
normal metal provided a measure of the curvature of this surface, near the effective electrons.

In 1955 he married Charlotte, and carried her away immediately for a sabbatical year in Chicago. While there, he delivered an undergraduate course, which he later wrote up as Elements of Classical Thermodynamics. But he was also developing his Fermi surface ideas, and during this sabbatical he took the opportunity of measuring the surface resistances of a series of single-crystal samples of pure copper in various orientations.

On his return to Cambridge, he used the curvatures deduced from these observations to map out the Fermi surface of copper, a widely recognised tour de force. This was the first time any Fermi surface had been obtained experimentally. Brian was elected to the Royal Society in 1956, received its Hughes Medal in 1959, and was elected to the John Humphrey Plummer Chair of Physics in 1960.

By 1959 so many new phenomena were under investigation involving normal electrons orbiting Fermi surfaces in large magnetic fields that Brian decided to design a facility that would provide steady fields of 100 kgauss over a 2 inch bore. (Up to this point the Mond laboratory was able to investigate such phenomena only by using pulsed fields.) This was achieved, at a cost of £43,000, and the new Magnet Laboratory, tucked into a corner of the old Cyclotron Lab, was opened in 1961. Its design was workmanlike and brute-force, using up to 2 MW of power (cheaper at night), a large transformer, and a bank of silicon rectifiers delivering 27 kA at 75 V. The magnet windings were flat coils of 75mm ? 1.5 mm copper strip through which cooling water was driven by powerful pumps, from a large reservoir in the basement. During the Magnet Lab period, Brian was writing extensively on Fermi surface phenomena, and, for instance, in 1962 he published an important note showing that in the de Haas–van Alphen effect, the field acting on the electrons is the magnetic induction , not the applied field , which explained why the magnetic moment was in some circumstances multi-valued. His 1962 Dynamics of Conduction Electrons established him as an omni-competent expert on Fermi surface affairs, especially magneto-resistance, helicons, and magnetic breakdown in which electrons tunnel through momentum space from one part of the surface to another. (Although much was achieved in it, the Magnet Lab was short-lived: reliable commercial superconducting magnets became available, and no attempt was made to reproduce the facility in West Cambridge when the Cavendish moved.)

In 1961, Brian’s student B. D. Josephson was working on an obscure experimental project (the magnetic field dependence of the penetration depth), when, in his spare time, he developed a new theory of quantum tunnelling between superconductors. He submitted it for a Fellowship dissertation at Trinity—and it subsequently earned him a Nobel Prize. Brian always asserted that, at the time, he couldn’t understand Josephson’s idea, but he encouraged him to consult Phil Anderson, who did grasp its importance, and defended it against the trenchant criticisms of Bardeen and others. Later, however, Brian took up with enthusiasm the physics of SNS Josephson junctions, especially the non-linear solutions of their governing equations, and new notions concerning the proximity effect, the leakage of superconductivity into neighbouring normal metals. He also made important contributions concerning the related phenomena that arise when supercurrent is converted to normal current at an SN interface, especially branch imbalance (when the electron and hole branches of the excitation spectrum get out of equilibrium) and Pippard boundary resistance (in which electrons feel the effect of scattering centres by quantum tunnelling).

In 1961, Brian was invited to give a banquet speech at an IBM international conference on superconductivity. He took as his title ‘The Cat and the Cream’, and startled his audience by asserting that physics, apart from fundamental particle physics, was largely worked out (which didn’t endear him to those hunting for research grants at the time). Perhaps it was tongue in cheek, or perhaps he felt it so in a personal sense, for his extraordinary productivity did decline somewhat thereafter. But this must not be exaggerated. He was always interested, his views were eagerly sought, and he continued to contribute important ideas. A good example is his 1969 paper on the mechanism of the peak effect (a strengthening near a particular magnetic field of the critical current density in type II superconductors), in which he pointed out that a lattice of quantised flux lines would be more effectively pinned if it were not too rigid.

In 1966 Brian became the first President of the newly founded Clare Hall, and as soon as the building was ready moved into the President’s Lodge with Charlotte, his three daughters and his grand piano.

He succeeded in making the College an informal and happy home for graduates, distinguished visitors and their families—and also a liberal one: he actively defended ‘Red Rudi’ against Conservative attempts to have him deported. (Rudi Dutschke was a left-wing German student activist who had been shot during a Berlin street protest, and appeared at Clare Hall while recuperating.)

During the late 1950s, Neville Mott had become convinced of the need to move the Cavendish to new buildings in West Cambridge, and Brian quickly became the front man for promoting this enterprise within the University and raising the money, as well as being active (with Ian Nicol) in making sure that the architecture was practical and the right services provided, and (with John Payne) in planning the complex decanting operation when the great trek finally took place.

Brian was elected Cavendish Professor in 1971, which at that time made him automatically Head of Department. As Head, he discouraged horse-trading between research groups on appointments, and aimed to establish laboratory-wide standards, encouraging innovative research and trying persistently, though not always successfully, to close down areas judged more plodding.

He strengthened the Teaching Committee, was proactive in the reform of undergraduate teaching in Cambridge and beyond, and demanded high lecturing ability in promotions and new appointments. Though choosy about what he undertook at national level, he was President of the Institute of Physics from 1974 to 1976.

He was knighted in 1974, and took early retirement in 1982.

In retirement, he maintained to the end of his life an active interest in areas of physics he found absorbing, becoming particularly intrigued by non-linear phenomena of all sorts in classical physics. In 1989 published a text on Magnetoresistance, in which he sorted us all out on this most complex of Fermi surface phenomena.

As an experimenter, Brian was exceptional: always hands-on, he tackled extraordinarily difficult things at times, and they always worked as planned, for him and for his many research students.

If one tries to assess Brian as a thinker, it has to be said that he disliked mathematical formalism, which he felt often obscured the essence of things (although he was actually rather proficient at solving difficult equations once a problem had been formulated). He had, for instance, irrational horrors of the grand canonical ensemble and 4-vectors in special relativity. He always preferred to think of quantum problems in terms of semi-classical wave packets, never eigenfunctions and eigenvalues; and he refused to learn second quantisation (in terms of which the BCS theory and Josephson’s theory were couched), just as he refused to learn to drive. His strength was his unerring instinct for the right, often subtle, illuminating idea. His semiclassical concepts of ineffectiveness and coherence length, for instance, though imprecise, were essentially correct, and were immediately grasped by a whole generation of physicists and applied
to a wide range of new discoveries. A second characteristic of his thought was a love of phenomenological theories, theories which did not require fundamental microscopic understanding, but were based on some key insight into the nature of the phenomena—theories such as classical thermodynamics itself, or the quantum fluid idea, or Ginzburg–Landau theory, or his own non-local theory of superconductors, or even dimensional analysis, which he used extensively. Interestingly, of physicists he had met and worked with, he particularly admired Onsager and Landau—two theorists who combined mastery of the illuminating idea (which he loved) with mastery of difficult formalism (which he probably felt was beyond him).

He had a strong sense of style in spoken and written English, and an equally strong sense of humour. As supervisor and lecturer he was always stimulating, and his perceptive Elements of Classical Thermodynamics and challenging Cavendish Problems in Classical Physics excited and tormented generations of students. He taught a wide range of courses, notably Thermal Physics, the Wave Mechanics course in the new Advanced Half-Subject in 1958 (delivered from memory, without notes) and, later, various versions of the opening course in Part IA, which led to his book Forces and Particles. However, it also has to be said that his approach sometimes proved too quirky and personal for weaker students, who needed first to grasp the essentials.

As will have appeared, Brian could be idiosyncratic. He was capable of great kindness, but also had an enormous boyish relish in simply being clever, which all who knew him will remember vividly: his inaugural lecture as Cavendish Professor, for instance, was planned around an intriguing series of bench experiments, whose outcomes the assembled practitioners, young and old, were invited to predict, by show of hands. We duly got most of our predictions wrong, as he intended.

John Waldram