Research Profile

by Roberto Lalli

Sir Nevill Francis Mott (1905-1996)

Nobel Prize in Physics 1977 together with Philip W. Anderson and John H. van Vleck "for their fundamental theoretical investigations of the electronic structure of magnetic and disordered systems".

Nevill Francis Mott was born in Leeds on September 30, 1905, to Charles Francis Mott and Lilian Mary Reynolds. Although his parents had not pursued an academic career, both of them had received a robust education in mathematics and the physical sciences. In the early years of the 20th century, they had indeed met each other when working at the eminent Cavendish Laboratory under the directorship of J. J. Thomson, who shortly after would win the 1906 Nobel Prize in Physics.
Nevill Mott followed in the footsteps of his parents and showed a natural talent and great curiosity for natural sciences since an early age. Like his parents, he also went to Cambridge University to read the Mathematical Tripos. He studied mathematics and physics at St. John’s College from 1924 to 1928, in a period of great turmoil generated by the development of the new quantum mechanics. Although he did extremely well during his undergraduate studies, he felt that he was not prepared enough to cope with these radical advances and struggled to learn the new theory with solitary efforts and the occasional help of more senior researchers, such as P. Dirac.
Determined to become a theoretical physicist, he continued to do research at Cambridge under the supervision of Ralph H. Fowler—a British physicist and astronomer who had recently elaborated, in collaboration with Dirac, a statistical mechanical model of white dwarfs. After Mott wrote his first paper on quantum mechanics in 1928, he began a two-year period in which he visited, and worked in, other institutions, some of them regarded as major centres of modern physics. Mott had the opportunity to spend some months with N. Bohr at the Institute for Theoretical Physics of the University of Copenhagen. Since its establishment in 1921, the Institute had been considered a Mecca of theoretical physics, which had an enormous importance in the development from old quantum physics to quantum mechanics. When Mott went there, the institute was still attracting a number of early-career theoretical physicists who were eager to work with one of the founding fathers of the recently formalized quantum mechanics as well as the main proponent of the Copenhagen Interpretation, the main understanding of the quantum mechanical theoretical formalism.
Mott also worked in Göttingen, where Born had built a powerful group of mathematical physics, and in Manchester with W. L. Bragg, before coming back to Cambridge. From 1928 to 1932, his papers had a mathematical character and were aimed at improving and applying to nuclear physics and particle interactions the theories that had been recently developed, such as the Schrödinger equation, the Dirac theory of electrons, and the Bose-Einstein and Fermi-Dirac statistics.

Becoming the British Leader of Solid-State Physics
In 1932, Mott was invited by A. M. Tyndall to become the chair of theoretical physics at Bristol University. The relocation from Cambridge to Bristol had deep consequences in various aspects of Mott’s research, including the change of topics on which he would focus and the closer connection with experimental research. In a few months, Mott became an expert on the application of quantum mechanics to solid-state physics—a field that had recently made enormous progress especially after the publication of Felix Bloch’s dissertation in 1928, which laid out the foundation of the quantum theory of electrons in an ionic lattice. When Mott began working on the field, many principles and theoretical tools for studying the properties of metals and semiconductors had been developed, including the Brillouin zones, the Wilson theory of energy bands in solids, Heisenberg’s theory of ferromagnetism, and the concept of spin waves.
The first physicists to produce effective calculations on real metals starting from the principles of quantum mechanics were the Jewish Hungarian physicist E. Wigner and his PhD student F. Seitz. They put forward a model based on some simple assumptions for calculating the properties of sodium at Princeton in 1933. This novel approach led to a series of extensions of the Wigner-Seitz model to produce more and more accurate predictions about the properties of real solids. In the 1930s, this research project was pursued especially in three small research groups. In collaboration with the British physicist Harry Jones, Mott headed the only British group devoted to research on realistic applications of the band theory of metals, the other two being at Princeton around Wigner and at MIT around the American theoretical physicist J. Slater.
Already in 1934, together with Jones and the British experimental physicists H. W. B. Skinner, Mott published an important paper aimed at explaining some experimental results on the x-ray emission bands in metals, which confirmed that conduction electrons obeyed Fermi-Dirac statistics. Two years later, Mott co-authored with Jones a textbook entitled The Theory of the Properties of Metals and Alloys, which would rapidly become influential to train a younger generation of solid-state physicists. Especially relevant to the pedagogical success of the book was its presentation of simple approximated models that could be related to empirical results as well as the attention to laboratory practice concerning solid-state physics.
During the 1930s, Mott and his Bristol group made many contributions to the theory of real solids and promoted the field within the larger physics community. As far as Mott’s personal contributions are concerned, one of the most relevant was the model of rectification at the metal-semiconductor junction, which he developed in 1938 independently of Walter Schottky, working at Siemens. In 1936, Mott had begun working with R. W. Gurney on the theoretical description of the properties of semiconductors. In 1938, building on the work of the German physicist Robert Pohl on the physical properties due to defects in crystal—especially the F-center (Farbzentrum or color centre) in which one anionic vacancy is filled by electrons—Mott and Gurney put forward the basic mechanism to explain the formation of latent image in photographic films—namely, the formation at surface of silver clusters due to the action of photoelectrons in silver halides. When the beginning of the Second World War disrupted the normal research activities of many British scientists, including Mott, he had already reached an international status of one of the leaders of solid-state physics and head of one of the most active research centres in this field.

Bringing Solid-State Physics at Cavendish Laboratory
World War II sharply interrupted Mott’s research activities to divert him towards different kinds of duties. Contrarily to many American colleagues, he was not fortunate enough to work on projects at the scientific or technological frontiers. He did make war-related scientific work, but he later considered these activities useless. As soon as the war ended Mott refused an offer from Cambridge, and remained in Bristol where he had already built a very strong research group. In the immediate postwar period, one of his main interests concerned the theory of dislocation—or linear crystal defect—which was considered a persuasive theoretical explanation of the ductility of crystalline solids—namely, the phenomenon that crystalline solids retain a new form after they have been deformed by a certain force. Mott had begun working on this theory with F. R. N. Nabarro in 1938 when they explained the exceptional resistance to deformation of aluminium alloys by arguing that the introduction of other materials in a pure metal obstructs the dislocation. After the war ended, Mott was influential in creating the conditions for further research made at Bristol by F. C. Frank, A. Cottrell, and Nabarro himself, who all made important contributions to the field of plasticity and crystal growth.
Mott returned instead to do research on the properties of electrons in metals and insulators. In the 1940s, his major contribution was the study of the transition from insulators to conductors under variations of pressure. In 1949, Mott hypothesised that as soon as the pressure becomes sufficiently large, all the electrons of the non-metallic elements become free at once. This insulator-metal transition—soon to be called Mott transition—became a highly debated topic. It sparked experimental research to provide evidence for or against the reality of the effect for a number of elements and in relation to other changing conditions such as the variation of temperature or of the density of impurities (doping).
His research activities were again interrupted in 1954, when Mott returned to Cambridge to replace Bragg as director of the Cavendish Laboratory and Cavendish Professor at Cambridge University. The Cavendish Laboratory had a strong tradition in nuclear physics, strengthened by Rutherford’s directorship in 1919-1937 and continued by Bragg from 1938 to 1953, and had recently established itself as a major centre for molecular biology. A costly linear accelerator had been planned as the next important step to increase the relevance of the Cavendish Laboratory in particle physics. Mott, however, decided to abandon the project to support other experimental endeavours, especially because he believed that in this field the United States would remain much ahead in spite of British efforts. Instead, Mott made pressure to improve the level of the Cavendish laboratory in solid-state physics and to encourage nuclear and particle physicists to strengthen their international cooperation, especially with the CERN.

The Search for the Theory of Disordered Systems
At Cambridge, Mott was busy with administrative and teaching duties, modernising the educational system. He especially struggled to reform the natural science tripos in order to introduce modern physics earlier in the curriculum. These and other administrative commitments considerably diminished the time Mott could dedicate to pure research. In spite of his strong involvement in education, which occupied him till his retirement in 1971, Mott was able to direct younger co-workers towards important discoveries, but he also made contributions in the new field of disordered systems—especially non-crystalline semiconductors—that would eventually gain him the Nobel Prize. The field was novel enough that important foundational work could be make without complex mathematics, and without excessively costly devices.
His teaching and administrative duties left him enough time to dedicate to physics research only after 1965, and from that year he worked on the theory of disordered systems. His interest in this field was born out of his 1949 work on the insulator-metal transition. A way to experimentally test the Mott transition was to increase the concentration of impurities in a semiconductor. The problem was that Mott had developed his theory for regular crystals, while the increasing of impurities did not follow a regular pattern and created disordered systems, whose behaviour was much more difficult to schematize.
When Mott turned his attention to this kind of problem, he suddenly recognized that a fundamental step had been made by the American theoretical physicist Philip W. Anderson in his 1958 paper “Absence of diffusion in certain random lattices,” which contained the model that is now called Anderson localization. In the paper, Anderson had argued that if the level of disorder is sufficiently large, electrons remain localized. While Anderson’s paper was ignored by the majority of solid-state physicists, Mott soon recognized its value because it fit very well with the observations of the insulator-metal transition of silicon doped with phosphorus, which he had been carrying out to test the Mott transition. In 1961, with his student W. D. Twose, Mott wrote a review article on the topic in which he supported the Anderson localization as an empirically proven fact. Although different from the theoretical perspective, the Mott transition and the Anderson transition were very hard to distinguish in practice. The renewal of the interest in the subject was sparked by the co-presence of the two theoretical descriptions, requiring more complex experimental settings to identify which kind of transition was actually occurring.
From 1965 onward, a lowering of his academic duties allowed him to immerse himself completely in the field of disordered systems. In 1966, Mott extended Ziman’s 1962 theory on the electrical resistance of liquid metals to apply it to specific cases. He also put forward a theoretical explanation of why in certain glassy semiconductors the increasing of impurities did not excessively alter the conductivity—a behaviour very different than that of crystals. Since the late 1960s, Mott became one of the greatest authorities in the theory of disordered systems as well as in their possible technological applications. He became very involved in the study of the electrical properties of such materials, which were much more affordable than highly purified crystalline solids.

His work as well as the contributions of several other researchers who join the field made it clear that the original proposal of the Mott transition was very simplistic. On the other hand, it the importance of Mott’s pioneering research in sparking and strengthening a novel field of research was recognized. In 1977, the Royal Swedish Academy of Science celebrated the importance of this long-lasting activity awarding Mott, along with van Vleck and Anderson, the Nobel Prize in Physics “for their fundamental contributions to the theory of the electronic structure of magnetic and disordered systems.” Usually, the Nobel Awards in Physics and Chemistry are awarded for specific discoveries and achievements. In this case, as the Nobel Prize motivation and the Award Ceremony Speech show, Mott was awarded for a series of contributions that shaped a field, which, at the time of the Prize, was still in its infancy.
Mott had already retired six years before receiving the Nobel Prize. His retirement, however, did not imply an interruption of his scientific activity. Mott continued to make research and to be a leading figure in British academia. He had also been knighted in 1962 for the relevance of his achievements. When he died in 1996, at the age of 91, he had published more than three hundreds scientific publications, including thirteen influential books.

Bibliography
Hoddeson, L., Braun, E., Teichmann, J., & Weart, S. (eds.) (1991) Out of the Crystal Maze: Chapters from the History of Solid-State Physics. Oxford University Press, New York.
Mott, N. F. (1977) Electrons in Glass Nobel Lectures, Physics 1971-1980, Editor Stig Lundqvist, World Scientific Publishing Co., Singapore, 1992
N. F. Mott, A Life in Science (Taylor & Francis, London, 1986).
Pippard, B. (1995) Electrons in Solids. In Brown, L., Pippard, B., & Pais, A. (Eds.) Twentieth Century Physics (Vol. 3). AIP, New York, pp. 1279-1383.
Pippard, B. (1998). Sir Nevill Francis Mott, C. H. 30 September 1905-8 August 1996. Biographical Memoirs of Fellows of the Royal Society, 44, pp. 315-328.
Sir Nevill F. Mott - Biographical. Nobelprize.org. Nobel Media AB 2014. Retrieved 24 December 2014. http://www.nobelprize.org/nobel_prizes/physics/laureates/1977/mott-bio.html


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