Royal Society publishing Informing the sence of the futue Memories of Early Days in Solid State Physics Author(s):N.F. Mott Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 371, No. 1744, The Beginnings of Solid State Physics(Jun 10, 1980), Pp 56-66 Published by: The Royal Society StableUrl:http://ww jstor.org/stable/2990276 Accessed:12/03/201002:19 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp.JstOr'sTermsandConditionsofUseprovidesinpartthatunless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showpublisher?publishercode=rsl Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission JStOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about STOR, please contact support@jstor. org The Royal Society is collaborating with JSTOR to digitize, preserve and extend access to Proceedings of the Royal Society of London. Series A, Mather atical and Phvsical sciences ittp://www.jstor.org
Memories of Early Days in Solid State Physics Author(s): N. F. Mott Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 371, No. 1744, The Beginnings of Solid State Physics (Jun. 10, 1980), pp. 56-66 Published by: The Royal Society Stable URL: http://www.jstor.org/stable/2990276 Accessed: 12/03/2010 02:19 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=rsl. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The Royal Society is collaborating with JSTOR to digitize, preserve and extend access to Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. http://www.jstor.org
Proc R. Soc. Lond. A 371, 56-66(1980) Printed in great Britain Memories of early days in solid state physics BY N.F. MoTT, F R S Cavendish Laboratory, cambridge Mott, Sir Nevill. Born Leeds 1905. Studied theoretical physics under R. H. Fowler in Cambridge, in Copenhagen under Niels Bohr and in Gottingen. Professor of Theoretical Physics in Bristol 1933-54, and Cavendish Professor of Physics, Cambridge 1954-71. Nobel Prize for Physics 1977. Author of several books and research papers on application of quantum mechanics to atomic collisions an since 1933 on problems of solid state science My interest in the subject began in 1933 when I left Cambridge to take up the chai of theoretical physics in Bristol In Cambridge I remember that A H. Wilson wrote an Adams prize essay on metals which led to his book, The theory of metals, and I have a curiously vivid recollection of R. H. Fowler explaining to C. D. Ellis that most semiconductors were what we would now call extrinsic, the electrons coming from impurities, and Ellis replying " very interesting in a tone of voice that implied that he was not very interested. Although a lecturer in the Faculty of Mathematics as were at that time all theorists in Cambridge, I spent much of my time in the Cavendish, and in Fowler's massive book on Statistical Mechanics Rutherfords Cavendish was not the place where a young man would naturall turn to the theory of electrons in solids. I do not remember being very interested myself, but I do remember going to a course of lectures by the late Ebenezer Cunningham of St John's College on electrons in metals when I was an under graduate; t our textbook was Richardsons Electron theory of metals. I re member being struck by the point in the book and in the lectures that the Hall effect gave an indication of the number of free electrons in a metal, often near one er atom, and that at least one quantity, the ratio of thermal to electrical conduc tivity, could be calculated; but there were many unexplained observations, parti- cularly the long mean free paths and the absence of any large contribution to the specific heat from the electrons. But most of all I wondered how it could be that the atoms of a metal gave up their electrons, so that they became free, while in an insulator they remained fixed in position and unable to move. t This was of course cleared up by wilson's work. When I went to Bristol in 1933 as Professor of Theoretical Physics, two influences turne he towards electrons in solids: Harry Jones(see the previous paper) had t Probably in 1925; J. C. Slater in his Scientific biography records that Dirac attended the same courge in 1923 t My recollection contrasts with Wilson' s in this volume of discussions at L feeling that an insulator is a'poor'metal. As far as I can remember, w period that in'insulators', temperature would be capable of allowing electrons to move [56]
Memories of early day s in solid state physics a theory explaining the Hume-Rotheryt rules in metals and Herbert Skinner was engaged in his experimental work on the soft X-ray emission bands of light metals i think that when I went to bristol I must have been aware of Sommerfeld's explanation of the absence of a major contribution to the specific heat from the electrons, assuming that they obeyed Fermi-Dirac statistics, and the treatments by Bloch, Peierls and Wilson of electrons moving in a periodic field, the long mean free paths, the separation of the energy states into zones and the distinction be tween metals and non-metals. Looking back on it, I am surprised how easily everyone accepted this strange theory, in which all the electrons, in insulators as well as in metals, were treated as free, and insulators appeared as materials in which all the energy states in each zone were either occupied or empty, so that a current due to electrons moving in one direction was exactly balanced by movement in the opposite direction. The papers by Bloch and Peierls tell us something about that. Moreover, the approximation in which each electron moved in the average field of all the others was very easily accepted; I suppose Hartree's success with the self- consistent'fields for atoms had a lot to do with this. More detailed treatment of the effect of the very large interaction term e2/r1 had to wait till later The monumental and comprehensive report in the Handbuch der Physik by Sommerfeld Bethe appeared in 1933 and formed a basis on which other workers could build. This report, I believe, had an immense influence on solid state physics Apart from the effects of the interaction term e /r12 everything seemed to be there worked out in detail. Whether I had seen this report when Harry Jones showed me his work in 1933 I cannot remember, but i do remember the impact that Jones's work made on me, He supposed that all the electrons in an alloy could be treated as free, that the effect on their energies, particularly of those with states in k-space near the Fermi surface, could be calculated as in the theory of Bloch, and so be depressed when that surface approached the boundaries of the zone. An alloy would therefore take up a structure such that the boundary of a zone lay just outside the Fermi surface.(I do not believe we used the term 'Fermi surface at that time, only 'Fermi energy'. The idea of the Fermi surface was, however, well brought out in Bethe's article which contains very clear illustrations of their shape calculated for certain cases. )I think my enthusiastic acceptance of the theory was typical of my generation at that time; quantum mechanics was new, all physics and chemistry lay there to be explained and if by making approximations and neglecting even large terms(like e/ r12)one could account for something that had been observed, the thing to do was to go ahead and not to worry. I remember many discussions with Hume-Rothery himself, who shared my point of view Turning now to Skinner's work(some of it with O Bryan)on X-ray emission by the light metals lithium, sodium and magnesium, the observations showed band of the form illustrated in figure la. The theory of non-interacting electrons, as set out in Sommerfeld Bethe's article and neglecting correlation, predicted a form of the band, corresponding to the density of states, as illustrated in figure 1b-so t See note on Hume- Rothery at end of the article by H. Jones
58 N. F. Mott N(E) FIGURE 1.(a)Intensity of X-ray emission spectra plotted against energy in volts for certain ght metals ( from H. M. O'Bryan h. w. B, Skinner(1934), Phys. Rev. 45, 379 (b)Theoretical form of bands long as the transition was to the Lnr state(of p-symmetry)so that no selection rule prohibited the transition from the s-like states at the bottom of the band. On the other hand, what was observed as as in figure la. The sharp cut-off at high energies was in fact very marked, as was its broadening at high temperatures pre dicted by Fermi-Dirac statistics, but the low energy limit showed a marked tail In a paperd published in 1934, Jones, Skinner and I put forward the explanati of the fact that the term e/r1 did not destroy the sharp cut-off, but did affect the low-energy limit: an electron excited just above the Fermi energy(by an energy AE)and could interact (collide)with an electron just below it, so that both changed their states, by a kind of Auger effect. but the number of electrons with which it could do this was proportional to AE, so the lifetime of such an excited electron was long, varying(as we found)as 1/(AE)2. This tended to infinity as AE became small, so the Fermi energy was sharp, even when electron-electron interaction was Lken into account. On the other hand, a ',in the Fermi distribution near the bottom of the band could be filled by a process in which any electron with above it moved down into it, giving up its energy to another electron. Thus the lifetime would be short, and the electron's energy according to the uncertainty principle would be weakly defined, leading to the observed tail There are two comments that I should like to make on this. The first is that Sommerfeld's prediction of a linear electronic specific heat, and equally Jones' theory of alloys, really did imply that the idea of a sharp Fermi energy was some thing that corresponded to physical reality and not just a consequence of neglecting the interaction between electrons. But it needed the visual evidence provided by Skinners work to make me(at any rate)see that there was something here that we really had to explain. The second is that we failed to go on and show that the Fermi surface was a real concept. This awaited the work of Landau(e)(1956), and its exper nental determination(for copper, @3) by Pippard in 1957)and the development of the de Haas-van Alphen effect for the purpose, mainly by Shoenberg, t together f An excellent account of experimental methods of measuring the Fermi surface is give by N. w. Ashcroft N. D. Mermin, Solid state physics, (New York: Holt, Rinehart Winston, 1976),p,263-281
Memories of early days in solid state physi orld War ll. None- ploration of its form through this same effect starting before extensive e heless, we often implicitly assumed it. For instance, in bristol my research student Baber(a) showed in 1937 that collisions between electrons, all in states within an energy ca kT of the Fermi surface, yielded a term in the resistivity proportional to T2; the proof assumed that the wavenumber k near the Fermi energy was a quantity with physical reality, and this was equivalent to assuming the existence of the Fermi surface. Peierls's memorandum shows that this result was anticipated by landau Interaction between electrons plays an essential role in our understanding of ferromagnetism. This was of course first shown by Heisenberg6) in his paper of 1928, which was essentially a theory of a non-metallic ferromagnetic material hich ascribed ferromagnetism to between two atoms. In Bristol, in the period 1933-8, our interest in metals made us start from the Pauli theory of the paramagnetism of a metal; here the electrons excited above the Fermi energy, of which the number per unit volume was N(EF)kT per unit volume, each contributed pB2/ kt to the paramagnetism, giving a total susceptibility x equal to N(EF)B. Here N(E)is the one-electron density of states b the Bohr magneton and Ef the Fe ergy. In Bristol, influenced by the experimental work of Potter and Sucksmith, I put forward in 1935 a model6) for the transition metals in which a narrow d-band overlaps a wide s band, as in figure 2 so that the density of states at the Fermi energy could be large, and in ferromagnets the saturation moment a non-integral multiple of the Bohr magneton. This was supported by results already existing on the effect on the paramagnetism of palla dium of alloying it with certain metals, such as silver with one extra electron which could be expected to displace the Fermi energy in figure 2 to the right, thus of Bohr B N(Er)and x. Ferromagnetism, and particularly the non-integral number magnetons per atom shown by nickel, cobalt and iron, was in our thinking the result of a 'Weiss molecular field 'which in nickel and cobalt, at any rate, polarized the spins of as many d-electrons as possible in one direction. The Weis field arose because two electrons of which the spins pointed in the same direction must have an antisymmetrical orbital wavefunction, so that the probability that two electrons approached within a distance rr2 of each other tended to zero for small les of r12. This idea goes back to Bloch's paper of 1929. This meant a decrease in the energy contributed by the repulsion e /r12 between each pair of electrons with parallel spins. f Stoner(B)in 1938 published the first of a series of papers using this model, and developing its consequences in detail, which came to be called the Stoner model t His obituary notice published by the Royal Society says that this t blocham in 1929 first saw that exchange correlations (as distinct from correlations of ntiparallel electrons) would enhance paramagnetism, and should give ferromagnetism fo a very extended lattice. Wigner pointed out that this was not likely to occur for nearly free electrons(see for instance Mott Jones(%), p. 141, and Seitz(o, p 602). The use of the equation for the susceptibility X=X/(1-X01) th I an exchange term, is due to the post-war work of Anderson and Hubbard t See note on Stoner's work at the end of this article