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Sizing up the Fermi Surface: Brian Pippard Speaks of Metals, Methods, and Songs

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Sizing up the Fermi Surface: Brian Pippard Speaks of Metals, Methods, and Songs PROFILES & PERSPECTIVES Sizing Up the Fermi Surface: Brian Pippard Speaks of Metals, Methods, and Songs tion about the dynamics of the electrons in the metals. The shape of the Fermi surface was not known in any metal at that time, but it had been conjectured and various calculations had been done. Then, I was absolutely delighted to find—when I did the calculations of the method—that the high-frequency resistance at the surface could be used as a way to gather straight- forward geometrical information about the surface. However, the skin effect only goes down to about ICH cm and the surface of a material can easily be damaged by cutting and polishing. So, one needed to study Sin­ gle crystals of, say, copper cut into thin plates (1 or 2 mm thick and about an inch in diameter) and one needed them to have very high purity and very smooth, dean, ! strain-free surfaces. I did not know how to proceed, but Morrel Cohen of the Institute for the Study i of Metals from Chicago was passing through Cambridge and I told him about this possibility. He was a very young staff member in Chicago in those days. I can't remember whether I had the distinct inten- tion that he should invite me to go to Sir Brian Pippard, a most distinguished alous skin effect* at microwave frequencies, Chicago but he thought I did and invited British physicist whose career has been devoted which is linked to the Fermi energy in differ- me to go where they had the techniques to to the Cavendish Laboratory at Cambridge ent crystal directions. We asked him to teil us do this. The Institute was very good about ^ University, agreed to meet with MRS Bulletin something about that year. it. Before I arrived they had grown a very at his home in Cambridge last fall. Sir Brian is large Single crystal of pure copper. It was a man whofollows his instincts without letting Would you say, Brian, that your time in about l'A in. in diameter and 6 in. long. Convention Interrupt his path. Research grants Chicago was really an application ofmetallur- They started chopping the sample and were virtually unknown mid-century, so out of gical skills to the physical problem that you their expert polisher went to work polish­ necessity he built his own research equipment had set for yourself on why skin-effect meas- ing it. When I arrived, the lab was set up, to pursue his work. Later, he put his efforts urements exposed geometrical results? which is jolly good if you only have a year. >• toward educational reform in Cambridge, hit- That is exactly right. I had realized the I suggested how they should do the cut­ ting a wall of indifference. year before, 1954 I think, that by doing ting. It was a question of getting the right While our agenda was to discuss physics measurements of the high-frequency skin set of orientations out of the given crystal. and Sir Brian's contributions to materials Sci­ effect on very pure metals with dean sur- They had diamond saws and that sort of ence, the surroundings reminded us that his faces, one could get geometrical informa- thing. They did it very nicely, indeed. scientific contributions are balanced by a love As it happened, I already had the appro- of music. A piano sat beside us, and a music *The anomalous skin effect method involves priate apparatus for doing the measure­ Stand served as a place to drape the micro- applying a high-frequency field to a very pure ments built in Cambridge and brought it phone to capture his words. Once, this engi- Single crystal of metal at very low temperatures. with me. I had no sooner begun working The field induces currents in the metal, which neering construct failed, causing the micro- tend to prevent penetration of the field into the with the new spedmens, however, when I phone and stand to tumblefrom the coffee table specimen, limiting it to a certain "skin depth." found that the apparatus was not working to the floor, reminding us that every path has At these low temperatures, the electron mean well. I scrapped it and got a new design side trails and pitfalls, but one does not dwell free path is much longer than the skin depth built in the Workshop of Chicago, which therefor long. and only those electrons that run nearly parallel took about three months. During those Sir Brian would rebut any Suggestion that to the surface and within the skin depth remain three months, I took the opportunity to he be termed a materials scientist, but his in the field long enough to receive appreciable write my book on thermodynamics, which energy from the field. The effective resistance experiences carry lessons for us nonetheless. under these conditions is a function of the I had been lecturing on at the undergradu- In 1956, he spent a period as a visiting profes- radius of curvature of the Fermi surface at those ate level for some years. sor at the Institute for the Study of Metals in points that refer to electrons moving parallel to The new apparatus was extremely good. Chicago and there he performed one ofthe key the surface; the anisotropy of the resistance for The design I had chosen was for measur- postwar experiments in solid-state physics, different crystallographic orientations can be ing the heat developed when centimeter- the determination of the shape of the Fermi used to test assumed modeis of the Fermi sur­ wavelength radiation feil on the specimen. surface in copper. He used as a tool the anom­ face and to determine its shape. I intended to do the measurements by SO MRS BULLETIN/AUGUST 1999 Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.58, on 27 Sep 2021 at 21:25:24, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms . https://doi.org/10.1557/S0883769400052908 PROFILES & PERSPECTIVES using a resistance thermometer. What I effect in bismuth. This effect had only been didn't realize was that the resistance ther­ found in bismuth. He put that aside and mometer would be very badly affected by turned to superconductivity. Shortly after the tiniest stray microwave field. the [Second World] War, Jules Marcus at Northwestern found the effect in cadmium, Didn't you also use a gas thermometer? which caused renewed interest. David, I started with the resistance thermome­ around 1950, began doing more measure­ ter, then switched to gas thermometers. ments on the deHaas-van Alphen effect. At the same time, Lars Onsager from Norway Going back to the 19th Century? was spending a year in Cambridge, study- Exactly, yes. And they worked very ing the deHaas-van Alphen effect. His short nicely, too. paper published in 1952 in Philosophical Magazine laid the foundation for interpret- It must have been an unusual experience for ing the deHaas-van Alphen effect in terms you to do your research by yourself. Other peo- of the geometry of the Fermi surface. ple prepared the samples, right, but you did all For the next two years or so, nobody received a telegram from David to say that the measurements and soforth. Whereas, when took his findings very seriously. When I the contact with the zone boundary does you returned to the Cavendish, you had the found that the skin-effect measurements not exist. He said it doesn't show up in the usual gaggle of research students? would give geometrical results, it certainly deHaas-van Alphen effect. I remarked in Yes, but in those happy days, each of the occurred to me: What if this is something my talk that I had this telegram, and indeed research students did his own thing. We of what Onsager is saying about geometry I hadn't found contacts directly, but had were all solo workers. In the days before I of Fermi surfaces? So, I went back to look inferred them from the fact that my Fermi went to Chicago, from '45 to '55, the only at his paper and found, my goodness, he's surface wouldn't fit into the Brillouin zone, help I had from research students was got something much more powerful. I which meant that the Fermi surface did cut when they helped by Controlling the tem- think that David Shoenberg probably had the Brillouin zone. My method was simply perature and taking down readings. realized this himself, but certainly when I not sensitive enough to get the shape at this The special thing about Chicago was pointed this out to him, it strengthened his critica] point. Onoe the crystallography was working Underground under the [base- motivation to make a serious attack on the worked out, everything went beautifully. ball] Stands. Some of the low-temperature deHaas-van Alphen effect as a means of work was conducted in a sort of basement determining Fermi surfaces. Your Fermi surface experiment depended on area, which was fine most of the year, but That takes us to 1954. "Why copper?" the anomalous skin effect. when the summer came on and the tem- you say. Well, because copper is an impor- I have been laughed at in a friendly way perature went to about 90°F and the tant metal! It was simple enough and one for calling it the anomalous skin effect. humidity to about 90%, it was extremely that was taken seriously. I had a research The reason I called it that is because Heinz unpleasant working there.
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