By Vladimir USTINOV, RAS Corresponding Member, Director of the Institute of Physics of Metals, RAS Ural Branch; Vladimir STARTSEV, Dr. Sc. (Phys. & Math.), Chief Researcher of the same Institute
The Institute of Physics of Metals (Ural Branch of the Russian Academy of Sciences), among other research centers, made good headway in refining a wide range of substances...
All that became possible owing to the advanced chemical and physical techniques of high- degree purification, of metals too. And so metallic monocrystals were obtained containing but 10 -5 10 -7 percent impurities. When these crystals were cooled from room temperature to that of liquid helium (4.2 K), the free-path length (truck) of conduction electrons in them attained several millimeters. That is to say, the electrons behaved like those in vacuum: without colliding, they could cover distances comparable with the dimensions of a monocrystal. And thus in a sample of ultra-pure tungsten crystals prepared for the purpose electric resistance falls dramatically to a 150,000th fraction of the usual value, while the free path of electrons becomes 6 mm. This means that should such a crystal be placed in an electric field, its electrons will be moving freely from contact to contact.
Now, a magnetic field gives rise to electron paths (tracks) in metallic crystals. The form of these paths depends on the Fermi surface(*) geometry of a particular metal, while their dimensions are a function of the magnitude and direction of the magnetic field. But in contrast to free (unbound) electrons in vacuum tubes (in TV-sets, oscillographs and the like) where, because of the electrostatic Coulomb repulsion, their concentration cannot be brought higher than 1010 e/cm 3 , in metals such concentration is up to 1022 e/cm 3 . For this reason we can expect rather strong electronic effects which someday can be used in elements of cryogenic electrotechnical devices.
Thus in a monocrystal of ultra-pure tungsten cooled to the liquid helium temperature, within a 150 kE magnetic field, electric resistance soars 30,000,000-fold, a value close to that of semiconductor materials; this phenomenon may help us in designing sensors for magnetic field measurements under low temperatures.
Or let us take the static skin effect when under the conditions of low temperatures an electric current in a metal conductor is concentrated in its subsurface layer about Larmor radius(*) thick. We could see that by experiments which our Institute carried out on
* Fermi surface-constant-energy surface in a pulsed space; this surface separates free (unbound) electrons from those fixed (bound). Its form is determined by a metal's crystallographic symmetry and the number of valence electrons.- Auth.
* Larmor radius-a radius of conductivity electron orbit in a constant homogeneous magnetic field.- Auth.
single crystals of tungsten. We took two samples in the form of bars with a cross section of 3 mm and measured their reluctance (magnetic resistance). One had the reluctance factor at room and helium temperatures (factor p273.2K/p4.2K) equal only to 1,000, i.e. the metal was "dirty" with the free path of electrons 0.04 mm long. (The above reluctance factor, let us add, is a measure of metals' "electric purity".) Well, with the other the corresponding factor was as much as 100,000, and the free path of conductivity electrons in it was up 100-fold. So, in the second case we had ultra-pure tungsten. Next, we cut out the core in both samples to diminish their cross section and determined electrical resistance. It rose in the "dirty" sample, for in it the free path length of electrons is shorter than its cross section, and so the electrons dispersed within the crystal.
But it is quite the reverse with the ultra-pure sample. Its resistance did not increase with a decrease of its cross section-on the contrary, it even fell. The point is that in metals with closed Fermi surfaces and the equal numbers of conduction electrons and holes
(tungsten belongs to this class of metals), electrons move along closed orbits and their mean velocity in the conductor is equal to zero. Therefore their role is insignificant in the conduction process. Implicated in the charge transfer are electrons in the subsurface layer, about Larmor radius thick, and these electrons interact with the conductor's surface. Should there be a cavity within the conductor, there will also be an inner surface drawing an additional current. That is why a cored (hollow) conductor has higher resistance than a solid one.
The subsurface electric current density in sufficiently strong magnetic fields may be 10- 10 4 times as high as a corresponding volumetric indicator. Say, in a field equal to 150 kE of a tungsten crystal with the p273.2K/p4.2K factor = 100,000 electric current is concentrated in the subsurface layer about 0.5 x 10 -3 mm thick, and the density of this current is close to 10 5 A/cm 2 , while in the crystal's core it is not above 10 2 A/cm 2 . But if we add impurities to the crystal or raise its temperature, such effects will disappear, and the metal will behave in an orthodox fashion.
Since at low temperatures the heat transfer in a metal is effected mostly by conduction electrons, a similar phenomenon is also observed in heat conduction. The joint experiments carried out by our Institute and the Physics Institute of the Daghestan Research Center of the RAS have shown this: at low temperatures in ultra-pure metals with the equal numbers of electrons and holes we detect a thermal analogue of the static skin effect when the heat flow is forced into the conductor's subsurface layer.
Even not so long ago it was commonly accepted in physics of metals that nonlinear phenomena within an electric field are impossible in metals due to the high density of conduction electrons. Yet this view had to be revised in the 1980s and 1990s. Several research teams in Russia and former Soviet republics now within the Community of Independent States (namely, at the Moscow Electrotechnical Institute, the Kharkov Physicotechnical Institute of Low Temperatures, Kharkov State University, RAS Institute of Solid Physics, the Sukhumi Physicotechnical Institute and our Institute too), working with pure metals, could watch nonlinear effects in currents- rectifications, electric current filaments(*) and electric self-excited oscillations in metals under the conditions of magnetic breakdown. Besides, they observed the phenomenon of thermal-electric instability, i.e. the formation of a high-intensity electric field within the conductor. They detected electric current turbulence in thin metal specimens as well as SHF oscillations generated with the excitation of the metal electronic system by pulsed current. This means that under certain conditions the fundamental law of electrical engineering-Ohm's law (current directly proportional to voltage)
* Current filament-a filament in which high-density current flows.- Ed.
may not hold for a variety of causes. One is due to the high current density in the subsurface layer under the static skin effect.
In ordinary metals electrical resistance is of two components: 1) residual resistance caused by electron scattering on impurities and other defects of the crystal lattice, and 2) electron background contribution on account of electron scattering on thermal oscillations of a crystal's ions. However, the situation is different at sufficiently low temperatures in ultra-pure metals. Our physicists have detected and studied a new mechanism of electron scattering- that of "electron-phonon(*)-surface". It operates under the dimensional effect conditions when the electron free-path length is larger than a specimen's cross section, which results in a significant contribution of a metal's electrical resistance. In this case the mechanism prevails over the above-listed ordinary components of a conductor's resistance.
Now the physical meaning of the "electron-phonon-surface" mechanism consists in the following: in very pure metallic crystals the collisions of electrons with phonons lead to electron scattering on a crystal's inner surface, and this ultimately accounts for an additional temperature-dependent "dimensional contribution".
Subsequently a similar phenomenon was discovered in metals-both in elementary (copper, silver, gold, aluminum) and in transition (molybdenum, rhenium, ruthenium, osmium) high- purity metals. The works carried out by our people have stimulated an analogous search in scientific centers of the former Soviet republics ("the near abroad" so-called) and other countries, including the Experimental Physics Institute of Lausanne University (Switzerland), Exter University (Britain) and elsewhere.
Yet another uncommon property: in ultra-pure metals conduction electrons may be reflected from a crystal's inner surface at a fairly good mirror reflection factor, which may be up to 0.8. Whereas formerly it was believed that the reflection of conduction electrons from a crystal's inner surface could only be diffuse (because the de Broglie wavelength of an electron is comparable to interatomic distances), the measurements of electrical resistance of ultra-pure metallic monocrystals, depending on their cross sections at T=4.2K, rebutted such ideas about the interaction of electrons with the crystal surface. More than that, different crystallographic surfaces reflect electrons differently.
As said above, in a magnetic field of metallic crystals the configuration of electron paths is determined by the form of the Fermi surface and a metal's compensation. But in ultra-pure samples the electron free-path length may exceed a sample's dimensions, and thus electric charges, heat as well as ultrasonic and electromagnetic excitations may be transferred from one surface to the opposite one exactly along these paths. So it might be possible to control the flow of conduction electrons in metallic crystals and alter their paths.
The point is that the electronic properties of an ultra-pure metal at low temperatures largely depend on whether closed or open paths are materialized in it. For instance, in the case of closed paths an intense magnetic field gives rise to a "localized state": an electron moves along a closed path within a plane normal to the magnetic field. Thereby the magnetic resistance of metal increases hundreds of thousands and even millions of times over with an increase of a magnetic field. But if an electron moves along an open path, a "current state" phenomenon takes place when resistance changes insignificantly. But how to pass from one state to the other and change
* Phonon-a quasi-particle representing a quantum of elastic vibrations of the medwm.-Ed.
respectively the configuration of electronic paths, from the closed to the open and vice versa?
This can be done in two ways at least-either by magnetic or temperature (phonon) breakdown. In the former case the rearrangement of electron paths occurs by dint of an electron's quantum tunneling from one orbit to another in a sufficiently strong magnetic field. And in the latter case such transition is effected through an electron's collisions with a low- energy phonon, though with a wave vector surpassing the minimum distance between separate closed sheets of the Fermi surface. But in either case variation in the electron path configuration is accompanied by strong macroscopic effects.
By now the focus of research is on objects other than pure metals-say, on manganites(*) with an immense magnetoresistance effect, or on multilayer compounds, the superlattices. However, there may be a revival of interest in the electronic properties of
* Manganite-a mineral of the subclass ofhydroxides.-Ed.
ultra-pure metals with the development of methods for obtaining superstrong magnetic fields.
The first studies of electric resistance of insufficiently pure metals in relatively weak magnetic fields, with the free-path length of electrons far shorter than the Larmor radius of their orbit, showed the resistance of all the specimens under study to increase in proportion to the square of the magnetic field value.
Late in the 1920s Academician Pyotr Kapitsa developed a method of obtaining strong magnetic fields with intensity of up to 300 kE. The magnetic resistance of a large group of metals he measured in such fields showed it to vary not with the square of the magnetic field value, but proportionally with its first degree; such is the substance of Kapitsa's law. No explicit explanation of this phenomenon has been suggested thus far.
Now, with the development of methods for obtaining strong magnetic fields and ultra-pure metals, it has been found that metals exhibit substantial differences. In some of them the resistance increases in square-law fashion with a magnetic field increase, while in others it is saturated. Quantum oscillations of kinetic factors, i.e. the effect of magnetic breakdown, were found in such magnetic fields in a number of metals. Experiments in this area of magnetic fields have largely stimulated the "birth" fermiology, a discipline within physics of metals studying the electronic structure of this or that metal or restoring the Fermi surface form in it.
But what is going to happen in magnetic fields stronger than that? Say, if the Larmor radius value is comparable with atomic spacing? It has been estimated that for conduction electrons with small effective masses this condition is attainable in fields of magnetic intensity of 1 to 10 million oersteds. It is quite possible that new electronic effects are to show up. Metal may become an insulator or else a compensated metal may turn into a noncompensated one, for groups of electron carriers or holes with small effective masses will be the first to be excluded from charge transfer. In short, research in this area of superintense magnetic fields may spring quite a few surprises.
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