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1 Electronic Structure ant! Properties of Matter INTRODUCTION Electronic structure and the properties of matter is a vast topic that is at the heart of all condensed-matter physics. It might be described as the electronic quantum many-body problem and is concerned with the ways in which the effects of the Pauli exclusion principle and the Coulomb interactions between electrons conspire to produce the remarkable varieties of matter. During the last decade, concerted efforts were made to determine the most efficient means of incorporat- ing the effects of exchange and correlation into the basic description of solids and liquids, with the result that significant advances have occurred in our understanding of the electronic structure of large systems with perfect order, with various types of defects, and with disorder, including both liquid and amorphous states. This period has also seen great strides in our understanding of the surfaces of condensed matter and the properties of interfaces. In addition, our attention has turned to systems of unusual chemical character, quasi-one- or two-dimensional solids, for example, with physical properties often remarkably different from those of the higher symmetry three-dimensional systems that have so influenced the development of condensed-matter physics. These low-dimensional materials demonstrate the effects of electron-electron interactions in the most dramatic way. The resulting electronic order can manifest 39

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40 A DECADE OF CONDENSED-MATTER PHYSICS itself in magnetically ordered states, in superconducting states, or in charge-density waves associated with unusual spatial structures, in the fractionally quantized Hall effect, and in many other new phenomena. These systems clearly demonstrate that the synthesis, characteriza- tion, and analysis of new materials may be expected to continue to lead to discoveries of fundamental significance. ADVANCES IN ELECTRONIC STRUCTURE DETERMINATIONS For simple systems of relatively high symmetry it is now possible, with little more than the atomic number of an element as primary input, to account for their major ground-state properties, such as the lattice structure, lattice constant, bulk modulus, and density. No information peculiar to the condensed state is used at all. The basis of this advance is a progressive acceptance of the density-functional method for treating exchange and correlation in the electronic ground state. This method utilizes the existence of a certain functional of the electron density and its gradients, and the Coulomb interactions, and kinetic quantum energies as the basis for constructing the free energy of an electron system. Although the functional is determined only from properties of the uniform, interacting electron gas, it is widely used in cases for which the electron density is grossly inhomogeneous, such as in crystals (Chapter 2) and on surfaces (Chapters 5 and 71. With the use of appropriate spin-polarized function- als it is also possible to study magnetically ordered states (Chapter 41. Together with the development of methods for calculating electronic states the first-principles pseudopotential, linearized muffin-tin or- bital, and linearized augmented-plane-wave methods- the density functional method has been used to study ground-state properties of a wide range of disparate systems. Band-theoretic methods of this kind are impressively predictive. In the near future they are expected to be applied to more complex real-space structures, to ionic and partially ionic systems where difficulties in its application still remain, and to the technologically important problems of interfaces. More challenging yet is the physics of the excited states of such systems. Their properties are directly probed by powerful techniques such as angle-resolved photoemission or radiation (ultraviolet and x-ray) from synchrotron sources. With ordinary photoemission, the so-called angle-integrated or energy-resolved photoemission, radiation impinging on the surface of a sample excites electrons in its interior to higher energy bands. Some of the excited electrons then move to the surface and tunnel through it to the exterior, where they are detected.

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ELECTRONIC STRUCTURE AND PROPERTIES OF MATTER 41 If selected only according to their final energy, the electrons give information, under certain conditions, about the joint density of states of the energy bands from which they were originally excited. Under other conditions, the electrons can also give information about the surface itself, and even about surface overlayer atoms deliberately adsorbed onto it. With angle-resolved techniques, the emergent electrons are selected not only according to energy but also as to direction or wave vector. With this new information it is possible to map out the energy-band structure itself and not merely the joint density of states. The experi- mental results can then be directly compared with calculated energy bands, providing information on the electronic structure of a given material. It is also possible to map out rather detailed features of the bulk-energy-band structures, which previously were not available from more traditional probes (e.g., optical excitation and interband absorp- tion). This information, especially for higher bands, is nicely comple- mented by data obtained from brehmsstrahlung isochromat spectros- copy (often referred to as inverse photoemission). The band-theory density-functional methods can in principle be adapted and extended to excited states as well. This is an area of great current activity, where there is as yet no solution to such basic problems as obtaining the fundamental band gaps in crystalline semi- conductors accurately. In summary, it is clear that some aspects of electron structure in ordered systems are quite well understood, to the point where appli- cation of theory to materials exhibiting unusual properties (the high- temperature, superconducting A-15 compounds, for example) leads to further suggestions for exploiting the particular properties of interest. Other aspects, particularly involving the many-body problems of electronic excited states, are not understood and are currently the subject of much interest and controversy. MANY-ELECTRON EFFECTS The central task of those interested in electronic properties is to understand a problem involving an immense number (A 1023) of strongly interacting electrons. The historical approach to it was to begin by treating each electron as actually independent of its peers. Electron-electron interactions were not completely ignored but were treated in some average sense. It has been well known for many years that a large number of problems in condensed-matter physics require going considerably beyond this independent electron approximation. One such problem

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42 A DECADE OF CONDENSED-MA TTER PHYSICS that has received much attention during the past 10 years concerns the way in which an electron from the interacting-electron system can make a transition to a prepared, "deep," atomic state of one of the atoms. In doing so, the electron emits an x ray that can be detected. As well as giving information on the width of the band from which the electron fell, the x-ray intensity probes the ejects of electron-electron repulsion in the dense, interacting electron system. In particular, the edge structure, reflecting the onset of the radiation, is dramatically affected (the so-called x-ray edge problem). This problem has been treated using the extremely powerful re- normalization group techniques (see Chapter 3) in which short-wave- length degrees of freedom are systematically replaced by averages over successively larger length scales. This method, remarkable in its accu- racy and generality, involves extremely creative use of the computer. Another recent development in the study of many-electron effects is the use of statistical Monte Carlo methods to find accurate numerical solutions of the full many-body problem. These methods are in essence computer simulations of systems containing finite, but large, numbers of interacting particles. (The name comes from the use of random numbers that could be generated on a small scale by a roulette wheel but that are produced by complicated mathematical algorithms for research studies.) The applications of these methods have included obtaining the thermodynamic properties of condensed matter, such as the equation of state of solid and liquid phases. Recently these methods have been extended to quantum-mechanical problems and applied to liquid and solid 4He, considered as bosons interacting via realistic potentials. They have yielded excellent agreement with experiment for the equation of state and for the probability distribution of the distances between atoms in the liquid. Related methods have been applied to other systems, such as electrons in one dimension interact- ing with each other and with a lattice. This has made possible a rigorous study of phase transitions that takes into account the full quantum fluctuations present in one dimension and has revealed important differences from mean-field descriptions of the transitions. These developments have also led to Monte Carlo techniques for the determination of properties of fermion systems, which are difficult to calculate because of the antisymmetry of the wave function. QUANTIZED HALL EFFECT One of the most surprising recent developments in condensed-matter physics has been the discovery of a set of phenomena collectively

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ELECTRONIC STRUCTURE AND PROPERTIES OF MATTER 43 known as the quantized Hall effect. These phenomena are associated with two-dimensional electron systems, in a strong magnetic field and at low temperatures. In practice, the electron systems studied are semiconductor inversion layers, such as occur in a metal-oxide- semiconductor (silicon, for example) field-effect transistor (MOS-FET) or at a GaAs-GaAlAs heterojunction. When a current-carrying wire is placed in a steady magnetic field (Figure 1.1), a voltage Vet is developed across the wire in direct proportion to the current density. This well-known phenomenon is the Hall effect, and the voltage VH across the wire is known as the Hall voltage. Classically, the Hall resistance RH, defined as the ratio of VH to the current I, is expected to vary linearly with the applied magnetic field and inversely with the carrier concentration in the sample. For two-dimensional electron systems at very low temperatures, however, the Hall resistance was found to exhibit a series of plateaus, with varying carrier concentration or magnetic field, and the value of Hall conductance (1lRH) on these plateaus was found to be quantized in precise integer multiples of the fundamental unit each, where e is the electron charge and h is Planck's constant. (The resistance hoer has the B ~ _ /~/ / Z~ VH NEWS HALL RESISTANCE VH W EH RESISTIVITY =E =VW PXX I I L FIGURE 1.1 Schematic representation of a Hall experiment. The magnetic field B is perpendicular to the plane of the specimen and to the current 1. The Hall resistance R', and the resistivity pit ~ are determined through the equations shown in the figure. [Courtesy of H. L. Stormer, AT&T Bell Laboratories, Murray Hill, New Jersey; adapted from K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).]

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12 10 ~8 - x lo: 6 41 2 01 - ---h/2e2 \,- RH V_h/~2 44 A DECADE OF CONDENSED-MA TTER PHYSICS value of 25,812.8 ohms.) Moreover, when a Hall plateau occurs, the voltage drop parallel to the current is essentially found to vanish, so that the current appears to flow through the sample with no observable dissipation (see Figure 1.21. The surprising precision with which e2lh can be measured in this way may lead to a new, practical, secondary resistance standard and to an improvement in the determination of the fundamental constants. The precision of the effect (now established to about 2 parts in 108) is observed in spite of considerable variations in sample properties, and this has led theorists to propose fundamental explanations of the effect. The discovery of the quantized Hall effect was honored by the award of the Nobel Prize in 1985. In 1982, Hall conductance plateaus at certain simplefractions of the quantum e2/h were discovered in GaAs heterojunctions of exception- ally high mobility, in magnetic fields so high that the first magnetic quantum level is fractionally occupied. These results are perhaps even more remarkable and surprising than the original observations of integral, quantized Hall plateaus. Although the integral steps had been explained in terms of the quantum states of individual electrons, ex _ , . - - --h/4e2 R X I- -h/6e2 Si - Si O2 B= 1 89 kG - T=1.5 K --h/8e2 _~- il~l - ~1 ~, 10 20 30 GATE VOLTAGE V9 ( V ) FIGURE 1.2 The quantized Hall effect in a Si MOS-FET in which the electron density is varied by a gate voltage V,. Instead of being a smooth curve, the Hall resistance RH develops plateaus having values hlie~, where i is an integer and the resistance R.\ of the specimen drops to low values.

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ELECTRONIC STRUCTURE AND PROPERTIES OF MA TTER 45 planation of the new fractionally quantized Hall effect has required the hypothesis of a radically new type of quantum liquid state for the col- lective motion of electrons in a magnetic field. Many aspects of these systems of electrons in strong magnetic fields are still poorly under- stood, and this will certainly be an active area of research in the 1980s. ELECTRON-HOLE DROPLETS The conductivity of semiconductors arises from thermal excitation of electrons, or holes, from the bands or bound impurity levels that are normally filled at low or near-zero temperatures. However, by the use of intense laser radiation, immense numbers of electrons can be excited from lower-lying states, leaving behind the absent electrons (i.e., the hole states). The resulting nonequilibrium populations of electrons and holes can be formed quickly. Although they are initially dispersed, the electrons and holes rapidly partially equilibrate into a new state that consists of electron-hole droplets (Figure 1.31. The experimental signature of their existence is that, when the electrons do eventually return to their lowest-energy states, the distribution of radiation emitted is characteristic of the condensed Fermi seas, representing the arrangement of excited electrons and holes. During the last few years, the formation of electronlike droplets and their essential characteristics have become far better understood. It is known that band structure, many-electron effects, and specifically correlation effects also enter in an essential way so that this phenomenon has led to a substantially improved understanding of interacting electron systems. ELECTRONICALLY ORDERED STATES Historically, the paradigm of an electronically ordered system is a substance exhibiting one of the forms of magnetic order. The later discovery of superconductivity is another dramatic form of electronic order: these topics are discussed in Chapters 4 and 8, respectively. Both are now being viewed more broadly, especially in terms of their bearing on other manifestations of electronic order, some of which have been discovered quite recently. Important to the discovery of these new forms of order has been the fabrication, characterization, and analysis of new materials, especially those that exhibit different states of order as temperature is altered (see Appendix C). In the context of ordered electron states and the connection with atomic arrangement, the dimensionality of the system, once again, plays a crucial role in the physics. Thus, we now find quasi-one

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46 A DECADE OF CONDENSED-MATTER PHYSICS FIGURE 1.3 Photograph of the 1.75-~m recombination luminescence emanating from a strain-confined drop of electron-hole liquid. The 4-mm-diameter disk of ultrapure Ge is pressed along ( I 10) at the top with a nylon screw creating a stress maximum inside the crystal. The liquid is a degenerate sea of electrons and holes with a density of ~10'7 cm-3. (Courtesy of Carson Jeffries' University of California, Berkeley.) dimensional materials whose constituent atoms are not drawn from the metals but that nevertheless do behave, quite remarkably, as metals. A striking example is polyacetylene, a quasi-one-dimensional system that is formed by catalytic polymerization of acetylene gas. It is apparently the first organic polymer to be made to conduct and joins materials such as tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) as examples of linear metals (see Chapter 101.

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ELECTRONIC STRUCTURE AND PROPERTIES OF MATTER 47 A particularly interesting category of materials is the class of layered compounds, examples of which are TaS2, TaSe2, and NbSe2. The name comes from their tendency to group atoms in planar, sandwich arrays. Most compounds with relative chemical simplicity crystallize into regular and often relatively simple structures. In some, however (certain transition-metal chalcogenides), and especially at low temper- atures, structural instabilities are observed to result from the interplay of the interactions among electrons and the interactions among the electrons and the ions of the material. The ensuing states may then display modulations in charge density, modulations in spin density, or even modulations in the ion density. What is especially fascinating is that the resulting systems are no longer truly periodic. In the two- dimensional or layered compounds, experiments have revealed the curious feature that the period of these modulations can actually be incommensurate with the fundamental repeat distance of the original underlying lattice (see Figure 1.41. The energy balance in these systems is such that relatively modest changes in temperature can cause changes in the states of order. This is also true in another interesting class of materials formed by inter- posing (or intercalating) atoms of certain substances between the planes of graphite crystals. An example is graphite intercalated with cesium. It is possible to stage such materials, i.e., to interpose a fixed number of layers of the host system between consecutive intercalate planes (see Figure 1.5), and the resulting systems exhibit a variety of interesting phase transitions. This competition among possible orderings also exists in linear systems as well: thus, for example, (SN)X has been observed to be superconducting. DISORDERED SYSTEMS The study of electronic states in systems that do not have long-range order has become of increasing importance in the understanding of condensed matter. The most striking phenomenon in disordered sys- tems is the localization of the true quantum-mechanical eigenstates. Localization by disorder alone, the Anderson transition, occurs when fluctuations in the potential associated with the disorder exceed a particular value. Close to, but below, this value, it is believed that there exists a mobility edge, at which energy the states change character from localized to delocalized. The various manifestations of disorder are being probed experimen- tally in a variety of systems by photoemission, photoluminescence,

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48 A DECADE OF CONDENSED-MATTER PHYSICS (b)

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ELECTRONIC STR UCTURE AND PROPERTIES OF MA TTER 49 (C) FIGURE 1.4 X-ray diffraction patterns of charge-density wave-bearing layered com pounds. (a) lT-TaSe~ just above the commensurate-incommensurate phase transition at 473 K, in the incommensurate state. (b) ~aO superlattice of lT-TaSe2 in the commensurate charge-density wave state at room temperature. (c) 4Hb-TaSe2 at room temperature in the commensurate state, producing the 13aO superlattice. (Courtesy of F. J. DiSalvo, AT&T Bell Laboratories, Murray Hill, New Jersey.) optical response, soft-x-ray emission, phonon echo, extended x-ray absorption fine structure, and many other techniques. The metal- insulator transition (the precipitous drop in conductivity itself) has been unambiguously reported, at low temperatures, in doped semicon- ductor systems. Furthermore, the behavior of the conductivity near the transition is related to critical phenomena in phase transitions. There is

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50 A DECADE OF CONDENSED-MATTER PHYSICS a growing realization of the importance of long-range Coulomb inter- actions in disordered as well as ordered systems. They can contribute to a transition from an insulating to metallic state or vice versa. In contrast to Anderson localization, in the picture associated with the Mott transition, the view is that the electrons in the system can only be cooperatively mobile to the extent that the Coulomb interac- tions, included through screening, act to reduce the possibility of cooperative recombination with the charge centers from which they originate. Accordingly, as the mean-charge-center separation in- creases, the electronic bandwidths do not shrink continuously to zero but instead vanish suddenly at a certain critical density. If the system contains more than one electron per atom, then two or more Hubbard bands can be made to overlap as the lattice constant decreases. The effects may be particularly subtle and interesting in disordered sys- tems, and the interplay between correlation effects and the effects of disorder itself is an emerging area of research. One aspect of the metal-insulator transition where there has been much theoretical and experimental progress in the last few years has been the study of localization phenomena in one- and two-dimensional systems-in particular the exploration of a class of phenomena known as weak localization. For example, it has been proposed that for a :~ ::::: 0 ~ 25A = __ [.~ ~.~ - : . ~ ~1 . JO N,j ~'$ `ri ~\~F~ -, ' ~"' "''"'s at'' `'~-,-"'"'In' ON ~ FIGURE 1.5 High-resolution electron micrograph showing the existence of mixed staging in ferric chloride graphite intercalate. Clearly shown are regions with two and three layers of graphite between the layers of Feces. (Courtesy of John M. Thomas and coworkers, University of Cambridge. )

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ELECTRONIC STRUCTURE AND PROPERTIES OF MATTER 51 sufficiently thin wire at very low temperatures the resistance of the wire will no longer depend linearly on the length of the system. (In practice, to observe this departure from common behavior it is necessary to fabricate wires with diameters slog A.) Similarly, the electrical resistance of a two-dimensional system is expected to increase logarithmically as the temperature is lowered. The theoretical methods used in making these predictions have included renormaliza- tion group techniques and scaling ideas similar to those used in the theory of critical phenomena (Chapter 31. Interpretation of weak localization experiments is complicated by subtle effects of electron-electron interactions and of the presence of impurities with local magnetic moments or with strong spin-orbit coupling; moreover, the effects are small in practice and require precise low-temperature measurements. Nevertheless, the effects have been observed, and the dependence on temperature, on magnetic field, and on other parameters has been found to follow theoretical predic- tions rather closely in many cases. Flux quantization, which is ex- pected in superconducting systems, has also been predicted and observed in normal metallic systems (Figure 1.61. These observations provide convincing evidence that the physical basis underlying the theory of localization is correct. There are also important questions connected with the general nature of electron states in systems with weaker disorder. These can differ considerably from electron states in their crystalline counter- parts. A striking example is Si (or Gel, which in crystalline form is a semiconductor but as a liquid is a metal. In the area of liquid metals and their alloys new efforts continue to focus on understanding electron transport, atomic transport, structure, and thermodynamics. Here the electrons may not be localized, but these systems are strong scatterers. The difficulties in understanding their static and frequency-dependent conductivities lies in our incomplete knowledge of the microscopic theory of dense classical liquids, which include the liquid metals (see Chapter 91. Some liquid binary alloys exhibit transport coefficients that actually become singular as a function of the relative concentration of the two species. Here the balance between electron-electron interac- tions and disorder can be altered by the alloying process. Conse- quently, the tendency toward localization can be increased and con- trolled by the experimentalist. The range of the metallic state can be extended considerably both to low densities and to high temperatures. The resulting systems consti- tute forms of matter that are of intrinsic interest, because of both their similarity to dense, strongly coupled plasmas and their proximity to two quite fundamental phase transitions (liquid-vapor and metal

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52 A DECADE OF CONDENSED-MATTER PHYSICS _ . . . .;_ ~ .....~..~: i. a. in... I i. ~, .. s .~ iS. .> ~ it. ~ :. ~ iS i.S ... :~ . . .. ~ . ~ at. . ..... ! . . i i . i . -.. ,..,, . FIGURE 1.6 A gold metal ring of diameter approximately 3500 A. The width of the line is approximately 400 A. These rings are used to search for flux quanta of the kind seen in superconducting rings. The gold is not superconducting. The large darker area to which the lines attach are the pads that provide connection to the external world. The dot is used for calibration. (Courtesy of IBM Thomas J. Watson Research Center.) insulator). On the vapor side, the interactions are largely short ranged; on the metal side, they are screened, long-ranged interactions. During the transitions, the character of the interactions changes, an unusual behavior in the context of the standard theories of critical phenomena and associated transport. Though the effects are extremely interesting and at the core of some fundamental issues, the experimental situation presents serious challenges because of the extremely high critical temperature of most metallic systems. The conduction electrons play an important role in disordered metals, as they do in metallic crystals. They contribute not only to transport phenomena but, through screening, to the actual forces acting between the ions themselves. The forces are expressible in terms of two (and often higher) center potentials, which in turn

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ELECTRON/C STRUCTURk AND PROPERTIES OF MA77ER 53 determine the structure of the disordered metal. These interactions differ qualitatively from those in insulating systems. Because they vary with electron density, they can again be altered by alloying. This effect may be of some consequence in resolving the issue of why some metal- lic mixtures can be made to form metallic glasses, and why some can not. MIXED MEDIA It is now possible to fabricate materials that are mixtures of a number of constituents (either insulators or metals) and in which the charac- teristic length scales may be as small as 50 A. Such heterogeneous, microcondensed forms of matter are particularly interesting because one can tailor desired bulk properties by altering the constituents, their size distributions, or their relative concentrations. As one example, the wavelength of ordinary light is a few thousand angstroms and generally exceeds such scales of inhomogeneity. But, so far as the optical properties of these systems are concerned, they appear to behave as continua, and now one can tune the basic dielectric properties in a way not often possible with homogeneous systems. It should be noted that mixed or granular media, or composites, often display a great deal of order at the microscopic scale yet should still be properly regarded as disordered systems. Depending on the disposition of the matter in these systems, the topology of the arrangements of the constituents, and their detailed connectivity, it is possible to find percolative and critical behavior characteristic of the localization problem (impurities in semiconductors, for instance) discussed above. Some small metal particle systems show clear evidence of a superconducting transition persisting in the metal for particle sizes as o small as 100 A or smaller. CONDENSED MATTER AT HIGH PRESSURE By application of pressure to a sample, we change its density and hence its physical properties, often quite dramatically. However, condensed matter is generally considered quite incompressible, and to achieve even modest fractional changes in density has often required pressures of thousands or even tens of thousands of atmospheres. During the past few years, notable advances in high-pressure physics have occurred. Though so-called dynamic techniques (shock-wave methods) have also developed, the advances in static high-pressure physics have centered largely on the active use of the diamond anvil

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54 A DECADE OF CONDENSED-MATTER PHYSICS cell (see Figure 1.71. With these devices it is possible to develop pressures in excess of 1 Mbar. More importantly, such pressures can change by a significant factor the average volume available to an atom or molecule in a solid or liquid. Minerals may be exposed to pressure ranges reminiscent of their original environment in the Earth's interior. This is having an impact on geophysics and planetary physics, as well as on materials science and solid-state chemistry. Though electrical and even thermal measurements are now possible in these devices, most of the probes used to detect changes induced in samples have been either optical or x ray in origin. They exploit the transparency of the diamond. It is possible to utilize diamond-cell devices in conjunc- tion with radiation environments that are unusual in their degree of intensity, polarization, time structure, or wavelength (synchrotron radiation and pulsed lasers are examples of these). One of the most striking uses of diamond cells has been the transformation of insulators into metals. This most fundamental of all phase transitions has been observed in molecular crystals, in ionic crystals, in transition-metal oxides, and in mixed valence compounds. For example, iodine has traditionally been regarded as an insulator, but it appears to be a metal at pressures in excess of 200 kbar. Above l Mbar the noble gas xenon should also become a metal, and at about 2 Mbar, even hydrogen should become metallic. Useful pressures much over 1 Mbar have not yet been achieved statically, however, but hydrogen has been compressed to about 7 times its normal low {a) TRANSLATING DIAMOND DIAMOND ANVILS MOUNT PLATE- DIAMOND MOUNT HEMISPH E R E ~O ...... J ~ 1. K__ ~---r-~~~d PLATES ~- YOKE ~ ~ i BELLEVILLE SPRING WASHERS ~ _ 1'' ' '1 ADJUSTING SCREWS , 1 tPRESSURE PLATE YOKE BEARING (a ANVI LS /~6ASKET HEMISPHERE - ,, ~ FIGURE 1.7 An ultrahigh-pressure diamond cell. The complete cutaway cross section (a) shows the essential components including the anvil supports, alignments design, Iever-arm assembly, and spring-washer loading system. The detail (b) shows an enlargement of the opposed diamond anvil configuration with a metal gasket confining the sample. The cell was developed at the National Bureau of Standards. (Courtesy of G. Piermarini, National Bureau of Standards, Gaithersburg. Maryland.)

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ELECTRONIC STR UCTURE AND PROPERTIES OF MA TTER 55 temperature solid density, and its vibrational modes have been studied using Raman-scattering techniques. Though static methods are developing rapidly, advances in instru- mentation and concept have also been reported in shock-wave physics. With these techniques a substance can be brought into high- temperature, high-pressure regions of its phase diagram that are inaccessible by any other means. These experiments yield information such as the compressibility, plasticity, phase stability, and optical properties of condensed matter pertinent to planetary and even stellar physics. OPPORTUNITIES Further simplifications in the pseudopotential and other band- theoretic techniques employed in the calculation of the electronic structure of perfect metallic crystals can be hoped for. Their applica- tion to defect- or disorder-related problems, however, will certainly hinge on the availability of substantially increased computational facilities. In view of the importance of this work to technology, further investment in it is certainly warranted. It is expected that the density-functional method will be used widely in the future in the theoretical study of the electronic properties of crystalline solids and in cases, such as surfaces and crystalline defects, where the electron density is strongly inhomogeneous. Considerable effort will be devoted to trying to understand why this method, in its so-called local-approximation, works as well as it does, and why it occasionally fails. Despite the considerable success of the preceding methods for the calculation of the ground-state, and even the excited-state electronic properties of metals, no comparably simple and accurate methods exist for the calculation of the excited electronic states of semiconductors and insulators, in which these states are separated from the ground state by an energy gap. These excited states are needed in the calculation of the response of such materials to time-dependent per- turbations, such as externally applied electromagnetic fields. In view of the importance of being able to calculate such responses for the interpretation of data obtained by a variety of experimental probes, we can expect attention to be directed to the development of methods that will yield the excited states of semiconductors and insulators accu- rately. High-pressure physics appears to be entering an exciting and pro- ductive phase and is a good example of a strong feedback mechanism

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56 A DECADE OF CONDENSED-MA TTER PH YSICS operating between science and technology. High pressure is expected to play a prominent role in elucidating the physics of the metal- insulator transition, both in ordered and disordered systems. It will certainly be used to address the questions associated with s-d and fed transitions in the heavy elements and also to aid in unraveling the puzzles of the interesting classes of intermediate-valence compounds and heavy-fermion systems. It may even shed light on the nature of the ground state of the light alkali metals, which have been thought of as reasonably well understood but continue to behave in ways (particu- larly at low temperatures) that are not easily explained. More gener- ally, static high-pressure methods are expected to play an ever- increasing role in determining the electronic structure of new materials. in complex materials, in semiconductors, in artificial superlattice systems, in amorphous solids, in glasses both insulating and metallic, and in polymers, liquid crystals, and simple fluids and their mixtures. Because of their continuing technological importance, disordered materials, including metallic glasses and amorphous semiconductors, are expected to receive growing experimental and theoretical attention in the future. Much has been learned in the past decade about the existence of new kinds of states, the so-called tunneling states, in highly disordered matter. However, much is still to be understood about the nature of the elementary excitations in glasses, especially at low temperatures. Glassy metals can be formed by rapid cooling techniques, during which they may possibly preserve certain aspects of the structure and dynamics of the liquid from which they were formed. Accordingly, such systems offer the prospect of studying the dynamics of disorder in a manner that is not possible when the system acts as a classical liquid. The glass transition (in insulating and metallic glasses) is not well understood, and further activity in this area, both experi- mental and theoretical, is expected. Crucial to this endeavor is a deeper understanding of the systematics of bonding in condensed matter within a framework going considerably beyond the current picture. Though there has been a rejuvenation of mean-field theories used to describe the response properties of mixed media, they are still not well understood in detail. In particular, the far-infrared response of metal- particle composites is yet to be unraveled. Experimental probes, of both their real-space and electronic structure, will continue to be developed. The frequency dependence of their optical response in the superconducting state, and its ultimate understanding, will also be a subfield of interest. Driven largely by the impetus toward very-large-scale integration in electronics, small structures can also be made with substantial long

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ELECTRONIC STRUCTURE AND PROPERTIES OF MATTER 57 range order (arrays of small metal spheroids, for example). The particles themselves are of such a length scale that many of the con- ventional methods of solid-state physics no longer apply in determining their essential physical properties. The field of ordered micro- condensed-matter science is still in its infancy but is perceived widely as one in which many of the traditional subareas of solid-state physics will yet have a considerable impact. In this technologically crucial area, interface states, ballistic transport, Kapitza resistance, quantum- well effects, electromigration and thermomigration, and noise are all topics of fundamental interest and will offer research opportunities for the future.