Condensed-Matter Physics (1986) / Chapter Skim
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1 Electronic Structure and Properties of Matter
1 Electronic Structure and Properties of Matter
Pages 39-57
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From page 39... ...
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 incorporating 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.
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From page 40... ...
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.
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From page 41... ...
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 semiconductors accurately. In summary, it is clear that some aspects of electron structure in ordered systems are quite well understood, to the point where application of theory to materials exhibiting unusual properties (the hightemperature, superconducting A-15 compounds, for example)
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From page 42... ...
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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From page 43... ...
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)
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From page 44... ...
In 1982, Hall conductance plateaus at certain simplefractions of the quantum e2/h were discovered in GaAs heterojunctions of exceptionally 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.
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From page 45... ...
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.
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From page 46... ...
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.
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From page 47... ...
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 systems is the localization of the true quantum-mechanical eigenstates.
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From page 49... ...
has been unambiguously reported, at low temperatures, in doped semiconductor systems. Furthermore, the behavior of the conductivity near the transition is related to critical phenomena in phase transitions.
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From page 50... ...
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 interactions, 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 increases, the electronic bandwidths do not shrink continuously to zero but instead vanish suddenly at a certain critical density.
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From page 51... ...
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 predictions rather closely in many cases.
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From page 52... ...
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.
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From page 53... ...
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.
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From page 54... ...
The complete cutaway cross section (a) shows the essential components including the anvil supports, alignments design, Iever-arm assembly, and spring-washer loading system.
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From page 55... ...
These excited states are needed in the calculation of the response of such materials to time-dependent perturbations, 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 accurately.
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From page 56... ...
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.
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From page 57... ...
The field of ordered microcondensed-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, quantumwell effects, electromigration and thermomigration, and noise are all topics of fundamental interest and will offer research opportunities for the future.
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