Metal-insulator transitions are accompanied by huge resistivity changes, even over tens of orders of magnitude, and are widely observed in condensed-matter systems. This article presents the observations and current understanding of the metal-insulator transition with a pedagogical introduction to the subject. Especially important are the transitions driven by correlation effects associated with the electron-electron interaction. The insulating phase caused by the correlation effects is categorized as the Mott Insulator. Near the transition point the metallic state shows fluctuations and orderings in the spin, charge, and orbital degrees of freedom. The properties of these metals are frequently quite different from those of ordinary metals, as measured by transport, optical, and magnetic probes. The review first describes theoretical approaches to the unusual metallic states and to the metal-insulator transition. The Fermi-liquid theory treats the correlations that can be adiabatically connected with the noninteracting picture. Strong-coupling models that do not require Fermi-liquid behavior have also been developed. Much work has also been done on the scaling theory of the transition. A central issue for this review is the evaluation of these approaches in simple theoretical systems such as the Hubbard model and $t\ensuremath{-}J$ models. Another key issue is strong competition among various orderings as in the interplay of spin and orbital fluctuations. Experimentally, the unusual properties of the metallic state near the insulating transition have been most extensively studied in $d$-electron systems. In particular, there is revived interest in transition-metal oxides, motivated by the epoch-making findings of high-temperature superconductivity in cuprates and colossal magnetoresistance in manganites. The article reviews the rich phenomena of anomalous metallicity, taking as examples Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Ru compounds. The diverse phenomena include strong spin and orbital fluctuations, mass renormalization effects, incoherence of charge dynamics, and phase transitions under control of key parameters such as band filling, bandwidth, and dimensionality. These parameters are experimentally varied by doping, pressure, chemical composition, and magnetic fields. Much of the observed behavior can be described by the current theory. Open questions and future problems are also extracted from comparison between experimental results and theoretical achievements.

Metal-insulator transitions

An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Theory of Dynamic Critical Phenomena

Since the discovery by Steglich et al. (1979) of superconductivity in the high-effective-mass ($\ensuremath{\sim}200{m}_{e}$) electrons in Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$, the search for and characterization of such "heavy-fermion" systems has been a rapidly growing field of study. The eight heavy-fermion systems known to date include superconductors (Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$, U${\mathrm{Be}}_{13}$, U${\mathrm{Pt}}_{3}$), magnets (Np${\mathrm{Be}}_{13}$, ${\mathrm{U}}_{2}$${\mathrm{Zn}}_{17}$, U${\mathrm{Cd}}_{11}$), and materials in which no ordering is observed (Ce${\mathrm{Al}}_{3}$, Ce${\mathrm{Cu}}_{6}$). These $f$-electron materials have, in comparison to normal metals, enormous specific heat $\ensuremath{\gamma}$ values (450-1600 mJ/mol ${\mathrm{K}}^{2}$), large values of the low-temperature magnetic susceptibility $\ensuremath{\chi}$ (8-50\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ emu/mol G), maxima in the resistivity at low temperatures with large ${\ensuremath{\rho}}_{max}$ values (100-200 \ensuremath{\mu}\ensuremath{\Omega} cm), and unusual temperature dependences of their specific heats below 10 K. The three heavy-fermion superconductors show such unusual behavior that the possibility of $p$-wave pairing of the superconducting electrons, rather than the usual BCS $s$-wave pairing, cannot be ruled out. This paper reviews the experimental results to date, to serve both as a status report and as a starting point for future research. Several correlations between properties are pointed out, including the observation that a low value of the Wilson ratio ($\ensuremath{\sim}\frac{\ensuremath{\chi}}{\ensuremath{\gamma}}$) appears to correlate with the occurrence of superconductivity.

Heavy-fermion systems

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

One of Feynman's early applications of path integrals was to superfluid $^{4}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

Path integrals in the theory of condensed helium

High-precision specific-heat measurements were made on pure liquid $^{3}\mathrm{He}$ in both the normal and superfluid phases for temperatures between 0.6 and 5 mK and for pressures between 0 and 34 bars. The data were obtained using a magnetic susceptibility thermometer which was calibrated against the National Bureau of Standards scale near 15 mK and at lower temperatures principally by the condition that the zero-pressure normal-phase specific heat be linear in temperature. The $^{3}\mathrm{He}$ phase diagram based on this scale is presented. In particular we find that ${T}_{A}$=2.49 mK which differs quite substantially from the currently accepted value of about 2.7 mK. Multiplying the Pt NMR temperatures determined by Haavasoja and co-workers by a factor of 0.89 or subtracting 0.13 mK from the magnetic temperatures of Paulson et al. brings both of these scales into excellent agreement with the new scale. The $^{3}\mathrm{He}$ quasiparticle effective mass, ${m}_{3}^{\mathrm{*}}$(P), extracted from the normal-phase data agrees well with our previously reported results based on higher-temperature specific-heat data. The values of ${m}_{3}^{\mathrm{*}}$(P) from Haavasoja and co-workers are \ensuremath{\sim}20% smaller. However, if their specific-heat data are reanalyzed using the new temperature scale, the two sets of ${m}_{3}^{\mathrm{*}}$(P) values are brought into good agreement. We thus claim that the large discrepancies between previous specific-heat measurements are due almost entirely to differences in temperature scales. The new normal-phase specific-heat data at low pressures show no evidence of the anomalous behavior observed by Haavasoja and co-workers. Consequently, the size of the specific-heat jump at ${T}_{c}$ could be determined with little ambiguity over the entire pressure range. \ensuremath{\Delta}C/${C}_{g}$ is only a few percent larger than the weak-coupling value at P=0 and increases linearly with sample density. At high density the temperature dependence of the specific heat below ${T}_{c}$ shows small deviations from theory.

3He specific heat and thermometry at millikelvin temperatures.

High-precision, constant-volume specific-heat measurements were made on pure liquid $^{3}\mathrm{He}$ in the normal phase. The data were obtained for temperatures between 7 mK and 2.5 K and in the pressure range 0-32.5 bar. Below 30 mK the results are about 25% greater than those from two other very recent experiments and about 10% less than the earliest values. Between 30 and 500 mK the data agree with all previous measurements to within about \ifmmode\pm\else\textpm\fi{}5%. Above 500 mK the present measurements are the first to be reported at other than saturated vapor pressure. Several checks indicate that only the present very-low-temperature data are thermodynamically consistent. Consequently, adjustments must be made in all of the previously determined Landau parameters. In agreement with theory, the low-temperature specific-heat data at all densities can be described well by a function which includes terms only in $T$ and in ${T}^{3}\mathrm{ln}T$. This form, however, seems to apply out to higher temperatures than expected. From the coefficient of the ${T}^{3}\mathrm{ln}T$ term values of the Landau parameter ${F}_{1}^{a}$ are extracted which are consistent with other determinations.

Specific heat of normal liquid He 3

The design and performance of several generations of wavelength-selective 1/spl times/K switches are reviewed. These optical subsystems combine the functionality of a demultiplexer, per-wavelength switch, and multiplexer in a single, low-loss unit. Free-space optics is utilized for spatially separating the constituent wavelength division multiplexing (WDM) channels as well as for space-division switching from an input optical fiber to one of K output fibers (1/spl times/K functionality) on a channel-by-channel basis using a microelectromechanical system (MEMS) micromirror array. The switches are designed to provide wide and flat passbands for minimal signal distortion. They can also provide spectral equalization and channel blocking functionality, making them well suited for use in transparent WDM optical mesh networks.

Wavelength-selective 1/spl times/K switches using free-space optics and MEMS micromirrors: theory, design, and implementation

An improved modulator and methods for making the modulator are disclosed. A membrane, preferably circular in shape, is formed over a region of a substrate in such a way that a gap results between the membrane and substrate forming a modulator cavity. The membrane forms a continuous surface over the cavity. In particular, the membrane is not supported by discrete support arms, but rather extends beyond the modulator cavity. Preferably, holes are formed in the membrane to aid in damping its motion and to allow access to underlying layers during modulator formation. According to the method, the modulator is formed by forming a means for creating a gap between the substrate and the membrane, forming a membrane, forming a lateral conduit to aid in removing the means for creating the gap and, finally, by removing the means for creating the gap.

Method and apparatus for an improved micromechanical modulator

The heat capacity of $^{4}\mathrm{He}$ adsorbed on graphite has been precisely measured over a fine grid of coverages for temperatures extending down to 100 mK and for coverages up to five atomic layers. The data indicate that the two-dimensional liquid is self-bound in each of the first three layers with an areal density of about 0.04 atom/\AA{} $^{2}$. There is also evidence suggesting that this liquid undergoes a Kosterlitz-Thouless transition.

Heat capacity of fluid monolayers of 4He

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