Fermi Glass Research Articles

Impurity band conduction in CdHgTe crystals

Electrical conduction at 77 K in Cd x Hg 1− x Te, with the composition x ⩽ 0.2, is by electrons in the conduction band, by holes in the valence band and by holes in the impurity band. In samples with zero energy gap, x < 0.14, electrical conduction by holes in the valence band is comparable to electrical conduction by holes in the impurity band. In the open energy gap CdHgTe, electrical conduction by holes in the valence band is negligible in comparison to electrical conduction by holes in the impurity band. In CdHgTe samples, electrical conduction in the impurity band is described by the “Fermi Glass” model.

The localization of injected charges in polymers and molecular solids

Polymers and molecular solids are characterized by two fundamental features: the retention of molecular identity in the solid state and the occurrence of relatively weak interactions between the individual molecular entities. The weak interactions lead to a high degree of disorder caused both by defects and by thermally induced motions of the molecules. A model of charges injected into polymers and molecular solids is developed. Photoemission and transport measurements are utilized to evaluate the parameters in this model. Results for metal free phthalocyanine are presented as an illustrative example. For molecular glasses and aromatic pendant-group polymers this analysis predicts that disorder causes injected charges to form a Fermi glass of self-trapped polarons, i.e., they occupy localized states characterized by a high degree of local atomic and electronic polarization. Successful interpretations of photoemission spectra, contact charge exchange, and injected carrier drift mobilities verify this prediction. The boundary of the Fermi-glass region of localized-state molecular-ion behavior is identified by consideration of molecular crystals in which injected charges may occupy extended energy-band states at low temperatures.

Insulating phase of a disordered system: Fermi glass versus electron glass

The authors examine the critical divergence of the low-frequency conductivity of the noninteracting Fermi glass and interacting electron glass models of the insulating phase of a disordered system as the metallic phase is approached. Results for the two are found to be rather different, which can be tested experimentally. In particular, for the electron glass, there exists a nonvanishing contribution to the dielectric constants from the low-frequency (hopping) conductivity even at low temperatures, which scales with the high-frequency (optical) contribution, and diverges with the same exponent at the insulator-metal transition.

Properties of multicomponent amorphous silicon forming a tetrahedrally-bonded continuous random network

A multicomponent amorphous silicon, a-Si-Ge-B, is prepared and its properties studied. Various data indicate that a tetrahedrally-bonded CRN is realized in a-Si-Ge-B. The electronic structure of this alloy is characterized as being the same as for Fermi glass in which a large number of localized states exist over a wide energy range. It is also found that a metal-insulator transition takes place as the composition is varied.

The metal-insulator transitions in the Peierls chain

The ground state (at 0K) of a discrete molecular-crystal model for the Peierls chain with classical atoms and non-interacting spinless quantum electrons is calculated numerically as a function of the electron-phonon coupling for an 'irrational' electron concentration. A metal-insulator transition arising from the extinction of the Frohlich conductivity for the incommensurate system is observed when the Peierls gap is only 10% of the total unperturbed bandwidth. Beyond the critical coupling, the Frohlich mode disappears and the electrons are exponentially localised but the lattice distortion remains incommensurate (the polaron lattice). In this region, the Peierls-Nabarro barrier does not vanish and is calculated. The existence of metastable Fermi glasses is also proved, but they are shown to have an energy larger than that of the incommensurate ground state. The observed transition is identified as a transition by breaking of analyticity, which is similar to the one found previously in the Frenkel-Kontorova model. This behaviour is explained as being a consequence of the competition between the Fermi and the lattice wavevectors, which are incommensurate with each other.

Electrical conduction in biotite micas

The direct current electrical conductivity tensor of biotitic phyllosilicates (mica) has been measured as a function of temperature, of electric field, and of chemical composition. It is found that conductivity depends exponentially upon iron impurity content, and upon electric field at high fields. The dependence upon temperature is more complicated. These results are best interpreted by a model in which mica is an isotropic Fermi glass in which electrical conduction takes places by nonadiabatic hopping of small polarons between iron sites in the crystal.

The Wigner glass and conductance oscillations in silicon inversion layers

The authors show that on changing the nature of the background random potential the inversion layer of the Si MOSFET exhibits the conductance oscillations previously observed in both GaAs, the source and drain regions of Si MOSFETS and MOSFETS with a very high concentration of Na+ ions at the Si-SiO2 interface. Measurements of the temperature dependence of conductance show that oscillations are found when conductance is by an excitation process as well as hopping. The oscillations arise from an oscillating activation energy which is due to either an oscillating interaction contribution to the activation energy, or a negative effective density of states at certain values of carrier concentration. This appears due to electron ordering in a small current limiting region and is contrasted with the case where the oscillations are absent, although localisation is due to both background disorder and the random field of localised electrons. It is shown that near the transition, localisation is due almost entirely to the random field of the localised electrons, and the system is a strongly interacting Fermi glass (or Wigner glass), even though the oscillations are not apparent.

Defect-induced tunnelling and the conductivity of strongly disordered systems

For a model describing the motion of a zero-temperature electron gas in an environment causing a fluctuating potential and a fluctuating effective mass, a theory is developed which allows for an approximate calculation of the particle density propagation self-consistently with momentum relaxation and defect-induced tunnelling processes. All correlation functions of the system are expressed in terms of two causal kernels for which non-linear equations are derived and solved. A detailed discussion of the influence of the defect-induced tunnelling on the mobility, in particular on mobility edges, and on the Fermi glass stiffness is given and an anomalous high-frequency tail of the dynamical conductivity is predicted.

The conductivity and Seebeck coefficient in the nearest-neighbour hopping regime of a Fermi glass

An effective medium theory is used to calculate the conductivity activation energy and the Seebeck coefficient for nearest-neighbour hopping in a band of Anderson localised states at the Fermi level. The results of these calculations are compared with experimental observations on cerium sulphide, fluorine-substituted magnetite and 'pure' magnetite Fe3O4.

Variable-range hopping including correlation between energies and positions

Variable-range hopping theory is modified to include a correlator between the distances and the energy differences of localised states. The DC conductivity for a Fermi glass at very low temperatures that he would predict if no correlation between energies and positions were included.

Metal-insulator transitions induced by a magnetic field

The theory of impurity conduction is discussed and a summary is presented of some experimental aspects of the metal-insulator transition in impurity bands and inversion layers. The various transport mechanisms in the Fermi glass, and results from the literature, are reviewed showing how these mechanisms are affected by the application of a magnetic field.

Elementary Excitations in the Fermi Glass

We evaluate the lifetime of quasiparticles in the Fermi glass. An anomalous contribution to the lifetime is found. It is shown that this effect leads to a ${T}^{\frac{1}{4}}$ law for the dc conductivity of a disordered system.

THEORETICAL PERSPECTIVES IN THE INVERSION LAYER

The problem of Anderson-localization in two dimensions has been extensively studied recently [1-3] with particular regard to the role of this transition in the inversion layer [4, 5] at semiconductor surface. During the last tow or three years, it has been realized that this system affords a particularly useful tool for studying both electron correlation and disorder in 2D. Interest is further stimulated by our suggestion that the minimum metallic conductivity in 2D is a constant independent of the nature of the system where it is measured and our numerical results [1, 2] suggest a maximum metallic resistivity of about 30 000 O. This result has been verified on a number of samples of the MOS sutructure. In addition, an application [6, 7] of substrate bias to the same system allows the possibility of affecting a change in the random potential fluctuations as seen by the charge layer and several anomalous properties which have been reported using this technique are explained [8] within the framework of localization theory. These experiments provide the first experimental verification of certain aspects of the localization theory. There has also been reported an apparent variation [9] of the minimum metallic conductivity in some samples of the MOS device. Our universality suggestion derived within the framework of a one-electron model of homogeneous potential fluctuations points to the importance of considering either many-electron contributions or long range fluctuations (or both) in these systems. The macroscopic fluctuations (inhomogeneities) will have the effect of reducing the temperature at which true metallic behaviour will be observed thus obscuring the transition over the experimentally available temperatures. Such samples will show an apparent σmin at a higher value than the universal one. In order to address this problem further, we have performed a numerical experiment [10] in which we impose a longer range potential fluctuation in addition to the short ranged Anderson-like distribution and examined the consequences of a spatial dependent mobility edge. This has required the diagonalization of extremely large matrices and we have exploited an extension of the Lanzos algorithm developed by the author and Thouless (unpublished) for this problem. Most strikingly, our preliminary results show no variation of σmin in the presence of such long ranged fluctuations and in addition give further support for our universal value of σ ≈ 0.1 e2/h. Thus it is clear that if the measured σmin on these samples persists at values much larger than 0.1 e2/h at lower temperatures, the importance of interaction effects is established. As mentioned above, several properties which have been reported on the transport properties of the inversion layer are satisfactorily explained within the framework of localization theory if one allows a mechanism of Fermi level pinning. A detailed theory for this effect has not yet been put forward although the evidence for such an effect, I believe, is substantial. One possibility which takes into Coulomb repulsion supposes a strong interaction of the localized electron with the Fermi glass. The Coulomb repulsion between electrons in neighboring localized states encourages the occupied states to be more uniformly distributed. The empty ones, the, act as interstitial states which serve both to screen the electrons and are higher in energy. Such an effect has been dscussed by Efros and Shlovskii [11] and by Thouless in these proceedings. Under these circumstances, the Fermi level is rather more stable with respect to changes in the width of the external potential fluctuation (e. g. by applying a substrate bias which moves the layer closer to the surface) than the mobility edge which occurs at the unoccupied states for low electron densities.