M. Kaveh

Metal-insulator transitions in non-crystalline systems

Abstract This review gives an account of the changes in our understanding of the metal-insulator transition in non-crystalline systems since the application to it of scaling theory and experiments on doped semiconductors at millikelvin temperatures. The first four sections give an account of previous work. §5 discusses briefly the scaling theory, and §6 deduces from the Kubo-Greenwood formula that when the Fermi energy of a ‘metal’ lies at a small energy ΔE above a mobility edge, the conductivity is of the form 0.03 e 2 ħL, where L is the size of the specimen, the inelastic diffusion length, or, in a magnetic field, LH = (cħ/eH)½, or the localization length at an energy ΔE below the transition, whichever is the smaller. Motts ‘σmin’ is observed in doped semiconductors in a magnetic field such that LH < a, a being the distance between donors, and in some liquid systems. The solved and unsolved problems of long-range Coulomb interaction are described, both for metallic conduction and for hopping. Applicati...

Electron-electron scattering in conducting materials

Abstract Recent developments are reviewed in the theory and measurement of electron-electron scattering and its contribution to the electrical and thermal resistivities for different types of conducting materials, such as extremely impure metals, one-dimensional and two-dimensional conductors, the simple metals, transition metals, semimetals, organic conductors and the A15 compounds. The discussion includes the following topics: quantum corrections to the Fermi-liquid theory of electron-electron scattering (EES) due to static disorder, the effect of the dimensionality of the system on EES, the measurement and the calculation of the EES contribution to the resistivity of metals, the observed sample dependence of EES for the simple metals, the effect of EES on electron-surface scattering for thin wires, the contribution of EES to the anomalous surface impedance and to the optical relaxation time and the effect of a magnetic field on EES. Comparison is made between theory and recent experimental data for eac...

Universal dependences of the conductivity of metallic disordered systems on temperature, magnetic field and frequency

The authors generalise the Mooij rule (1973) for disordered metals. They find that the temperature dependence of the conductivity sigma of a disordered metal as a function of temperature must change slope due to diffusion effects, and if interaction effects are included, sigma changes its slope three times. The crossover temperature (if it occurs at high temperatures) from positive to negative d sigma /dT due to diffusion effects varies as C5, where C is the average concentration of impurities or scattering centres. Another crossover temperature which separates electron correlation effects from diffusion effects is predicted. This explains the temperature dependence observed for Ge1-xAux. It is also shown that the non-metallic behaviour of the AC conductivity is accounted for by diffusion effects and there is no need to invoke the concept of a pseudogap due to electron interaction. The negative magnetoresistance follows from the theory for diffusion effects in agreement with the perturbation theory of Kawabata (1980).

Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium

Statistical properties of coherent radiation propagating in a quasi-one-dimensional random medium are studied in the framework of random-matrix theory. Distribution functions for the total transmission coefficient and the angular transmission coefficient are obtained.

Magnetic-field-induced insulator-quantum Hall-insulator transition in a disordered two-dimensional electron gas

We present low-temperature transport measurements on the two-dimensional electron gas in delta -doped GaAs which undergoes an insulator-quantum Hall-insulator transition as the magnetic field is increased. Both low- and high-held transitions are marked by peaks in sigma xx and the temperature-independent critical value of sigma xy of 0.5e2/h per spin. We map out the phase diagram versus disorder and magnetic field and study the temperature dependence of sigma xx throughout. In the quantum Hall region we observe Mott variable range hopping and, around the high-field transitions, scaling via a single parameter: z=(B-B*)T-0.45. The functional dependence on z above this transition is fitted by recent network percolation calculations.

Logarithmic corrections to two-dimensional transport in silicon inversion layers

It is shown that the logarithmic corrections to the two-dimensional conductance arise from both interaction and incipient localisation effects. A transition between these two type of behaviour can be achieved by a change of electron temperature in the presence of a magnetic field, or just by the application of a magnetic field. The magnetic field suppresses the weak localisation and enhances the effects of the interaction. Results on conductance, magnetoconductance and Hall effect are presented and discussed.

Magnetic delocalisation of a two-dimensional electron gas and the quantum law of electron-electron scattering

Discusses the effect of a magnetic field on the weak localisation of a two-dimensional electron gas. It is shown that due to quantum corrections the electron-electron relaxation time tau ee varies with electron temperature T and tau ee-1=A1T+A2T2, in the temperature range 3K-0.1K. This short tau ee causes a rapid transition between states which are weakly localised and so reduces the logarithmic correction to the conductance. Negative magnetoresistance measurements are reported for (100) silicon MOSFETs in the temperature range 0.1-4K.

The metal-insulator transition in disordered 3d systems: a new view

The authors show that for an uncompensated semiconductor such as Si:P the metal-insulator transition occurs for -KFl>1 and the decrease of the conductivity sigma near the transition can be accounted for by perturbation theory. A universal dependence of sigma as a function of electron density n is given. sigma decreases with decreasing n due to formation of wavefunctions decaying with distance as a power law, causing a decrease of the diffusion constant. Electron correlation has only a small effect on sigma far above the metal-insulator transition. However, as n decreases and tends to nc, electron correlations cause a sharper decrease of sigma . For uncompensated samples transport is in a conduction band, the density of states deviates only slightly from a free-electron-like behaviour, whereas sigma drops below sigma B, the Boltzmann value of the conductivity, due to a reduction of the diffusion constant. A discontinuous transition to an impurity band occurs when the conductivity in the conduction band is about 0.03 sigma B and thus somewhat below Motts value sigma min=0.03 e2/h(cross)a, which is correct for compensated samples. Conductivities much below sigma min for any sample must be due to long-range fluctuations or inhomogeneities. For uncompensated Si:P the authors argue for a minimum metallic conductivity of about 1/3 sigma min.

Enhancement of susceptibility and the electrical resistivity of organic metals with a small mean free path

Abstract The spin susceptibility of organic metals is enhanced over the Pauli value at ambient temperature, where the mean free path is close to one lattice constant. The resistivity continues to follow the T 2 law in this regime. A theory is described which accounts for these unusual effects. The theory is somewhat analogous to polaron theory and makes use of the quadratic nature of the electron-phonon coupling. The electrons are localized by short-lived “phonon traps”, accounting for the transition to a Curie-like behaviour. Tunnelling between these nun-degenerate molecular sites gives rise to a T 2 law with a coefficient close to that of the low-temperature state, where the conductivity is metallic.

Propagation of waves through a slab near the Anderson transition: a local scaling approach

The authors use a local scaling approach to calculate the following properties near the Anderson transition: (i) the time-dependent pulse shape of the transmitted wave through a slab; (ii) the wavelength dependence of the intensity-intensity autocorrelation function C( Delta lambda ); (iii) the time dependence of the intensity-intensity autocorrelation function C( Delta t) for dynamic disorder; (iv) the correlation function for the memory effect. Their local scaling approach is shown to be consistent with Andersons global scaling theory and yields the same scaling behaviour for the transmission coefficient. All the correlation functions are shown to depend explicitly on the averaged intensity pulse shape for small values of Delta lambda or Delta t.