M. Pollak

Correlation effects in hopping transport

Abstract The effects of intersite Coulomb interactions on transport in a system of localized states is examined. Correlation effects are seen to inhibit the DC conduction but to enhance the AC conduction. It is shown that the interactions lead to a Coulomb gap in the one-electron excitation spectrum for DC conduction of width E g ∝ E c (E c /W) 1 2 , where E c is the average intersite Coulomb energy and W is the random potential. The need to excite across the Coulomb gap can be alleviated by multi-electron hopping, which can lead to a non-activated T − 1 4 -like behavior as transport becomes collective in nature. Examples of systems where correlations effects have been observed are given. The possibility of a many-electron delocalization is also discussed.

Molecular‐Orbital Studies of Intermolecular Interaction Energies. I. On the Role of π Electrons in Intermolecular Interactions, with Some Application to DNA

A semiemphirical method, based on molecular orbitals, is presented for the treatment of intermolecular interactions which involve π‐electron systems, as is common in biopolymers. In the application of the method, a numerical analysis is performed on the interaction energy between the bases of a guanine—cytosine homo‐dinucleotide. The computed values of the exchange, the electrostatic, the polarization, and dispersion energies are given for an interaction between base pairs in configurations corresponding to some of the possible occurences in DNA. The following conclusions are based on the numerical results. It is incorrect to assume that the π‐electron systems of the two monomers are separable. It seems acceptable, for the purpose of a perturbation treatment, to confine the set of wavefunctions to the π orbitals. The interaction energy between more distant monomers is not negligible relative to the interaction between nearest neighbors. While the energy of attraction between π‐electron systems is signific...

Molecular‐Orbital Studies of Intermolecular Interaction Energies. II. Approximations Concerned with Coulomb Interactions and Comparison of the Two London Schemes

In the semiempirical calculations of wavefunctions in molecules with π‐electron systems, molecular orbitals are constructed from atomic orbitals that are assumed to be orthogonal to each other. Since the Slater orbitals are not orthogonal, the atomic orbitals are usually interpreted to be the Lowdin orbitals. The Lowdin orbitals are delocalized, and therefore a question arises of how to use the computed coefficients of these orbitals for calculating the electronic charge distribution. It is found that the charge distribution may be somewhat different from the distribution where Slater orbitals are used instead of Lowdin orbitals. The magnitude of the difference depends on the kind of approximation used for the product functions of two Slater orbitals centered on different atoms. The difference vanishes for the Mulliken approximation. Numerical analysis for a guanine—cytosine base pair indicates that when the Lowdin approximation, or a similar approximation, is used instead of the Mulliken approximation, t...

Effect of carrier-carrier interactions on some transport properties in disordered semiconductors

Interactions between electrons are likely to play an important role in certain transport properties of disordered semiconductors, particularly where these properties depend on electrons in localized states. A working classification of these interactions into intra-site interactions, inter-site interactions and polarization, is made. The first class is believed to affect primarily the transport properties o carriers around the mobility gap, by introducing two-electron wave functions into this region. The second class can introduce an activation energy into the d.c. hopping conductivity at very low temperatures, affect the thermo-electric power, and increase noticeably the a.c. hopping conductivity above a certain frequency. The third class may reduce the activation energy of the d.c. conductivity; a reduction to zero is theoretically possible. Instances where some of the above effects may have been observed are cited.

Hall mobility due to hopping-type conduction in disordered systems

Abstract The Hall mobility due to hopping-type transport in spatially random systems is calculated by means of percolation arguments and is expressed as a function of the ratio of the mean intersite spacing to the size of the localized wave-function. The result is found to be smaller than that of the corresponding ordered system, and differs from the result obtained by other authors. Finally, an estimate is made for the additional reduction in the magnitude of the Hall mobility caused by disorder in the local site energies.

Effect of electron-electron interactions on hopping and on delocalization

Abstract In impurity bands the Coulomb interaction energies are of the same order as the disorder energy, and must therefore be considered. The effect of these interactions on the density of one-electron excitations (the Coulomb gap) is discussed. The Coulomb gap can be alleviated by many-electron hops. The role of such many-electron hops on hopping transport at very low temperatures is evaluated, and a tentative formula for the conductivity obtained. Relevant experimental work from the literature is discussed in the context of the many-electron effects. Finally, a brief discussion of the effects of interactions on the Anderson transition is presented.

Correlation effects in hopping conduction: Hopping as a multi-electron transition

Abstract The treatment of hopping between localized states as a one electron transition breaks down at high densities. We have treated the problem in terms of a correlated two electron (one phonon) transition. We neglect exchange effects. The correlation effect consists of the movement of two (or more) electrons simultaneously whenever it lowers the energy difference between initial and final state of the system. This is seen to lower the activation energy over the one electron process, an effect noticeable at low temperatures, moderate densities, and moderate compensation in impurity conduction. The onset of the effect is seen to occur at a density on the order of ( 3 4 π) (e 2 a/2kTK)− 3 2 for a temperature T, where K is the dielectric constant of the host medium and a is the Bohr radius of an impurity state.

Non-ergodic behaviour of Anderson insulators with and without Coulomb interactions

Abstract In some recent papers in which Monte Carlo methods have been used, it has been found that disordered Anderson insulators with Coulomb interactions may become glassy at low temperatures. This was indicated by a non-vanishing value of an order parameter. In the present paper, the transition to a glassy state is investigated analytically for systems with and without Coulomb interactions. For the purposes of the analysis, a system is taken to be in the glassy state if it fails to satisfy the ergodic hypothesis. A transition to non-ergodic behaviour is found for both interacting and non-interacting systems, but the transition for the interacting system is softer and occurs at a higher temperature. The results are subject to certain approximations and assumptions, which are specified.

Hopping transport in a-Ge and a-Si

Abstract An unreasonably large pre-exponential factor for conductivity is an old problem with interpretations of hopping transport data on a-Si and a-Ge. It is shown that an appropriate concave density of states eliminates this problem, and explains some other experimental features. Results of a percolation theory for exponential densities of states are presented. Comparison with experiments on high-density Si and Ge gives Bohr radii of 6 and 13 A and values for N(E F) of 7 × 1020 and 2 × 1018 eV−1 cm−3, respectively.

The Coulomb gap: A review, and new developments

Abstract A survey is presented of experimental and theoretical work on the problem of Coulomb interactions in a Mott-Anderson insulator, since its inception, but emphasizing recent developments. The paper also attempts to explain the basic physical considerations, to point out some existing disagreements and to assess to what degree these may have been resolved by recent work.