The effect of a magnetic field on the crossover from the linear to quadratic frequency dependence of phononless hopping conductivity in disordered systems

The effect of an external magnetic field on the frequency dependence of phononless hopping conductivity in disordered system is studied. The dependence of the low-temperature phononless conductivity on the applied magnetic field is established. It is shown that in the limit of a strong magnetic field, the frequency of the transition (crossover) from linear to quadratic frequency dependence of phononless conductivity grows logarithmically with the value of a magnetic field.     

The special features of the frequency dependence of phononless hopping conduction

Within the framework of perturbation theory the imaginary part of the phononless conduction of a lightly doped compensated semiconductor is calculated. It is shown that when the basis of localized atomic-like functions is used, the superlinear frequency dependence of the real part of the conduction corresponds to the approximately linear frequency dependence of the imaginary part of the conductivity. It has been found that at frequencies below the transition (crossover) frequency ??_cr from the linear to quadratic frequency dependence of the real part of conductivity, the dielectric loss tangent depends weakly on the frequency and it is determined by the relationship of ???_cr to the width of the impurity band. It is shown that measurements of the dielectric loss tangent can provide information on the localization radius of impurity states.     

Frequency dependence of low-temperature phononless conductivity in disordered systems

The frequency dependence of resonant phononless hopping conductivity in disordered systems with pointlike centers of localization in the low-temperature limit is considered within the framework of the pair approximation. It is shown that the existing theory that predicts the power-mode frequency dependence of the low-frequency phononless hopping conductivity σ(ω) and a transition from linear to quadratic dependence (crossover) when frequency increases may become invalid, and the quadratic frequency dependence may never manifest itself at all.     

The effect of electron state hybridization on the frequency dependence of hopping conductivity in disordered systems

The effect of electron state hybridization on phononless hopping conductivity in a disordered system of point localization centers in the intermediate frequency range corresponding to electron transitions to distant centers is discussed. When the basis of the atom-type localized functions is applied, with the hybridization of the wave functions of the distant centers not being taken into account, the frequency dependence of phononless conductivity is shown to be superlinear and monotonic in a wide frequency range. In this case, the kink in the vicinity of a crossover from a linear to a quadratic frequency dependence of the conductivity turns out to be sharper as distinct from the standard theory.     

On the high - frequency impurity hopping conductivity

Pair approximation for ac impurity hopping conduction is considered. The density of pairs is studied with the Monte-Carlo computer simulation over a wide range of compensation degrees. At low compensations analytical results are also obtained and agree with simulation results. In some points our results differ from those by Pollak and Golin. Comparison with the experimental data is given.     

Low frequency hopping conductivity in disordered one-dimensional lattice

We investigate classical hopping on a one-dimensional chain with random nearest-neighbour transfer rates. It is found, by studying corrections, that an Effective-Medium approach gives the exact asymptotic hopping conductivity at low frequencies for certain distributions of the transfer rates.     

Scaling approach to the theory of frequency dependent hopping conductivity of disordered systems

By studying the change of the probability distribution function for the hopping propagation of carriers under differential changes of the temperature and density of sites partial differential equations are derived which couple the frequency, temperature, and density dependence of the conductivity. In certain special cases the conductivity can be calculated explicitly for zero frequency as well as in regions where the frequency dependence is known from experiment or some other theory. This leads to results which are well suited for experimental tests. Approximations used in this treatment are discussed and related to other types of theories for hopping conductivity.     

Universal crossover from band to hopping conduction in molecular organic semiconductors

The charge transport in a variety of herringbone-stacked organic molecular semiconductors is investigated in the temperature range from 10 to 550 K. A crossover from coherent bandlike charge transport with mobilities up to several thousand cm (2)/V s at low temperature to an incoherent hopping motion at high temperatures is observed. This is attributed to the localization of the charge carrier due to increased electron-phonon interaction and, finally, the formation of a lattice polaron.     

The temperature dependence of the conductivity and thermal emf due to multiphonon hopping in disordered semiconductors

Using transport theory, we studied the temperature dependence of the static conductivity and of the thermal emf due to multiphonon hopping in disordered semiconductors. In the low-temperature region when T < _m ( _m is the maximum phonon frequency), the temperature dependences of the conductivity and the thermal emf are the same as when single-phonon hopping is dominant. At higher temperatures (T _m), the hopping conductivity and thermal emf are characterized by a slower dependence on reciprocal temperature than in the low-temperature region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.2, pp.42–47, February, 1976.The author is to V. L. Bonch-Bruevich and A. G. Mironov for discussing this work.     

Single-phonon contribution to the hopping conductivity of amorphous solids

The electronic d.c. hopping conductivity of amorphous materials is calculated exactly up to the second power of the coupling constant of electrons and acoustic phonons. Its temperature dependence is discussed.Ke Karlovu 3, Praha 2, Czechoslovakia.     

From classical mobility to hopping conductivity: charge hopping in an ultracold gas

Studies of charge mobilities in an ultracold gas are reported. Calculations for the Na + Na+ system have been carried out as a function of temperature T and densities, and the conductivity of the ultracold charged gas is obtained. The total charge mobility exhibits a sharp increase as T is lowered, indicating a transition from an almost insulating to a conducting system at few microK. It is shown that the nature of the charge mobility changes with temperature: at high T, the charges are transported by massive centers (i.e., the ions), and at low T, by electrons jumping from neighboring atoms onto the positive ions (the positive holes exhibit hopping conductivity). An experiment is proposed to detect this effect.     

Evidence for a crossover in the frequency dependence of the acoustic attenuation in vitreous silica

We report measurements of the sound attenuation coefficient in vitreous silica, for sound waves of wavelength between 50 and 80 nm, performed with the new inelastic UV light scattering technique. These data indicate that in silica glass a crossover between a temperature-dependent (at low frequency) and a temperature-independent (at high frequency) acoustic attenuation mechanism occurs at Q approximately equal to 0.15 nm(-1). The absence of any signature in the static structure factor at this Q value suggests that the observed crossover should be associated with local elastic constant fluctuations.     

Spin dynamics in the regime of hopping conductivity

Spin dynamics in the impurity band of a semiconductor with the spin-split spectrum is considered. Due to the splitting, phonon-assisted hops from one impurity to another axe accompanied by rotation of the electron spin, which leads to spin relaxation. The system is strongly inhomogeneous because of exponential variation of hopping times. However, at very small coupling an electron diffuses over a distance exceeding the characteristic scale of the inhomogeneity during the time of spin relaxation, so one can introduce an averaged spin relaxation rate. At larger values of coupling, the system is effectively divided into two subsystems: one where relaxation is very fast and another where relaxation is rather slow. In this case, spin decays due to the escape of the electrons from one subsystem to another. As a result, the spin dynamics is nonexponential and hardly depends on spin-orbit coupling. The text was submitted by the authors in English.     

Theory of hopping conductivity in disordered semiconductors

The bond percolation method is used to investigate the conditions under which a linear (and not exponential) temperature dependence of hopping conductivity can be observed.Translated from Izvestiya Vysshikh Uchbenykh Zavedenii, Fizika, No.2, pp. 52–62, February, 1976.