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.     

On thermopower in hopping transport

Certain general aspects of hopping transport in the context of thermopower are reinvestigated. Onsager symmetry of the macroscopic kinetic coefficients is derived from detailed balance of the microscopic coefficients of the kinetic equation by an expansion of the kinetic equation around local equilibrium in an external potential and temperature gradient. The resulting expression for the thermopower differs from expressions proposed in the literature. The difference however, seems to be small.     

Multiphonon hopping in disordered semiconductors

Equations of motion for the nonequilibrium single-frequency density matrix are used to obtain a balance equation describing the kinetics of electron hopping between localized states in disordered semiconductors. Conclusions are drawn about the applicability of the theory of multiphonon processes to systems with a small nonadiabaticity. The decoupling used is a generalization of one used earlier to the multiphonon case. The balance equation found in the Markov approximation for the average number of sites occupied in an electric field contains the field dependence of the multiphonon-transition probability, tending to the well-known weak-field limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.2, pp.35–42, February, 1976.In conclusion the author is grateful to V. L. Bonch-Bruevich and A. G. Mironov for discussing this work.     

Synchronization of chaotic mode hopping

We propose and demonstrate a scheme for generating synchronized chaotic mode hopping in two wavelength-tunable lasers whose tuning range covers multiple longitudinal modes. Chaotic mode hopping resulting in large hops in wavelength is induced by delayed electrical feedback. We show that, by coupling part of the output of one laser into another, one can synchronize the chaotic mode hopping of two separate lasers and obtain synchronized chaotic on-off modulation patterns in multiple corresponding wavelength bands.     

Symmetrized general hopping current equation

We show that within the validity range of local thermal equilibrium--therein, however, irrespective of the magnitude of the driving force--a simple current equation can be formulated that expresses the current in terms of a product of a local nonequilibrium conductivity and a sinh function of half the electrochemical potential drop (normalized with respect to kBT) over the local hopping distance. This local current/driving force relation takes account of both electrical and compositional effects and can be generalized as to include interactions and structural variations.     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

Rate equations in the hopping transport

The rate equation formulation of the hopping transport problem is analyzed in detail. It is shown that the usual form of the rate equations for the system of electrons in localized states interacting with phonons is incorrect in the dc limit. A generalized form of the rate equations is derived. Both usual solution and that one corresponding to the result ofKasuya andKoide for the dc conductivity are shown to solve these equations. However, the former one is shown to be improper from the physical point of view as well as from the point of view of a (for a given model) exact asymptotic identity derived. For high frequencies, both forms of the rate equations are shown to be indistinguishable.     

Organic magnetoresistance based on hopping theory

For the organic magnetoresistance(OMAR) effect, we suggest a spin-related hopping of carriers(polarons) based on Marcus theory. The mobility of polarons is calculated with the master equation(ME) and then the magnetoresistance(MR)is obtained. The theoretical results are consistent with the experimental observation. Especially, the sign inversion of the MR under different driving bias voltages found in the experiment is predicted. Besides, the effects of molecule disorder,hyperfine interaction(HFI), polaron localization, and temperature on the MR are investigated.     

Variable range hopping conductivity in manganites

The nature of variable range hopping (VRH) conductivity which is observed in the insulating state of doped rare-earth manganites with perovskite structure is considered in the two component model of metallic-like droplets embedded in dielectric matrix. When the density of the metallic droplets is less than the percolation limit, the system falls into the insulating state with VRH conductivity defined by inter granular tunneling and electrostatic barriers. With temperature increasing the VRH regime is transforming into the hopping regime of small radius polarons.     

ac Impurity hopping conducting in p-InSb

We report the first measurement of the ac conductivity of p-InSb at low temperatures in the fréquency range 10 −10¹⁰ Hz. The conductivity has been determined from the gathering of three sets of data, the dc conductivity curve, the conductivity data obtained from an ultrasonic experiment and the microwave conductivity. Frequency effects have only been observed in the hopping conduction regime. It was found that the ac conductivity varies as ω (S=0.75). The results are discussed in relation with the single-phonon hopping theory.     

Activation energies in hopping transport systems

A phenomenological theory of carrier transport under non-isothermal conditions has been developed to deduce the activation energies (δ) from thermally stimulated current measurements. This theory applies to hopping transport systems as well as band transport systems, but unlike existing theories, it is not limited to band transport systems. The determination of δ by the new method is intrinsically more accurate than existing heating-rate methods, making it possible to study small changes in δ such as field-dependence. The discussion is illustrated with data measured in amorphous PVK.     

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.     

Direct current hopping conductance along DNA chain

This paper proposes a model of direct current (DC) electron hopping transport in DNA, in which DNA is considered as a binary one-dimensional disordered system. To quantitatively study the DC conductivity in DNA, it numerically calculates the DC conductivity of DNA chains with different parameter values. The result shows that the DC conductivity of DNA chain increases with the increase of temperature. And the conductivity of DNA chain is depended on the probability p, which represents the degree of compositional disorder in a DNA sequence to some extent. For p<0.5, the conductivity of DNA chain decreases with the increase of p, while for p\geq0.5, the conductivity increases with the increase of p. The DC conductivity in DNA chain also varies with the change of the electric field, it presents non-Ohm's law conductivity characteristics.     

Giant magnetoresistance in the variable-range hopping regime

We predict the universal power-law dependence of the localization length on the magnetic field in the strongly localized regime. This effect is due to the orbital quantum interference. Physically, this dependence shows up in an anomalously large negative magnetoresistance in the hopping regime. The reason for the universality is that the problem of the electron tunneling in a random media belongs to the same universality class as the directed polymer problem even in the case of wave functions of random sign. We present numerical simulations that prove this conjecture. We discuss the existing experiments that show anomalously large magnetoresistance. We also discuss the role of localized spins in real materials and the spin polarizing effect of the magnetic field.