Dispersive hopping conduction in quasi-one-dimensional systems

The a.c. conductivity of aperiodic DNA revisited

“…The s value for the base pair stack was at v ¼ 10 11 s 21 in the order of 1 V 21 cm 21 , while for the single base stack it reached saturation already at v ¼ 10 5 s 21 with a value of s ¼ 10 25 V 21 cm 21 : The large difference between the lsl values belonging to the single-and double stack could be easily understand by the fact that in the theory a Boltzmann factor of the form e 2 DE ij k B T plays an essential role [10][11][12][13]. Since in base pair stacks the level differences are much smaller than in the case of a single base stack, the Boltzmann factors are much larger in base pair stacks, than in the single base stack.…”

“…In the first paper the conductivity was determined as a function of frequency at room temperature and also correlation effects [1] have been taken into account. This was performed (1) by applying the negative factor (NFC) method for the density of states of the disordered stacks [4][5][6][7][8] (2) the Anderson localization of the wave functions was computed by the inverse iteration method [9] (3) as third step, the hopping frequencies were determined with the help of the simple expression given in the book of Mott and Davis [10] assuming the interaction of the free charge carriers with the acoustic phonons (they are in the case of the stacked nucleotide base pairs the vibrations of the base (pairs) with respect to each other along the main axis of the DNA double helix) (4) as last step the random walk theory of Lax and coworkers was applied in a somewhat generalized form [11][12][13][14]. After obtaining in this way the diffusion constant of the electrons, this was substituted into Einstein's relation providing the frequency and temperature-dependent complex hopping conductivity.…”

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“…Subsequently, we will only consider charge motion in some semiconducting crystalline compounds in which small-polaron hopping occurs on sites distributed regularly. Odagaki et al [24] have studied the stochastic transport in one-dimensional hopping conductors (electronic or ionic), in which two or more kinds of hopping rate are distributed regularly. If we consider a double-well system between two finite potential barriers, the model of Odagaki et al [24] predicts one Debye dielectric relaxation.…”

“…Odagaki et al [24] have studied the stochastic transport in one-dimensional hopping conductors (electronic or ionic), in which two or more kinds of hopping rate are distributed regularly. If we consider a double-well system between two finite potential barriers, the model of Odagaki et al [24] predicts one Debye dielectric relaxation. According to Fröhlich [25] and Bosman and van Daal [17], the Debye dielectric relaxation can only occur with small-polaron formation in low-mobility semiconductors [26][27][28][29][30][31][32][33][34][35][36][37][38].…”

“…According to Fröhlich [25] and Bosman and van Daal [17], the Debye dielectric relaxation can only occur with small-polaron formation in low-mobility semiconductors [26][27][28][29][30][31][32][33][34][35][36][37][38]. As the dielectric relaxation is the result of an electric dipole reorientation, we have to consider only local (confined) hopping of small polarons around an immobile ion [17,21,29] or in a double-well system between two finite potential barriers [24,30]. The dielectric relaxation time corresponds to the hopping time of the charge and is generally thermally activated.…”