The electrical properties of DNA molecules have attracted increasing attention both among biologists and physicists. It has been shown that the thermal fluctuations in base-base couplings in a DNA can have dramatic effects on its dc conductance. However, the effects of the thermal fluctuations on the ac transport have only been poorly studied. In this work, we present a numerical study of the ac conductance of a poly(C)-poly(G) DNA molecule using nonequilibrium Green's function technique.
The system we consider is a 60-base-pair poly(C)-poly(G) DNA sequence connected to the outside electrodes via semi-infinite type-G DNA molecules. The whole system is described by a tight-binding model. The thermal expansions and fluctuations of the twist angles between neighboring bases are considered and treated by a temperature-dependent hopping integral model. A general formula for the charge current through the system under an ac bias is derived. It is shown that for a small input ac signal, the charge current can be written as a sum of the steady-state component and the ac response component. The charge-current conductance is then obtained based on its definition, and the full ac conductance is obtained by summing up the contributions from both the charge and the displacement current.
It is found that the thermal fluctuations of the hopping integrals play the prominent role in determining the ac conductance behavior of the DNA molecule. At low frequencies, the role of the thermal fluctuations is largely to suppress the conductance. However, when the frequency becomes higher, the major role of the thermal fluctuations is to smooth out the full conductance curve. It is also found that at low temperatures the carrier transport is dominated by thermal excitation mechanism and, thus, the conductance is increased with increasing temperature. However, when the temperature becomes higher than a critical point, the effect of the thermal fluctuations of the hopping integrals will overwhelm the thermal excitation mechanism, and the conductance quickly decreases to zero with increasing temperature. Finally we find that the thermal fluctuations can turn the inductive behavior of the ac conductance into the capacitive behavior at low signal frequencies.
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