Characteristic Of Electronic Transport In One-dimensional And Quasi-one-Dimensional Disordered Systems

Based on the Hamiltonian of the tight-binding model describing a single electron band, the methods solving the multi-diagonal sysmetric random matrixes which are developed from the negative eigenvalue theory and infinite order perturbation theory, the transfer-matrix approach and the renormalization group method, the thesis studies the electronic stucture and the characteristic of electron transport of the one-dimensional binary disordered DNA chain, qausi-periodic sequence of Cantor and Rudin-Shapiro DNA chains, SRY (Sex determining Region Y) gene sequence one-dimensional, quasi-one-dimensional disordered systems, quasi-one-dimensional DNA chain of fish-bone model and quasi-one-dimensional DNA chain of Ladder model.(1) The saturation current intensity of one-dimensional binary disordered DNA chain composed by one kind of nucleotide base pair is much higher than that composed by two kinds of nucleotide base pairs. And when the contents of the two base pairs are equal, the saturation current intensity is the minimum. Meanwhile, the DNA molecule which is rich in G-C base pair has higher electronic transport ability than that of A-T. The effects of metal electrode potential on the electronic transport of DNA molecules are reflected in two aspects:when the bias is small, the electrode potential has the effect of impeding charge injection; when the bias is larger, the electrode potential enhances the charge injection. In addition, when the coupling strength is equal to the interactions between the base pairs of DNA molecules, there is a resonance injection, and is optimized for electron transport. When the coupling strength is greater than the interactions between the base pairs of DNA molecules, as the coupling strength increases, the charge injection capacity decreases and its saturation current density decreases accordingly.(2) In the qausi-periodic sequence of Cantor and Rudin-Shapiro DNA chains, the extended states, localized states and critical states are coexisted. The displacement and the stability of the change of the scale about the standard diviation curve prove the scaling invariability and and self-similarity in the qausi-periodic sequence of Cantor and Rudin-Shapiro DNA chains. The Hurst exponent of Cantor DNA chains is about 0.23, which is less than 0.5, indicating that the system has an inherent positive correlation. The Hurst exponent of Rudin-Shapiro DNA chains fluctuates around 0.5, indicating that different parts of the sequence associated with different correlation attributes, that is, some parts show positive correlation while some parts show negatively correlation. There are a considerable number of extended states which are propitious to transmit in the qausi-periodic DNA sequence. And with the increase of the sequence length, the energy range of extended states become bits and pieces; meanwhile, the number, height and localization position of formants also change, lead to the decrease of extended states which are propitious to transmit but they can maintain to exit in the relatively long sequences. It is speculated that there is correlation in qausi-periodic sequence of Cantor and Rudin-Shapiro DNA chains, and relatively speaking, the correlation in Rudin-Shapiro DNA chains is weaker than that in the Cantor DNA chains.(3) The energy eigenvalues of SRY (Sex determining Region Y) gene sequence distribute in the interval of 7.6-7.9eV. There is low density of states in the low-energy range, and there are some energy gaps with fixed width. When the number of states increases in SRY sequence, the increased states rarely appear in the energy gaps and most of which only lead to the greater densitiy in the original energy range. In most cases, the localization length of the electronic states is less than the chain length in this kind of DNA, which indicates that most of the states are localized states and the extended states only exist in a few isolated energies. Although there are some energy ranges existing in extended states, there are no continuous extended states existed, which result in the conductance in the SRY sequence can almost ignored in the thermodynamic limit. The Hurst exponent of SRY sequence is not a single value, that is, the Hurst exponent can be over or below 0.5 in different sequences, indicating that there exists positive or negative correlation in the sequence.(4) Comparing the electronic structure of one-dimensional system and quasi-one-dimensional system with two and three chains in diagonal disorder case, it is found that the non-diagonal disorder and the dimensional effect strongly affect the electronic structure in the low-dimensional disordered system; that is, the diagonal disorder causes the increase of the number of localized electrons, and the non-diagonal disorder leads to change of the distribution of the system energy; meanwhile, the peak number of the DOS increases with the increase of number of the chains, and the band gap of zero decreases.(5) The electronic states of the quasi-one-dimensional disordered systems are localized due to energy disorder of the lattices. The localization length increases with the decrease of the strength of energy disorder of the lattices. At the energy band center, there exist extent states whose localization lengths are larger than the number of the atoms of the chains in weak disorder. With the increase of the number of the chains, the delocalization is also found. Moreover, the transmission coefficient of electron transportion in quasi-one-dimensional disordered systems is much higher in the energy band center than in high and low energy region; and it decreases with the increase of the strength of energy disorder of the lattices, while increase with the increase of of the number of the chains.(6) In the quasi-one-dimensional DNA chain of fish-bone model, the skeleton greatly affects the properties of DNA molecules. With the degree of disorder W increases, the peak of electronic density of states spectrum decreases, the scope of energy eigenvalues broadens, the bands gradually tend to integrate, and the band gaps turn narrow. This reveals some characteristics of disordered systems, and various effects are resulted from various disorder cases, in which the effect of binary disorder is the most important. The electronic states of DNA sequence with environmental disorder are localized. The localized length of most of the localized states is less than the length of the system. The DNA molecules with skeleton on-site potential may have semiconductor properties with almost a stable threshold and the conductivity changes with the degree of disorder W non-monotonicly. As for quasi-one-dimensional DNA chain of Ladder model, the study shows that in the human chromosome Ch22 there should have a weak correlation. Although the correlation is still not strong enough to make the DNA chain become conductors, it can help the DNA chain have a certain ability to charge transport.