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Correlated Disorder in One-dimensional Electronic Systems

Niaz Ali Khan

Published Jul 30, 2019• 6 citations
Publisher
DOI
10.34626/x741-2n42

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We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger-liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit. Our approach provides a framework for a systematic study of mesoscopic effects in strongly correlated electron systems.
The effects of long-range power-law correlation on the intrinsic energy,intrinsic wave function and entanglement of one-dimensional disorder system were studied,and the changes of localization were observed.The results show that the entanglement of the three measures is fully enough to reflect the properties of correlation.As an example of correlation,the entanglement of DNA molecular chain was studied using the Anderson model.The results show that the entanglement has similar properties with the correlation and reflects the properties of the correlation.
We investigate a freezing transition of correlated electrons in coupled two-dimensional layers in the presence of small levels of disorder using mode-coupling theory. The transition is primarily driven by correlations within the layers, but coupling between the layers is essential for the transition to occur. When the layers are far apart the ground state is a coupled electron liquid, but as the layers are brought closer, the Coulomb interactions between the layers drives the system to a coupled solid phase. The presence of one solid layer acts like additional disorder for the other layer. If the density of one layer is increased, at some critical value there is a transition in that layer to a solid phase that is weakly localized.