Quantum Transport Properties Driven By Different Mechanisms In The Fano Interferometers

Quantum dot (QD), due to its bound electronic states, shows rich physicalproperties and potential application value. Thus, during past long time, it has beena major concern in field of mesoscopic physics. A remarkable property of QD isthat mutiple QDs can be coupled together to form a QD molecule structure.Compared to the single QD, QD molecule structure can provide multipleFeynman paths for the electron motion. Quantum interference between differentFeynman paths makes the QD structures exhibit rich quantum transport results.With respect to the complicated quantum interference, Fano interference is typicaland shows marked property. If QD system provides nonresonant and resonantchannels for electron motion, Fano interference will occur, manifested byantisymmetric transport spectrum. On the other hand, another bound state, i.e.,Majorana bound state (MBS) has been successfully observed in theone-dimensional topological superconductors. Although this bound state isdifferent from the electronic bound states, the quantum transport in its-existedmesoscopic circuit will also be affected by the quantum interference, and showthe rich physics properties. Under this background, this thesis is to research thequantum transport through the Fano interferometer formed by QDs or MBSs,using the non-equilibrium Green’s functions and the scattering matrix method.And then we will analyze the realization of spin manipulation and feasibility toimprove thermoelectric efficiency in such systems. The basic physical ideas ofthis thesis are as follows: quantum coherence is a basic physical mechanismleading mesoscopic quantum transport properties, transport properties ofmesoscopic systems. So, we must reveal the quantum coherent picture whenstudying the quantum transport properties, which is a main line through in thisthesis. This paper carried out the following research work:First of all, we investigate the spin accumulations of the Fano interferometers,by considering spin bias in the leads. We found that regardless of theinterferometer configurations, the spin accumulations are closely determined by their quantum interference features. This is mainly manifested in the dependenceof spin accumulations on the threaded magnetic flux and the transmission process.Namely, in the single-QD Fano interferometer, the Fano effect is a necessarycondition to achieve the spin accumulation in the QD of the resonant channel. Inthe Fano interferometer with parellel coupled multiple-QDs, we find that the spinaccumulation can be achieved via electrically adjusting the left-rightantisymmetry of the QD-lead couplings or introducing different magnetic fluxesthrough the sub-rings of this system. And, the spin accumulation properties areclosely dependent on the number of QDs in this structure. Compared with theelectrical method, the magnetic method is more efficient to manipulate the spinaccumulation. When the intradot Coulomb interaction is considered, theelectrically induced spin accumulation is somewhat suppressed, but in themagnetic method the spin accumulation is efficiently enhanced. We believe thatthe results can be observed in the experiment of spintronics, which provides analternative scheme for spin manipulation.Secondly, the Andreev reflection in an Aharonov-Bohm-Fano ring induced byMBSs is theoretically investigated. We find that compared with the Fano effect inthe normal electron tunneling process, the Fano effect here is more determined bythe structural parameters, i.e., the quantum dot level, the dot-MBS coupling, andthe dot-MBS and MBS-lead couplings. By transforming the ring into its Namburepresentation, we present a comprehensive analysis about the quantuminterference in the Andreev reflection, and then explain the reason for theoccurrence of the Fano effect. These results will be helpful for understanding thequantum interference in the MBS-assisted Andreev reflection.Thirdly, the transport properties in paired MBSs in a parallel junction aretheoretically investigated, by considering the influence of different MBS-leadcoupling manners, i.e., left-right asymmetric coupling, upper-down asymmetriccoupling, and left-right upper-down asymmetric coupling. The calculation resultsshow that the MBS-lead coupling manners affect the transport properties in asubstantial way. For the former two configurations, the shot noise Fano factor inthe zero-bias limit is related to the value of the conductance maximum withF0=1+0.5Tmax(Conductance G=e2/hT). When both the left-right and upper-downsymmetries are broken, such a relation is modified into F0=1-0.5T0. These results will be helpful for describing the transport characteristics of the junction withMBSs.Finally, we investigate the thermoelectric properties of a laterally coupleddouble-QD structure. For this structure, a one-dimensional QD chain between twoleads forms a main channel for electron transmission, and each QD in the chainlaterally couples to an additional QD. It is found that at low temperature, similarinsulating bands emerge around the antiresonant points in the electronic andthermal conductance spectra. And, the edges of the insulating bands become steeprapidly with the increase of QD numbers. What’s interesting is that strikingthermoelectric effect exists in the energy region where the insulating bands appear.Furthermore, with the formation of the insulation bands, the magnitude of theSeebeck coefficient becomes stable, whereas the thermoelectric efficiency isincreased. By plotting the Lorentz number spectrum, we observe that in such astructure, the Lorentz number strongly violates the Wiedemann-Franz law in theinsulating-band region with its maximum at the point of antiresonance. Whenweak intradot Coulomb interaction is taken into account, the weakenedthermoelectric effect can still be improved with the increase of QD numbers.