Quantum Transport In Mesoscopic Interferometers

The concept of mesoscopic sysyems is gradually formed when the physicistsstudying the disordered systems in the condensed matter physics. Due to the uniquequantum mechanics properties, it already leded the semiconductor nanoelectronics,which is based on the quantum theories, becoming to one of the hot topic in condensedmatter physics, materials and semiconductor physics. Nowadays, with the developmentsof the science, technology and micro-machining technology, it is possible to product thequantum device whose size can reach to the mesoscopic size. Hence, studing of theelecton transport in mesoscopic systems, whatever for theory or experiment, has beenattracted much interests.Futhermore, the quantum coherent phenomenons have been observed in varies ofthe mesoscopic systems for electron transport, especially the Aharonov-Bohm (AB)effects exhibited the quantum coherence in mesoscopic ring structutes. When applyingan external magnetic field, quantum coherence from electrons passing through twopaths will result conductance oscillation in parallel quantum resistances. Due to themagnetic flux in an isolated mesoscopic ring, it can produce a circulating current alongthe ring direction. This current is namely the persitent currents. After the study of thepersitent currents, in1995, Javarnnar and Deo found that, when they investigate theopen mesoscopic ring, it also exists a current circulating along the ring direction withoutthe external magnetic field. Moreover, if the applied bias is stable, this current isdissipation and has exists forever. It breaks down the thinking way of physicists for that,only with the case of the magnetic field existing, the current can circulate in themesoscopic ring. At the beginning, people called this current to be persistent current.However, with the deeper understanding this current, people found that this currentcirculating along the ring direction is totally different from the persisten current. Until tonow, people still can not clearly understand the properties and oringin of the persistencurrents and the circulating currents.This work will study the quantum transport in mesoscopic interfere devices,especially for the essence of further comparison between the persistent current and thecirculating current in mesoscopic rings. It is also studied the difference from thecirculating current definitions in the pictures of Buttiker and Jayannavar-Deo, and gavea circulating current definition original from the different physics in mesoscopic interferometer rings. Actally, for the electron transport with AB magnetic flux, Onsagerrelations require the transport current should be the even function of the AB magneticflux. Due to this necessary requirement, we count that this two current formulas havedifferent origin in physics. One of them is the circulating current produced by thequantum interference which is based on the even function of the local current.To the above illustrating, in Sec. II, we will study a two-lead mesoscopicinterferometer ring without the applied magnetic field. We will answer the Fanoantiresonance is the necessary requirement to produce the circulating current in electrontransport. We give a universal definition of the circulating current for the two-leadmesoscopic interferometers. This definition can distinguish the Buttik’s definition inclassical and quantum parts which are confused quite often. It also removes the classicalpart completely.It is found that the quantum interference between the propagating andthe evanescent waves can induce a circulating current without transmissions zeros evenfor a mesoscopic interferometer with symmetric arm lengths. A Fano antiresonance ofthe electron transmission was shown to start appearing at a critical value of theasymmetric arm lengths. As a result, it was shown that Fano antiresonance is not anecessary requirement for circulating currents in two-terminal mesoscopicinterferometers.Furthermore, in Sec. III, we have investigated the quantum interference andcorrelation for electron transport through an Andreev interferometer. We found that theasymmetric line shape of Fanoantiresonances transmissions is generated in ourinterferometer when the quasiparticle excitation energy is zero. When the quasiparticleexcitation energy less than the superconducting gap energy, the Fano-antiresonances ofthe electrons and holes is split into two, which locate at a lower and a higher energiesthan the antiresonance energy, due to the superconducting correlation andFano-interference. However, the electron-like quasiparticle can directly transport intothe superconductor if the excitation energy becomes bigger than the superconductor gapenergy, it lead to the Fano-Andreev antiresonances survive for hole-like quasiparticletransport but the higher energy one for electron-like quasiparticle disappears. We alsofound that the circulating quasiparticle currents can be induced in the interferometeraround the Fano-Andreev antiresonant energies due to the asymmetric arm lengthes ofthe interferometer. We also discussed the effects of non-zero interfacial potential on thetransport and circulating currents. We find that, at the superconductor interface, thetransport and the circulating currents normalized by their current amplitudes for the clean superconductor interface have the same I(Z)-Z curve. Based on this universalnormalized current, the three types of normalized current behaviors are clarified.Compared to normal superconducting junctions, one of the three types of the currentbehaviors shows a quasi-oscillating suppression as the interface potential strengthincreases. It is shown that, when the Fermi energy near the Fano-Andreev antiresonanceenergy, the interplay between the superconducting correlation and quantum interferenceraise the unique oscillating-like behavior due to the manybody correlation and thequantum interference in our interferometer for the Andreev transport. The quasiparticletransport currents do not exhibit such a behavior. Also, for given Fermi energies, wediscuss the critical values of the excitation energy for the current behavior transitionamong the three types of the normalized currents. Hence, the current behaviors show acharacteristic transition diagram in association with the excitation energy. When theFermi energy becomes far away from the Fano-Andreev antiresonance, it is found thatonly Andreev hole current can circulate along the interferometer loop for a certainFermi energy region. It may be another demonstration of the existence of Andreev hole.In Sec. IV, I briefed the summery and conclusion for this thesis, and mentionedsome deficiencies which should be improved henceforth. Also, I give several goodprospects for keeping study this area.