介观干涉仪中的量子输运
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摘要
介观体系这一概念是人们在研究凝聚态物理时从无序系统中逐渐形成的。由于介观系统所具有的独特量子行为，使得以量子理论为基础的半导体介观电子学成为凝聚态物理及半导体材料物理等领域的研究前沿之一。当前，随着科学技术的发展和微加工技术的进步，实验上已经能够制备出尺寸能够达到介观尺寸的量子器件。因此，对介观系统中的电子输运的研究不论从理论上还是从实验上都引起了物理学家们的极大兴趣。另外，量子相干现象已在各种介观器件的电子输运实验中观测到。Aharonov-Bohm (AB)效应展示的介观环结构中量子相干现象就是一个典型的实例。当外加磁场改变时，电子通过两条路径所产生的量子干涉效应将引起量子平行电阻中的电导振荡。对于一个孤立的介观环，磁通可以在环内产生沿着环路流动的电流，这种电流被称作持续流。1995年，Javarnnar和Deo等人在研究开放介观环的过程中发现，在无磁场的情况下介观环里也会出现一个沿着环路循环的电流。而且只要在环两端施加的偏压不变，这个电流就是无耗散的，会一直存在。这就打破了以前人们认为的只有在有磁场存在的情况下环路中才会出现循环电流的观念。刚开始人们把这个电流也叫做持续流。但是随着研究的不断深入，人们发现这个电流和前面的持续流截然不同。直到现在，人们对持续流和循环流的性质和物理起源仍然不是很了解。
本论文主要是研究介观干涉器件中的量子输运现象。特别是对介观环中的持续流和循环流的本质做了进一步的比较。具体将研究Buttiker和Jayannavar-Deo图像中的持续流定义引起的差别，以及介观干涉仪中由不同的物理根源引起的持续流定义。实际上，对于存在AB磁通的电子输运，Onsager关系要求输运电流必须是AB磁通的偶函数。由这个必要条件，我们预言这两个不同的电流公式有不同的物理起源。而其中的一个是基于局域电流的量子干涉性所引起的循环流。
在第二章中，为利用上述结论来研究量子器件中的量子输运现象，我们设计了一个不存在外磁场存在情况下的理想的两端口环路介观干涉仪（介观环）。我们回答了电子透射中Fano反共振点是否是出现循环流的必要条件的问题。同时，我们总结出了一个普适的两端口介观环中循环流的定义式。此定义式区分了Buttiker定义式中经典循环流和量子循环流混淆的部分，完全抛开了其经典的一面。从根源上阐明了其具有的普适性。我们发现即使在介观环的上下两臂长相等而量子干涉发生在传播波和衰减波之间的时候，在透射系数不为点（Fano反共振点）的时候仍然会出现一个循环流。由此可以看出循环流不仅仅在上下臂长不相等的时候才会出现。这就打破了以往人们对循环流的普遍认识。当介观环上下臂长的不对称性一直增加到某一临界值的时候，第一个Fano反共振点才会出现，而且Fano反共振点附近有循环流的存在。简言之，本章的研究证明在两端口的介观干涉仪中Fano反共振点并不是循环流产生的必要条件。
在第三章中，我们进一步研究了当两端口的介观环的其中一端连接一个超导体的情形。我们主要关注于电子在此介观干涉仪中由于超导体相关性和Fano干涉效应的共同作用下所产生的一系列量子输运现象。我们发现由于超导体相关性和量子干涉效应，在准粒子激发能为零的时候，介观干涉仪中的量子输运产生了所谓的Fano-Andreev反共振现象。在准粒子激发能为有限值的时候，每一个Fano-Andreev反共振点都会被劈裂成两个。在这些劈裂的Fano-Andreev反共振点上，包括输运电流和循环流在内的所有电流都会消失。但是对于较高的超过超导能隙的激发能量，准粒子会直接透射进超导体，从而破坏处于较高能量那个Fano-Andreev反共振点。在Fano-Andreev反共振能量附近，由于干涉仪中上下臂长不对称所引起的量子干涉形成的循环流在复能量空间上出现了两种类型的反共振结构。循环流的大小和方向在很大程度上依赖于超导相关性。在远离Fano-Andreev反共振点的地方，我们发现在特定的费米能区间内会出现只有电子型准粒子循环流或空穴型准粒子循环流的情形。因此，只有空穴型准粒子循环流存在的现象也可以作为一种用来实验上验证Andreev空穴准粒子存在的方法。另外，我们也讨论了超导体界面上的界面势效应对输运电流和循环流的影响。我们发现被纯净超导界面的电流幅值所归一化的输运电流和循环流有着同样的电流行为，并且它们显示出同样的I (Z) Z电流曲线。这就意味着超导界面势对输运电流和循环流的影响是相同的。这个普适的归一化电流随着界面势的变化遵循着三种不同的电流特征行为类型。我们也讨论到了Fano-Andreev反共振能量附近三种不同的电流特征行为类型之间的转变行为，并且给出了一个电流行为转变图。我们观察到此介观干涉仪中的一种准振荡行为的电流特征也是首次被发现。这也是由超导相关性和量子干涉的综合效应所引起的一个独特的介观现象。
在第四章中，对本论文做了简要的总结，概括了本论文中的不足之处，并展望了后续的研究工作和方向。
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.
本论文主要是研究介观干涉器件中的量子输运现象。特别是对介观环中的持续流和循环流的本质做了进一步的比较。具体将研究Buttiker和Jayannavar-Deo图像中的持续流定义引起的差别，以及介观干涉仪中由不同的物理根源引起的持续流定义。实际上，对于存在AB磁通的电子输运，Onsager关系要求输运电流必须是AB磁通的偶函数。由这个必要条件，我们预言这两个不同的电流公式有不同的物理起源。而其中的一个是基于局域电流的量子干涉性所引起的循环流。
在第二章中，为利用上述结论来研究量子器件中的量子输运现象，我们设计了一个不存在外磁场存在情况下的理想的两端口环路介观干涉仪（介观环）。我们回答了电子透射中Fano反共振点是否是出现循环流的必要条件的问题。同时，我们总结出了一个普适的两端口介观环中循环流的定义式。此定义式区分了Buttiker定义式中经典循环流和量子循环流混淆的部分，完全抛开了其经典的一面。从根源上阐明了其具有的普适性。我们发现即使在介观环的上下两臂长相等而量子干涉发生在传播波和衰减波之间的时候，在透射系数不为点（Fano反共振点）的时候仍然会出现一个循环流。由此可以看出循环流不仅仅在上下臂长不相等的时候才会出现。这就打破了以往人们对循环流的普遍认识。当介观环上下臂长的不对称性一直增加到某一临界值的时候，第一个Fano反共振点才会出现，而且Fano反共振点附近有循环流的存在。简言之，本章的研究证明在两端口的介观干涉仪中Fano反共振点并不是循环流产生的必要条件。
在第三章中，我们进一步研究了当两端口的介观环的其中一端连接一个超导体的情形。我们主要关注于电子在此介观干涉仪中由于超导体相关性和Fano干涉效应的共同作用下所产生的一系列量子输运现象。我们发现由于超导体相关性和量子干涉效应，在准粒子激发能为零的时候，介观干涉仪中的量子输运产生了所谓的Fano-Andreev反共振现象。在准粒子激发能为有限值的时候，每一个Fano-Andreev反共振点都会被劈裂成两个。在这些劈裂的Fano-Andreev反共振点上，包括输运电流和循环流在内的所有电流都会消失。但是对于较高的超过超导能隙的激发能量，准粒子会直接透射进超导体，从而破坏处于较高能量那个Fano-Andreev反共振点。在Fano-Andreev反共振能量附近，由于干涉仪中上下臂长不对称所引起的量子干涉形成的循环流在复能量空间上出现了两种类型的反共振结构。循环流的大小和方向在很大程度上依赖于超导相关性。在远离Fano-Andreev反共振点的地方，我们发现在特定的费米能区间内会出现只有电子型准粒子循环流或空穴型准粒子循环流的情形。因此，只有空穴型准粒子循环流存在的现象也可以作为一种用来实验上验证Andreev空穴准粒子存在的方法。另外，我们也讨论了超导体界面上的界面势效应对输运电流和循环流的影响。我们发现被纯净超导界面的电流幅值所归一化的输运电流和循环流有着同样的电流行为，并且它们显示出同样的I (Z) Z电流曲线。这就意味着超导界面势对输运电流和循环流的影响是相同的。这个普适的归一化电流随着界面势的变化遵循着三种不同的电流特征行为类型。我们也讨论到了Fano-Andreev反共振能量附近三种不同的电流特征行为类型之间的转变行为，并且给出了一个电流行为转变图。我们观察到此介观干涉仪中的一种准振荡行为的电流特征也是首次被发现。这也是由超导相关性和量子干涉的综合效应所引起的一个独特的介观现象。
在第四章中，对本论文做了简要的总结，概括了本论文中的不足之处，并展望了后续的研究工作和方向。
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.
引文
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