Fano干涉器中由不同机制驱动的量子输运性质

发布时间：2018-03-13 19:27

本文选题：Fano干涉器　切入点：量子点　出处：《吉林大学》2015年博士论文　论文类型：学位论文

【摘要】：介观体系中的Fano干涉做为一种典型的量子干涉机制，在很长时间以来一直受到研究者的关注。如果介观体系能够为电子运动同时提供非共振和共振通道，则将会导致Fano干涉发生，其标志为量子输运谱的反对称线型。量子点，由于其中电子束缚态的存在而能够为Fano干涉的实现提供共振通道，因此量子点体系中的Fano干涉机制以及由其驱动的各种输运现象有必要进行深入探讨。另一方面，最近实验物理学家在一维的拓扑超导体两端成功观察到另一种重要的束缚态—Majorana束缚态，虽然该束缚态与电子束缚态有着本质的不同，但是其介观电路中的量子输运同样也会受到量子干涉的影响，，并表现出丰富的性质。本论文正是在这种背景下，采用非平衡态格林函数以及散射矩阵方法，对由量子点或者Majorana束缚态构成的Fano干涉器中的量子输运性质进行了系统的理论研究，进而分析了在各种Fano干涉器中实现自旋操控和提高热电效率的可行性。本论文工作的基本思路如下：首先，讨论了量子点Fano干涉器件中由自旋偏压驱动的自旋积累特征。在对单量子点Fano干涉器进行研究的过程中，发现当该结构中存在局域磁通时，量子点中能够出现明显的自旋积累，而且自旋积累的方向可以通过调节磁通来实现控制。进一步研究发现，当该结构的结构参数满足W=1时(W为两引线间的直接耦合强度，为引线的态密度)，量子点将能够完全束缚某一自旋的电子。接下来，在由量子点链首尾均与引线耦合而形成的复杂Fano干涉器件中，我们看到，自旋积累能通过改变量子点-金属引线耦合的左右对称方式或在两个子环中引入不同磁通来实现，而且自旋积累性质对该结构的量子点数存在明显的依赖关系。另外，和电的方法对比，调节磁通量对于操纵自旋积累更为有效。在量子点内库仑相互作用不为零的情况下，由电的方法导致的自旋积累在一定程度上受到抑制，而由磁方法实现的自旋积累却被加强。对于这两种结构中的自旋积累特点，通过分析这两种结构中的Fano干涉和库仑相互作用两种因素对电子占据的影响，解释了自旋积累产生的物理原因。其次，分析了由常规金属电极与Majorana束缚态直接耦合以及通过量子点来间接耦合而形成的单量子点Fano干涉器中的量子输运性质。由于Majorana束缚态可以视为是零能量的电子和空穴形成的叠加态，因此，在金属引线中施加偏压将会引起Andreev反射的发生。通过计算，我们分析了受Fano干涉调制的Andreev反射现象。发现，和普通电子隧穿过程中的Fano效应对比，Andreev反射谱也会呈现出Fano线型，并且以成对的形式出现。然而，此时的Fano效应受到更多参数的影响，如量子点能级、量子点-Majorana束缚态的耦合强度、两Majorana束缚态之间的耦合以及Majorana束缚态与金属引线之间的耦合等。通过给出该体系在Nambu表象下的新几何结构，我们对其中的Andreev反射进行了详细的分析，并对Fano干涉能够在何种调件下得以加强给出了讨论。需要指出的是，在考虑自旋的情况下，Majorana束缚态将会仅与某一自旋的电子态耦合，因此，该Andreev反射也为自旋操控提供了新思路。再次，讨论了由两Majorana束缚态与分别与左右两引线耦合而形成的Majorana-Fano干涉器中的量子输运性质。通过考虑各种Majorana束缚态与金属引线之间的耦合方式，包括：左右非对称耦合，上下非对称耦合，左右上下均非对称耦合等情况，计算了其中由局域Andreev反射和交叉Andreev反射共同驱动的电导和Fano因子。发现，在该结构中交叉Andreev反射和局域Andreev反射的相互制约将显著依赖于该Fano干涉器的对称方式。对于前面两种情况，研究结果表明，零偏压极限的Fano因子和Andreev反射的电导最大值之间存在可以量化的关系，具体表示为F0=1+0.5Tmax(电导公式G=e2/h*T，T为Andreev反射函数)。而对于后者，即：左右和上下对称均被破坏的情况，这种关系将被改写为F0=1-0.5T0(T0为零偏压的Andreev反射函数值)。这两种不同结果的原因在于，前两种情况中Andreev反射将受到Fano干涉的影响，而在后一种情况下Fano干涉受到压制。最后，研究了侧向耦合的双量子点结构的热电性质。对于这个结构，两金属线之间的一维量子点链给电子输运提供一个主要通道，同时主链中每个量子点都有一量子点与之耦合。该结构可以被看作是多个T型双量子点通过串联而形成的结构。前期研究结果表明，在该结构中Fano干涉的增强将导致电导谱中有绝缘带出现。可以预测，绝缘带的出现将显著增强热电效应。通过计算，我们发现，在低温情况下电导和热导谱中在反共振点附近均会有绝缘带出现。并且，随着量子点数的增加绝缘带边缘迅速变陡。有趣的是，热电效应恰恰是在绝缘带出现的区域内得到明显加强。此外，随着绝缘带的形成，Seebeck系数的幅值变得稳定，而热电优值却仍然有所增加。另一方法，我们通过讨论Lorentz数的性质，发现在这个结构中Lorentz数与经典物理中的Wiedemann-Franz定律结果发生严重偏离，而在反共振点出将出现最大值。当整个体系中计入量子点内库仑相互作用时，热电效应将有所减弱，但是仍然能随着量子点数的增加而加强。
[Abstract]:Fano interference in a mesoscopic system as a typical quantum interference mechanism, in a very long time has been the concern of researchers. If the system is able to mesoscopic electron motion while providing non resonant and resonant channel, will lead to Fano interference, the symbol for the quantum transport spectrum of antisymmetric linear quantum dots. Among them, because of the presence of bound electronic states can provide resonant channel for realization of Fano interference, therefore the quantum dot Fano interference mechanism and driven by the transport phenomena should be investigated deeply. On the other hand, the most recent experimental physicist ends in one-dimensional topological superconductors is successfully observed in another bound Majorana important bound state, although the bound and bound electronic states are essentially different, but the quantum transport in the mesoscopic circuit also will be affected by the quantum interference effect , and exhibit rich properties. This paper is in this context, using the nonequilibrium Green function and the scattering matrix method of quantum dots or by Majorana bound Fano quantum interference in transport properties are studied, and then analyzes the realization of spin manipulation in a variety of Fano interference the feasibility and efficiency of the device. To improve the thermoelectric basic ideas of this dissertation are as follows:
First of all, discussed the quantum dot Fano interferometer driven by spin spin bias device. In the process of accumulation of single quantum dot Fano interferometer was developed, when the existence of local magnetic flux in the structure, obvious spin accumulation can in quantum dots, and spin accumulation can adjust the flux to the direction of to realize the control. Further study showed that when the structure parameters of the structure meet W=1 (W is the direct coupling strength between the two lead wire density), quantum dots can complete a bound electron spin. Next, Fano in complex with quantum dots and chain formed with wire coupling interference device and we see that the spin accumulation by changing the quantum dot coupled metal wire symmetrical way or in the two sub loop to achieve different flux, and the properties of the quantum spin accumulation structure Has a strong dependence on points. In addition, contrast and electrical methods, adjusting the flux for manipulation of spin accumulation is more effective. In quantum dot Coulomb interaction is not zero, spin caused by electrical methods accumulation was inhibited to a certain extent, while the spin is realized by the accumulation of magnetic method be strengthened. For these two kinds of spin accumulation in the structure characteristics, through the analysis of the interaction of these two kinds of structure of Fano interference and Coulomb two factors on the influence of electronic occupied, explained the physical reasons of spin accumulation generated.
Secondly, the analysis of a single quantum dot by conventional metal electrode and the Majorana bound directly to the indirect coupling and coupling of the quantum dot and the formation of Fano quantum interference in transport properties. Because Majorana bound state can be regarded as the superposition of zero energy electrons and holes formed so will bias in the metal wire cause Andreev reflection. Through calculation, we analyzed Andreev reflection interference modulation by Fano. And found that ordinary electron tunneling effect in contrast to Fano, Andreev reflection spectrum also shows the Fano line, and in pairs form. However, the effect of Fano by more parameters the level, such as quantum dots, coupling strength of -Majorana quantum dots bound, two Majorana bound state between the coupling and the coupling between the Majorana and the bound state of metal wire. Through to the body A new geometric structure system in Nambu representation, we carried out a detailed analysis on the Andreev reflection, and Fano interference can be strengthened are discussed in what tone condition. Need to point out that in the case of considering spin, Majorana bound electronic states will be coupled with a spin only. Therefore, the Andreev reflection also provides new ideas for spin manipulation.
Thirdly, we discuss the two Majorana bound states and respectively with about two lead coupling and the formation of Majorana-Fano quantum interference in transport properties. By considering all kinds of Majorana bound state and the coupling mode between the metal wire include: asymmetrical coupling, asymmetric coupling, on the left and right sides are asymmetric coupling. Among them, the conductance and Fano factor driven by local Andreev reflection and crossed Andreev reflection. The calculations show that the interaction of crossed Andreev reflection and local Andreev reflection in the structure will significantly depend on the Fano symmetry is involved in stem. For the previous two cases, the results show that the relationship can be quantified the maximum conductance between Fano factor and Andreev reflection zero bias limit, specifically expressed as F0=1+0.5Tmax (G=e2/h*T T Andreev conductance formula, the reflection function and for the latter), Namely: under symmetric and had been destroyed, this relationship will be rewritten as F0=1-0.5T0 (Andreev T0 for the reflection function of zero bias value). This is the reason the two different results, the first two cases of Andreev reflex will be affected by Fano interference, while in the latter case Fano the interference is suppressed.
Finally, the thermoelectric properties of double quantum dot structure lateral coupling. In this structure, a one-dimensional quantum dot chain between the two metal wire for electron transport provides a main channel, and the backbone of each quantum dot has a quantum dot coupled. The structure can be viewed as a T type structure double quantum point series formed. Our previous study showed that the enhancement in the structure of Fano interference will result in the conductance spectrum in an insulating band. With the emergence of insulation can be predicted, will significantly enhance the thermoelectric effect. Through calculation, we find that the conductance at low temperature conditions and the thermal conductivity spectrum in the vicinity of the anti the resonance are insulating tape. And, with the increase of the number of dots with insulation edges become steep. Interestingly, the thermoelectric effect is enhanced in the insulating tape area. In addition, with the formation of insulating tape Seebeck, the amplitude coefficient becomes stable, while the ZT value still increased. Another method, we discussed the properties of Lorentz numbers, it is found that Wiedemann-Franz's law in the structure of Lorentz number and classical physics results in serious deviation in the anti resonance point will appear. When the maximum quantum point the Coulomb interaction in the system, the thermoelectric effect will be weakened, but still increases with the increasing of the number of dots.

【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O471.1;O488

【参考文献】