本文選題：Fano干涉器　切入點：量子點　出處：《吉林大學》2015年博士論文　論文類型：學位論文

【摘要】：介觀體系中的Fano干涉做為一種典型的量子干涉機制，在很長時間以來一直受到研究者的關(guān)注。如果介觀體系能夠為電子運動同時提供非共振和共振通道，則將會導致Fano干涉發(fā)生，其標志為量子輸運譜的反對稱線型。量子點，由于其中電子束縛態(tài)的存在而能夠為Fano干涉的實現(xiàn)提供共振通道，因此量子點體系中的Fano干涉機制以及由其驅(qū)動的各種輸運現(xiàn)象有必要進行深入探討。另一方面，最近實驗物理學家在一維的拓撲超導體兩端成功觀察到另一種重要的束縛態(tài)—Majorana束縛態(tài)，雖然該束縛態(tài)與電子束縛態(tài)有著本質(zhì)的不同，但是其介觀電路中的量子輸運同樣也會受到量子干涉的影響，，并表現(xiàn)出豐富的性質(zhì)。本論文正是在這種背景下，采用非平衡態(tài)格林函數(shù)以及散射矩陣方法，對由量子點或者Majorana束縛態(tài)構(gòu)成的Fano干涉器中的量子輸運性質(zhì)進行了系統(tǒng)的理論研究，進而分析了在各種Fano干涉器中實現(xiàn)自旋操控和提高熱電效率的可行性。本論文工作的基本思路如下： 首先，討論了量子點Fano干涉器件中由自旋偏壓驅(qū)動的自旋積累特征。在對單量子點Fano干涉器進行研究的過程中，發(fā)現(xiàn)當該結(jié)構(gòu)中存在局域磁通時，量子點中能夠出現(xiàn)明顯的自旋積累，而且自旋積累的方向可以通過調(diào)節(jié)磁通來實現(xiàn)控制。進一步研究發(fā)現(xiàn)，當該結(jié)構(gòu)的結(jié)構(gòu)參數(shù)滿足W=1時(W為兩引線間的直接耦合強度，為引線的態(tài)密度)，量子點將能夠完全束縛某一自旋的電子。接下來，在由量子點鏈首尾均與引線耦合而形成的復雜Fano干涉器件中，我們看到，自旋積累能通過改變量子點-金屬引線耦合的左右對稱方式或在兩個子環(huán)中引入不同磁通來實現(xiàn)，而且自旋積累性質(zhì)對該結(jié)構(gòu)的量子點數(shù)存在明顯的依賴關(guān)系。另外，和電的方法對比，調(diào)節(jié)磁通量對于操縱自旋積累更為有效。在量子點內(nèi)庫侖相互作用不為零的情況下，由電的方法導致的自旋積累在一定程度上受到抑制，而由磁方法實現(xiàn)的自旋積累卻被加強。對于這兩種結(jié)構(gòu)中的自旋積累特點，通過分析這兩種結(jié)構(gòu)中的Fano干涉和庫侖相互作用兩種因素對電子占據(jù)的影響，解釋了自旋積累產(chǎn)生的物理原因。 其次，分析了由常規(guī)金屬電極與Majorana束縛態(tài)直接耦合以及通過量子點來間接耦合而形成的單量子點Fano干涉器中的量子輸運性質(zhì)。由于Majorana束縛態(tài)可以視為是零能量的電子和空穴形成的疊加態(tài)，因此，在金屬引線中施加偏壓將會引起Andreev反射的發(fā)生。通過計算，我們分析了受Fano干涉調(diào)制的Andreev反射現(xiàn)象。發(fā)現(xiàn)，和普通電子隧穿過程中的Fano效應對比，Andreev反射譜也會呈現(xiàn)出Fano線型，并且以成對的形式出現(xiàn)。然而，此時的Fano效應受到更多參數(shù)的影響，如量子點能級、量子點-Majorana束縛態(tài)的耦合強度、兩Majorana束縛態(tài)之間的耦合以及Majorana束縛態(tài)與金屬引線之間的耦合等。通過給出該體系在Nambu表象下的新幾何結(jié)構(gòu)，我們對其中的Andreev反射進行了詳細的分析，并對Fano干涉能夠在何種調(diào)件下得以加強給出了討論。需要指出的是，在考慮自旋的情況下，Majorana束縛態(tài)將會僅與某一自旋的電子態(tài)耦合，因此，該Andreev反射也為自旋操控提供了新思路。 再次，討論了由兩Majorana束縛態(tài)與分別與左右兩引線耦合而形成的Majorana-Fano干涉器中的量子輸運性質(zhì)。通過考慮各種Majorana束縛態(tài)與金屬引線之間的耦合方式，包括：左右非對稱耦合，上下非對稱耦合，左右上下均非對稱耦合等情況，計算了其中由局域Andreev反射和交叉Andreev反射共同驅(qū)動的電導和Fano因子。發(fā)現(xiàn)，在該結(jié)構(gòu)中交叉Andreev反射和局域Andreev反射的相互制約將顯著依賴于該Fano干涉器的對稱方式。對于前面兩種情況，研究結(jié)果表明，零偏壓極限的Fano因子和Andreev反射的電導最大值之間存在可以量化的關(guān)系，具體表示為F0=1+0.5Tmax(電導公式G=e2/h*T，T為Andreev反射函數(shù))。而對于后者，即：左右和上下對稱均被破壞的情況，這種關(guān)系將被改寫為F0=1-0.5T0(T0為零偏壓的Andreev反射函數(shù)值)。這兩種不同結(jié)果的原因在于，前兩種情況中Andreev反射將受到Fano干涉的影響，而在后一種情況下Fano干涉受到壓制。 最后，研究了側(cè)向耦合的雙量子點結(jié)構(gòu)的熱電性質(zhì)。對于這個結(jié)構(gòu)，兩金屬線之間的一維量子點鏈給電子輸運提供一個主要通道，同時主鏈中每個量子點都有一量子點與之耦合。該結(jié)構(gòu)可以被看作是多個T型雙量子點通過串聯(lián)而形成的結(jié)構(gòu)。前期研究結(jié)果表明，在該結(jié)構(gòu)中Fano干涉的增強將導致電導譜中有絕緣帶出現(xiàn)�？梢灶A測，絕緣帶的出現(xiàn)將顯著增強熱電效應。通過計算，我們發(fā)現(xiàn)，在低溫情況下電導和熱導譜中在反共振點附近均會有絕緣帶出現(xiàn)。并且，隨著量子點數(shù)的增加絕緣帶邊緣迅速變陡。有趣的是，熱電效應恰恰是在絕緣帶出現(xiàn)的區(qū)域內(nèi)得到明顯加強。此外，隨著絕緣帶的形成，Seebeck系數(shù)的幅值變得穩(wěn)定，而熱電優(yōu)值卻仍然有所增加。另一方法，我們通過討論Lorentz數(shù)的性質(zhì)，發(fā)現(xiàn)在這個結(jié)構(gòu)中Lorentz數(shù)與經(jīng)典物理中的Wiedemann-Franz定律結(jié)果發(fā)生嚴重偏離，而在反共振點出將出現(xiàn)最大值。當整個體系中計入量子點內(nèi)庫侖相互作用時，熱電效應將有所減弱，但是仍然能隨著量子點數(shù)的增加而加強。
[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.

【學位授予單位】：吉林大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：O471.1;O488

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