量子波導管中電子在非均勻磁場中性質之研究

Abstract

本論文研究了量子波導管(quantum waveguide)中電子在非均勻磁場中性質。量子波導管中的量子束縛態(quantum bound state)與電子傳輸(transport)現象被詳細的研究。我們的結果顯示波導管中的量子束縛態與電子傳輸都強烈的受到幾何參數的影響，無論是考慮外加磁場或不加磁場。無古典對應的量子現象有二：一是量子束縛態、二是無磁場區的電子行為受磁場的明顯影響。 L型與T型開放性波導管中量子束縛態，是真正的束縛態。它的特徵能級Ebs低於量子線中最低的次能帶(subband)能級E1，因此電子被束縛於L型波導管的角落區或T型的交界區。如果改變幾何參數(□=W1/W2)這個能級即產生變動。在極端的條件下這個量子束縛態的能級趨向較寬的波導管的最低的次能帶能級也就是說L型(□ > 1.14) 與T型(□□> 1.33) 時，Ebs~ E1。在外包磁場下，這個束縛態能級隨著磁場增強而單調昇高。雖然電子處於靜止狀態，卻仍受到磁場影響這純粹是一個量子現象。而且在弱場強時能級呈現出二次曲線形狀的趨勢，這乃是因為磁場的推排效應(depletion effect)，使得電子的活動空間縮小之故。反之在強場時，則較純為增高有效位能，因而呈現線性相依。 我們也研究了L型、T型與□型開放性波導管的傳輸，在不同的幾何參數與非均勻磁場下的行為。我們發現波導管具有幾何的本質散射特性，且電子能量需大於波導管的最低次能帶能級方能傳輸。在極端非對稱情形 (□<<1)，L-型波導管的傳輸變成只受比較窄的波導管所主控，而T-型波導管則變成幾近完美的一維量子線而成幾近完美的梯級(stepwise)傳輸行為。然而在(□>>1)情形L-型波導管的傳輸與(1/□)相同，而 T-型的波導管因為一端變寬 散射變的極強而使電子頃向轉彎所以直線傳輸被強烈的壓低。考慮外加磁場的影響，與束縛態不同的發現是不只場強會影響傳輸，場方向也強烈的影響傳輸。大致來說，加磁場可以協助電子轉彎因而加強了L-型波導管的傳輸，若加相反方向則可以壓制傳輸。另外當磁場強度增加到某個程度以上，我們可以從傳輸曲線上觀察到共振的 peak-dip 或 dip-peak 結構。這些共振現象是在L-型的角落區或T-型的交會區域形成準束縛態(quasi bound state)(又稱為弱局域態(weak localized state)。而且這個準束縛態，對於幾何非對稱很敏感，因而可對傳輸產生極劇烈的影響，我們發現幾何上 1.4%的漂移即可造成 80 %的傳輸變動。我們也可以發現量子傳輸現象與 Landau 能級極有相關。 在最後我們研究了連結了兩個同向(□QW)或反向(□CQW) L–型或T-型的結構。我們發現這樣的結構的傳輸具有本質的相異性。然而本身 L–型或T-型的結構的重複又造成雙共振(double resonance)的存在。這個雙共振對幾何的改變也很敏感。傳輸性質隨兩個L–型或T-型的結構間的距離 d呈現週期性的變化。又這兩種結構的傳輸大體上來說可以看成T-型波導管的傳輸再加上一些振盪趨勢，這些趨勢是由於上述雙 L (或T)產生的 Bragg 反射現象因此符合 d= n□l/2。我們也發現兩個L–型或T-型的結構之間有很強的耦合作用(coupling effect)不論 d 大或小。而這個耦合作用可以被外加場的調節。在考慮外加磁場於兩垂直波導管時，我們發現像 Aharonov-Bohm效應一樣，電子不經過加磁場的區域也受到磁場極大的影響。在極端的強場時，這樣的波導管則轉化為完美的一維量子線。

Electronic properties are studied for the opened quantum wavegudies(OQW) under inhomogeneous magnetic fields. Quantum bound state(BS) and transport properties are studied in details. Our results show that the energy of the QBS and the trasport are affected by the geometric parameters no matter take the magnetic fields into account or not. There are two quantum phenomena here without classical correspondence: 1) BS in OQW, 2)the behavior of electrons under the influence of the surrounding magnetic fields. The ''true'' bound states are also called localized states, which are resulted from some critical geometric structures. The electronic bound states in two-dimensional(2D) symmetric or asymmetric L-shaped (LOQW) and T-shaped opened quantum wires (TOQW) are lower than the first subband energy level. The level energies of the quantum wires, regardless of L-shaped or T-shaped, are found to depend strongly on the asymmetric parameter $\alpha=W_2/W_1$, i.e. the ratio of the widths. These energies approaches the first subband of the wider arm when $\alpha$ is large. It is found that $\alpha \geq 1.14$ for LOQW, and $\alpha \geq 1.33$ for TOQW, the bound state energy $E_{bs}\sim E_1$. We also study the effect of the inhomogeneous magnetic field on the bound state when magnetic field is applied to the arms. Our result shows that the bound state energies depend on magnetic field strength but not on the sign of the field. The electron transmission properties in LOQW or TOQW systems under inhomogeneous magnetic fields are also investigated numerically. Transmission probabilities are generally enhanced by the application of magnetic fields. Oscillation structures are observed. Peaks with unity amplitude occur regularly. Peak-dip structures take place in the profile of transmission probabilities. More complicated structures occur in higher field region. Peak-dip and/or dip-peak structures are related to the resonant transmission and reflection due to the existence of the magnetic field induced QBS (or weak--localized states in the field free region). Geometric asymmetry can destroy these QBS, results in disappearance of these structures. A 1.4\% deviation of gemoetry can cause more that 80 \% deviation of transmission. The field adds an effective potential which results in an additional energy needed to overcome the threshold potential. In other words, the mode--mode coupling between the wires and the cavity and multiple reflection of electrons in the cavity are attributed to lead to the appearance of these structures in transmission spectrum. In the magnetic depletion process of the propagating modes in wires, the transmission exhibits various patterns, such as stepped drop, wide valley, deep dips, large oscillations, or other structure, which are sensitively dependent on incident electron energy and magnetic configurations. $\Pi$-shaped ($\Pi$QW) and $\Pi$-clone quantum waveguides ($\Pi$CQW) are also proposed. These two systems are both four terminal structures. The essentially different transmission properties between these two structures manifests again the essential dependence on the global structures. A double resonance is observed that it occurs due to the localized states and the coupling between the two L-- (or T--shaped) parts. The magnetic fields are found to influence on the behavior of charge particles which are moving or stationary, even the charges are contained in the field free region. The famous Aharonov-Bohm oscillations has already elucidated this behavior. Here, we manifest again this characteristics by different method in the studies of the transmission properties of the quantum wire systems. In our consideration, the magnetic fields plays an important role in the transmission properties, therefore affects electronic transport drastically. Our results should be useful and important for understanding and designing totally new electronic devices.