二維拓樸絕緣體元件的量子傳輸

Abstract

近年來，拓樸絕緣體已成為一個很有潛力的研究領域，它有可能是製作新一代自旋電子學元件和量子資訊的材料。在理論方面，量子力學的拓樸學應用有許多階段的研究。拓樸絕緣體的內部性質為一般的絕緣體，但是邊緣（表面）卻是導體，這是由於固體內部的電子能帶結構所決定的二維拓樸絕緣體具有特殊的邊緣（表面）態，這種特殊的量子態是由強自旋軌道耦合下所產生，而它的電導取決於邊緣態的數目。在二為拓樸絕緣體外加電場的情況下，兩個邊緣態上的電流會有相反的自旋，稱為量子自旋霍爾效應。一般認為，沿著邊緣狀態的電子不能被非磁性雜質散射，這是由於時間反演對稱性所導致。 在本論文中，我們考慮兩種對量子自旋霍爾效應影響的作用。首先是幾何形狀的影響，我們計算了兩種分支形狀的拓樸絕緣體的電流和自旋極化。我們的結果發現，分支狀的結構將增強自旋極化電流。第二是非磁性雜質的影響，我們研究非磁性雜質加入拓樸絕緣體的傳輸性質。雖然拓樸絕緣體的時間反演對稱性會保護邊緣態的電子不會被非磁性雜質散射，但邊緣的電子會穿隧到另一側的邊緣，導致電子的穿透係數下降。對於雜質的小樣本，傳輸係數甚至可以下降到零。最後，考慮分叉結構和雜質所構成的元件中，我們發現了電子同時擁有量子穿隧和量子干涉的效應，而這兩種效應會影響電子的傳輸方向。從這些結果推得此結構可以成為一種電子元件，藉由閘電位控制電流的開關，且具有自旋性質。以上這些性質皆是由Landauer formula進行數值研究。

Recently, topological insulator is an emerged field in condensed matter physics and material science; it has been regarded as the materials which have potential applicate in the new generation of spintronics devices and quantum computer. For the theory, there are many phase and topology studies in the quantum mechanics in this topic. The topological insulator is the material that is insulating in the bulk but conducting on the edge (or surface). In two dimension, it exhibits the quantum spin Hall effect. The effect is caused by the strong spin-orbit coupling and the spin Hall conductance is determined by the number of edge state. It is believed that electron transport along the edge states cannot be backscattered by the non-magnetic impurity due to the time reversal symmetry. In the thesis, we study the transport property of quantum spin Hall effect in defined geometries and effect caused by the impurities. First, we calculated the current and polarization on two types of branching topological insulators. Our results indicate that the branch structure will enhance the spin polarizing current. Second, the influences of impurity on the electron density and transmission of a finite topological insulator sample are studied. Although the time-reversal symmetry topology insulators will protect the edges of the electronic states cannot be scattering by non-magnetic impurity, however, electrons from one side can tunnel into the other side and the quantized conductance can be broken down. For a small sample with impurity, the transmission coefficient can even drop to zero for the crosswalk between the helical edge states at two sample sides. At last, a device is designed based in those two influences. We found that quantum tunneling and quantum interference occur in the same time, and both effects influence the direction of the electron. Those properties are studied numerically in the framework of Landauer Formalism.