一維電子系統可以藉由電極給於二維電子氣電位能而形成，而現今已經有相當多的文獻研究是關於一維電子系統．當系統處於低電子密度的時候，電子的交互作用力所影響的比重會增大，此時的系統便不能忽略交互作用力的影響．在考慮交互作用力系統中的電子為了減少整體的電位能，此時電子會呈現等距離排列，形成維格納晶體．當形成維格納晶體時，逐漸增大電子的密度，電子的排列會漸漸的轉變成鋸齒狀排列，先前的文獻指出在足夠大的交互作用力的影響下，系統中的電子自旋會出現極化的現象．
　在本篇論文中，我們的元件是基於磁聚焦所設計的．元件中的電極主要是用來控制系統中的電位能強度跟電子密度．當加入垂直磁場並且調控系統的電位能和電子密度時，我們所量測到的磁聚焦的電位差峰會有一個逐漸轉變成兩個電位差峰，因此我們可以藉由磁聚焦來偵測電子在實空間的排列．之後，我們在元件中加入源汲偏壓，如此一來便可以偵測我們系統中的電子自旋．我們所量測到的數據顯示當我們加入偏壓時，在強交互作用力的區間電位差的峰值會增加，在弱交互作用力的區間電位差的峰值不會有所改變，這兩者之間的差別在於自旋極化的存在與否．我們的實驗提供了一種可以偵測電子在實空間排列的方法，也偵測電子在一維系統中的自旋情況．

There have been many studies of non-interacting one-dimensional system which can be created from two-dimensional electron gas by applying electrostatic confinement which is provided by a voltage applied to split gates. At low electron density, Coulomb potential dominate over the kinetic energy. In order to minimize the Coulomb repulsion, electrons occupy equidistance positions, forming a Wigner crystal. With increasing electron density in Wigner crystal regime, transforming the one-dimensional Wigner crystal into a staggered zig zag chain. Former research has shown that sufficiently strong interaction give rise to a ferromagnetic ground state.
In this thesis, we designed a device based on magnetic focusing geometry. The device contains a top gate and split gates which can be utilized to control the electron density and electrostatic confinement. By applying transverse magnetic field, the focusing peaks gradually evolve from single peak to two peaks when we tune the electrostatic confinement and carrier density. Through the magnetic focusing, we can detect the arrangement of electron in real space. Furthermore, we apply source-drain bias to our device, so we can detect the spin properties in one-dimensional system. In strongly interacting regime, the focusing peaks rise because of the spin polarization in strongly interacting regime. In addition, the peaks barely change in the weakly interacting regime. Our experiment provide a method to detect the arrangement of electrons and detect the spin dynamic in one-dimensional system.

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