弱無序銅鍺合金的二維三維量子傳輸

Abstract

電子如何在無序系統中傳輸，在近十幾年來一直都是被探討的課題。在弱無序地帶，弱局域效應與電子-電子作用力被用來解釋許多實驗的結果，例如：電阻與溫度的關係、磁電阻的表現行為。我們藉由此兩者物理量的量測與理論的比較，來探討無序銅鍺樣品的無序性對電子傳輸特性造成的影響。 我們用電弧爐製出一系列不同莫耳比例的銅鍺合金，樣品的無序程度隨著鍺含量增加而增加。再以熱蒸鍍對每種成份的合金，製作出不同厚度的銅鍺CuxGe100-x樣品( 42dxd92 )。用四點量測法量測樣品的電阻隨溫度的關係，由此，判斷出樣品本身的維度。 對二維、三維樣品，量測低溫下（0.3 K∼20 K）的磁電阻（磁場範圍從0 T∼4 T），並以弱局域理論擬合，求得自旋-軌道散射率1/tso與非彈性散射率1/tin。無論二維或三維的樣品，自旋-軌道散射機制都隨無序程度增加而變大，導致因弱局域效應造成的正磁電阻修正增加。在三維樣品中，非彈性散射主要是由電子-聲子散射所主導，電子-聲子散射率都隨溫度下降而減少，且與溫度成P次方關係，P值約1.8∼3。在二維樣品中，非彈性散射率也與溫度成P次方關係，P值約2∼3。另外，無論二維還是三維，非彈性散射率也隨無序程度增加而變大，造成弱局域造成的效應減少。

The electronic conduction in disordered system has been studied both theoretically and experimentally for decades. In weakly disordered regime, both weak localization and electron-electron interaction can describe well many experimental results such as temperature dependence of resistivity, magnetoresistance, and so on. In this work, we have studied the effects of the degree of disorder on electronic properties in CuGe samples. We have made a series of CuxGe100-x (42dxd92) alloys using arc-melting technique. For each alloy, a series of CuxGe100-x samples with different thickness were made by thermal evaporation. The degree of disorder decreases with increasing x, the relative molar concentration of Cu, systematically. Temperature dependence of resistances of all samples were measured using 4 probe AC measurements. The relation between resistivity and temperature reveals the dimensionality of the CuxGe100-x (42dxd92) sample. We have measured the magnetoresistances of both two-dimensional samples and three-dimensional samples in temperature range between 0.3K and 20K and in magnetic fields up to 4 Tesla. Fits to the weak localization theory allow us to obtain the spin-orbit scattering rate 1/tso and the temperature dependent inelastic scattering rate 1/tin. For all samples, 1/tso is temperature independent and increases with the increasing degree of disorder of samples. tin grows with decreasing temperature resulting in enhancement of localization effect. Moreover, it follows that 1/tin µ ATP. In 3-D system, the inelastic scattering mainly comes from the electron-phonon scattering. We found the temperature exponent p is in between 1.6 and 3. In 2-D samples, the temperature exponent p is in between 2 and 3. Furthermore, tin decreases with increasing disorder resulting in the reduction of localization effect.