外加磁場之量子線中雜質能階的研究

Abstract

本文乃針對量子線的結構來做研究。我們分析了在磁場的作用下 , 量子 線中加入雜質其電子能階的種種變化情形。經由理論推導及數值計算的結 果, 顯示出在強、弱不同的磁場影響下, 會出現不同型式的電子能階。例 如強磁場中, 電子能階偏向於量子線內未加入雜質的情形, 其能階的變 化, 隨主量子數的增加而等量遞增; 至於弱磁場中 , 因為庫侖作用相對 的顯得特別重要, 因此系統能階的變化主要由庫侖位勢所決定。另外加入 雜質的多寡, 與量子侷限結構的改變, 對某些能態亦有相當重要的影響。 像本文中所做線性雜質列與量子碟的研究即是。前者是改變雜質與電子間 的庫侖作用力; 而後者則是量子線邊界退化的極限。它們的結果, 在本文 中均有討論。 In this study,we analyze and calculate the eigenenergies' distribution of the cylindrical-shaped quantum confinement system, contains various impurities, with finite-potential barrier under an applied magnetic field. We find that there are different dependence of the energy level on the magnetic field strength for the strong and weak magnetic field regimes. For example, the energy level spectra are close to the them without any impurity in the strong magnetic field. The differ- ence of the energy levels increases equally for the increasing principle quantum number. In the weak magnetic regime, the energy levels are mainly determined by Coulomb potential profile because the Coulomb interaction is more significant compared with the other potentials. By changing the Coulomb interaction between the impurity and electron, we can calculate the energy levels of the linear impurity-array quantum wire eith the analog calculation proce- dures for the single impurity quantum wire. Similarly, we can also implement the developed numerical calculation method to the single impurity quantum disk, which is the special case of a cylindrical quantum wire with single impurity at origin and with longitudinal axis approaching to zero.