Electron correlation effects in anisotropic parabolic quantum dots

Abstract

The studies on the many-electron ground state in anisotropic parabolic quantum dots with the cylindrical symmetry were carried out using an unrestricted Hartree Fock method. The competition between the quantization energy and the electron-electron interaction was clarified. The change of the spin state of ground state from ferromagnetic to paramagnetic state was obeyed by the Hund rule. The lateral size of a dot decreased due to the competition between the exchange energy among electrons and the quantization energy of a confining potential. The chemical potential and the differential capacitance of quantum dots were calculated as a function of electron number N up to 20. The effect of the shell structure due to quantization, and the increase of capacitance related to the shell structure were discussed. The calculated differential capacitance was found to be different from the classical differential capacitance.

非抑制Hartree-Fock法を用いた、円柱対称形の異方性放物量子ドットの多電子基底状態研究を行った。量子化エネルギーと電子-電子相互作用の競合を明らかにした。基底状態におけるスピン状態の強磁性状態から常磁性状態への変化はHundの規則に従うことが分かった。量子ドットの横サイズの減少は、電子間の交換エネルギーと閉込めポテンシャルの量子化エネルギーとの間の競合のためである。化学ポテンシャルと量子ドットの微分キャパシタンスを電子数Nの関数としてN20まで計算した。量子化による殻構造の効果ならびに殻構造に関連したキャパシタンスの増加を論じた。計算した微分キャパシタンスが古典的微分キャパシタンスと異なることが分かった。