二維電子系統巢狀費米面對電漿子模態的效應

Abstract

本論文中我們研究二維電子系統□ 緊密束縛能帶對電漿子模態的效應。 我們使用了兩種近似方法: 平均場近似法以及哈伯近似法。 當費米能級位於二維的緊密束縛能帶的中間時， 會出現巢狀費米面的現象。 波向量空間的週期性對電漿子模態有很大的影響， 因此在我們的結果□，阻尼區域對於波向量是呈現週期性的。 另外巢狀費米面在波向量空間□方向上的不等同性質使得電漿子模態 也有空間方向上的不等同性質。我們得到的一個重要結果是介電函數 對於費米能級是呈現對稱關係的。因此阻尼區域以及電漿子模態對於 費米能級都呈現了對稱的關係。所以我們提出新的哈伯係數以使 哈伯近似法保有此對稱性。我們發現當費米能級大約位於能帶的 中央區域時，由哈伯近似法所求得的電漿子模態和由平均場近似法 所求得的在大約 0.3 < (aq \ π) < 1 的範圍 有明顯的差異。當費米能級接近能帶的頂端或底部時， 電漿子模態的分佈狀態在大約 (aq \ π) < 0.5 時 和二維自由電子氣的電漿子模態分佈是非常相似的。我們也發現 由哈伯近似法所求得的電漿子模態總是比由 平均場近似法所求得的來得小。 The plasmon modes in a two dimensional electron system that involves a tight-binding band is studied. Two approximation schemes, the random phase approximation (RPA) and the Hubbard approximation (HA), have been used. The tight-binding band has an interesting Fermi surface nesting feature when the Fermi energy is at the middle of the band. The periodicity in the wavevector space has important effect on the plasmon modes. Thus, in our results, the damping regions are periodic in the wave vector q. Besides, the nesting features leads to anisotropy in the wavevector space and also to the plasmon dispersion relation. An important observation in this work is the symmetry feature in Fermi level for the dielectric function (both real and imaginary parts) and thus the plasmon modes and damping regions. Based on this, we propose a Hubbard G(q), factor that preserves the symmetry. We find that when Fermi energy is not close to the top or bottom of the energy band, the plasmon modes of the HA deviate from those of the RPA appreciably for about 0.3 < (aq / Pi) < 1 . Near the band bottom, or the top of the band, the plasmon dispersion equal that of a 2D homogeneous electron gas for about (aq / Pi) < 0.5 Finally, the plasmon modes for HA are always smaller than that of the RPA.