單層石墨層在調制場之下的電子特性和光學性質

Abstract

這篇論文之中，我們以緊束模型及梯度近似法研究單層石墨系統在外加調制磁場和調制電場之下的電子和光譜特性。對於調制磁場而言，電子性質受到它的強烈影響而改變，這些改變包括能帶維度、能量色散關係、新的能量邊界態、能帶非對稱性、能帶簡併度以及能帶的非等方性特質。在能帶結構中，費米能為零的地方將會有局部平坦的能帶出現，而在其他能量對應的則是一維的拋物線能帶。這兩種能帶在態密度中分別造成零維對稱和一維非對稱的發散峰。對於每一條拋物線能帶而言，它具有一個原始邊界態和四個額外邊界態。這些邊界態所對應的能量和調制週期以及調制磁場強度之間的關係都有詳細的討論與分析。另外，在光學吸收譜中的吸收峰主要來自於原始邊界態和額外邊界態所產生。這兩種邊界態對應的吸收峰分別遵守不同的光學選擇律，其主要原因是由於它們的波函數擁有不同的特徵所造成。特別值得注意的是，光學吸收譜可以反應出調制磁場方向以及外加光的極化方向所造成的非等方性特質。對於調制電場而言，電子特性以及光學特性也會受到強烈的影響。在能帶結構中，靠近原始邊界態的能帶具有數個額外邊界態，並且展現出震盪行為和色散關係。另外，原本在沒有外加場之下的雙重簡併拋物線能帶變成沒有簡併的震盪能帶。態密度中所產生的一維非對稱峰主要是來自於額外邊界態。值得一提的是，態密度中對應費米能為零的有限值代表著自由電子的存在。換句話說，藉由調制電場的影響可以將單層石墨系統從半導體性變成金屬性的系統。對於光學性質而言，同樣的也展現了許多來自於額外邊界態所產生的吸收峰。然而，這些吸收峰並沒有展現出一個明確的光學選擇律。

The π-electronic structures and optical absorption spectra of a single-layer graphene in spatially modulated magnetic and electric fields are studied by the tight-binding model and gradient approximation. For modulated magnetic fields, they could strongly affect the low-energy electronic properties, i.e., the dimensionality, energy dispersions, extra band-edge states, asymmetry, state degeneracy, and anisotropy of energy bands. There are partial flat bands at Fermi level and one-dimensional parabolic bands at others. The two kinds of bands make density of states (DOS) exhibit a delta-function-like structure and asymmetric prominent peaks, respectively. Each parabolic band owns one original and four extra band-edge states, and their energy dependences on the period and strength are investigated in detail. In the optical absorption spectra, the absorption peaks originating in original band-edge state and extra band-edge states obey different selection rules because their wave functions present different features. It is noted that the anisotropic absorption spectra are induced by different mod-ulated directions and electric polarization directions. For modulated electric fields, they could drastically change the low-frequency electronic and optical properties. Each energy band displays oscillatory energy dispersions and several band-edge states near original band-edge state. The doubly degenerate parabolic bands become nondegenerate. DOS shows many prominent asymmetric peaks mainly owing to the band-edge states. The finite DOS at Fermi level means that there are free carriers, i.e., a modulated electric field could change a semiconducting graphene into a semimetallic one. The optical absorption spectra demonstrate rich peaks resulting from band-edge states, and reveal the anisotropy in the modulated direction. Such absorption peaks could not be ascribed to an obvious selection rule.