微觀理解石墨烯上單一吸附氫分子系統的pi能帶低能量區和其導致的自旋翻轉

Abstract

用位置表示V_H, 氫原子引發的作用在$ pi$能帶的位能, 是理解並且計算吸附氫原子的SOC效應的關鍵. 在這個討論中, 我們從微觀的和低能量角度出發去推導出V_H, 當中推導出來的參數可以做為和 ab initio 計算結果作比較. 如此, V_H可以提供較真實的描述, 同時了瞭解當中的物理機制. 原本電子只透過SOC躍遷於pi和sigma能帶, 而吸附造成的扭曲使得電子可不透過SOC躍遷於pi和sigma能帶. 我們計算得到的V_H的參數V_{ sf}^{(0)}~ 0.08\Delta^{at}_{so}, 當中\Delta^{at}_{so}是碳原子中SOC效應的參數, 數量級約是meV. 本篇討論建構氫吸附子和石墨烯互動的基礎.

Hydrogen adsorbate on graphene has been expected to enhance spin-orbital coupling (SOC) in the system \cite{PhysRevLett.103.026804}. A key to understand and calculate the SOC effect of hydrogen adsorbate is to obtain the site-representation of the hydrogen-induced potential $V_{\rm H}$ for the $ i$ band electrons. In this work, we take a microscopic approach to derive the form of $V_{\rm H}$ in the low energy regime, where the hopping constants could be related to ones derived from ab initio calculation. As such, $V_{\rm H}$ could provide more realistic description while allowing a transparent exposition of understanding physical mechanism. The microscopic approach involves the local distortion of the orbital for the carbon atom to which the hydrogen is adsorbed, allowing the back and forth transition of electron between $ i$ band and $\sigma$ bands. In the present of hydrogen adsorbate, the orbital distortion opens up a non-SOC channel for the electron to make the transition between $\sigma$ and $ i$ band; in contrast, without adsorbate, the transition is purely via SOC channel. The site-representation $V_{\rm H}$ has a SOC constant $V_{\rm sf}^{(0)}\sim 0.08 \Delta_{\rm so}^{\rm at}$, in which $\Delta_{\rm so}^{\rm at}\sim meV$ is the intrinsic (atomic) SOC of a carbon atom. This SOC constant is much larger than the intrinsic SOC in pristine graphene $(\sim 5\mu eV)$. Overall, this work lays a foundation for the future derivation of the exchange interaction for hydrogen adsorbate.