论文标题
WKB估计双层石墨烯的魔术扭转角度
WKB estimate of bilayer graphene's magic twist angles
论文作者
论文摘要
石墨烯双层在一系列魔术扭曲角度上表现出零能量的平坦带。在缺乏公共内部层间跳跃的情况下，零能量状态满足了一个零dirac方程，其非亚伯语SU（2）量规电位在全球范围内无法对角度化。我们通过引入无量纲的普朗克与扭曲角度成比例的恒定恒定，求解围绕AB和BA转动点的线性化DIRAC方程，并通过散装WKB波函数连接通风的函数解决方案，从而为此DIRAC方程开发了一个半经典的WKB近似方案。我们在无量纲普朗克常数的一组离散值集中找到零能量解，我们可以通过分析获得。我们的分析平坦谱带扭曲角与先前工作中数值确定的角度相对应。
Graphene bilayers exhibit zero-energy flat bands at a discrete series of magic twist angles. In the absence of intra-sublattice inter-layer hopping, zero-energy states satisfy a Dirac equation with a non-abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck's constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wavefunctions. We find zero energy solutions at a discrete set of values of the dimensionless Planck's constant, which we obtain analytically. Our analytic flat band twist angles correspond closely to those determined numerically in previous work.
