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首页> 外文期刊>Physical review >Geometric phase at a graphene edge: Scattering phase shift of Dirac fermions
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Geometric phase at a graphene edge: Scattering phase shift of Dirac fermions

机译：石墨烯边缘的几何相：狄拉克费米子的散射相移

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摘要

We study the scattering phase shift of Dirac fermions at graphene edge. We find that when a plane wave of a Dirac fermion is reflected at an edge of graphene, its reflection phase is shifted by the geometric phase resulting from the change of the pseudospin of the Dirac fermion in the reflection. The geometric phase is the Pancharatnam-Berry phase that equals the half of the solid angle on Bloch sphere determined by the propagation direction of the incident wave and also by the orientation angle of the graphene edge. The geometric phase is finite at the zigzag edge in general, while it always vanishes at the armchair edge because of intervalley mixing. To demonstrate its physical effects, we first connect the geometric phase with the energy band structure of graphene nanoribbon with the zigzag edge. The magnitude of the band gap of the nanoribbon, that opens in the presence of the staggered sublattice potential induced by edge magnetization, is related to the geometric phase. Second, we numerically study the effect of the geometric phase on the Veselago lens formed in a graphene nanoribbon. The interference pattern of the lens is distinguished between armchair and zigzag nanoribbons, which is useful for detecting the geometric phase.
机译：我们研究了狄拉克费米子在石墨烯边缘的散射相移。我们发现，当狄拉克费米子的平面波在石墨烯的边缘处反射时，其反射相位将由于狄拉克费米子的伪自旋在反射中的变化而导致的几何相位发生偏移。几何相是Pancharatnam-Berry相，它等于Bloch球上的立体角的一半，该角由入射波的传播方向以及石墨烯边缘的定向角确定。通常，几何相位在锯齿形边缘处是有限的，而由于间隔混合，它总是在扶手椅边缘处消失。为了证明其物理效果，我们首先将几何相与带有锯齿形边缘的石墨烯纳米带的能带结构连接起来。在边缘磁化引起的交错亚晶格电势存在时打开的纳米带的带隙大小与几何相位有关。其次，我们通过数值研究了几何相对石墨烯纳米带中形成的Veselago透镜的影响。镜片的干涉图案在扶手椅和锯齿形的纳米带之间有所区别，这对于检测几何相位很有用。

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