晶体中电子的波动和不确定性
Wave and uncertainty properties of electrons in crystalline solids
摘要：
本文导出了晶体金属和半导体周期势中载流子的粒子性质和波动性质之间的关系。利用准动量的性质讨论了周期势中电子和空穴的粒子态，而波态则用布洛赫波的波包描述.这两个方面相结合，推导出了任意非抛物性和非球性能带的QM-波长关系。定义了一个有效质量，将电子的平均速度与量子点的有效质量联系起来，并将其用于计算窄禁带半导体、石墨烯和拓扑绝缘体表面态中电子波长的能量依赖性。导出了周期势场中电子准动量与其空间坐标之间的测不准关系。需要强调的是，所描述的性质适用于平均（非瞬时）电子行为。类比之间的波动和不确定性性质的电子在晶体固体和那些在真空中被跟踪。
英文摘要：
Relations between particle and wave properties for charge carriers in periodic potentials of crystalline metals and semiconductors are derived. The particle aspects of electrons and holes in periodic potentials are considered using properties of quasimomentum (QM), while the wave aspects are described employing wave packets of Bloch waves. The two aspects are combined in the derivation of QM-wavelength relations for energy bands of arbitrary nonparabolicity and nonsphericity. An effective mass relating electron QM to its average velocity for spherical energy bands is defined and used to calculate energy dependences of wavelengths for electrons in narrow gap semiconductors, graphene and surface states of topological insulators. An uncertainty relation between electron quasimomentum and its spatial coordinate in periodic potentials is derived. It is emphasized that the described properties apply to the average (not instantaneous) electron behavior. Analogies between the wave and uncertainty properties of electrons in crystalline solids and those in vacuum are traced.
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