AI 中文总结
本文以二维晶格电场产生的万尼尔-斯塔克线性势场为例，阐释局域化等概念，介绍贝塞尔函数在物理模型求解中的应用，相关内容可用于固体物理教学。
AI 中文摘要
系统的体相与真空之间的边界可通过一种将电子限制在体内的势场来建模。本文以二维晶格某一轴上电场产生的万尼尔-斯塔克线性势场为例，沿该轴的势场会产生局域在每个晶格位点附近的电子态，其本征能量构成万尼尔-斯塔克梯；横向方向上，这些态由具有自由布洛赫态的紧束缚模型描述。基态下，根据泡利原理填充这些态会形成绝缘的体相，以及在横向方向可呈金属性的边缘。本文阐释了局域化、局域化长度、填充与受限的概念，还介绍了贝塞尔函数在简单物理模型求解中的应用。这些主题可轻松纳入固体物理课程，仅需具备量子力学的先验知识。
英文摘要
The boundary between a system's bulk and the vacuum can be modeled by a potential which confines the electrons to the bulk. Here we present the example of the Wannier-Stark linear potential, generated by an electric field along one axis of a two-dimensional lattice. Along that axis, the potential generates electronic states which are localized around each lattice site, with eigenenergies which form the Wannier-Stark ladder. In the transverse direction, the states are governed by a tight binding model with free Bloch states. In the ground state, filling these states under the Pauli principle generates an insulating bulk and an edge which can be metallic in the transverse direction. This paper explains the concepts of localization, localization length, filling and confinement. The paper also acquaints the readers with the use of Bessel functions in the solution of a simple physical model. These topics can be easily included in courses on solid state physics, and only require prior knowledge of quantum mechanics.
CommentsAccepted for publication in Am. J. Phys
