物理学进展

物理学进展 ›› 2024, Vol. 44 ›› Issue (1): 9-18.doi: 10.13725/j.cnki.pip.2024.01.002

所属专题： 2023年, 第43卷

• • 上一篇    下一篇

薄壁量子化方法进展

王永龙1,2, 杜 龙3   

  1. 1. 临沂大学物理与电子工程学院，临沂 276000 ；2. 南京大学固体微结构物理国家重点实验室，南京 210093； 3. 广西科技大学理学院，柳州 545006
  • 出版日期:2024-02-20 发布日期:2024-02-27
  • 基金资助:
    国家自然科学基金项目 (12247211，12147103 和 1200149)、山东省自然科学基金项目 (ZR2020MA091 和 ZR2020QA062)、广西科技计划项目 (2018AD19310) 和固体微结构物理重点实验室开放课题 (M35040 和 M35053) 的资助。

Progress in Thin-Layer Quantization

WANG Yonglong1,2, DU Long3   

  1. 1. Linyi University, School of Physics and Electronic Engineering, Linyi 276000； 2. Nanjing University, National Laboratory of Solid State Microstructures, Nanjing 21009；3. Guangxi University of Science and Technology, School of Science, Liuzhou 54500
  • Online:2024-02-20 Published:2024-02-27

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摘要：

微纳加工技术的快速发展实现了具有非平庸几何结构的低维材料与结构的制备，使得受几 何性质影响的有效动力学问题受到关注。作为研究低维弯曲系统中量子力学的有效方法，薄壁量 子化方法，它给出的几何势和几何动量也得到实验的证实。本文将回顾薄壁量子化方法，简述其 基本计算框架，明确给出几何量子效应是来自于微分同胚变换和局域标架间的旋转变换。这对于 理解引力规范场，演生规范场很有帮助，对理解人工规范场所隐含的几何结构也很有帮助。在特 定的量子体系中，几何量子效应可表现为共振隧穿、量子阻塞、量子霍尔效应、量子霍尔黏性、量 子自旋霍尔效应和单极磁场等，这些结果从不同角度展示了几何与新奇的物理现象之间的联系。

关键词: 几何势, 几何动量, 几何规范势, 薄壁量子化方法, 量子霍尔效应

Abstract:

With the rapid development of microtechnology, the low-dimensional materials are fabricated with nontrivial topological structures, and then the action of geometric properties on the effective dynamics receives increasing attention. It is an effective theory that the quantum mechanics of low-dimensional curved systems can be given by using the thin-layer quantization approach, in which the geometric potential and the geometric momentum have been demonstrated experimentally. In the present paper, the thin-layer quantization formalism is first recalled, its fundamental calculation framework is first clarified, and the geometric quantum effects result from the diffeomorphism transformation and the rotation transformation connecting the local frames of different points. The results are helpful to understand the gravitational gauge and emerging gauge, and to image the geometries implied in the artificial gauge. In the particular quantum systems, the novel physical phenomena are briefly recalled that are induced by geometry, such as resonation tunneling, quantum block, quantum Hall effect, quantum Hall viscosity, quantum spin Hall effect, effective monopole magnetic field and so on. The results will shed light from a different angle on the relationships between the geometry and the novel physical phenomenon.

Key words: geometric potential, geometric momentum, geometric gauge potential, thin-layer quantization, quantum Hall effect

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