Tutorial: From Topology to Hall Effects—Implications of Berry Phase Physics

IF 1.1 3区 物理与天体物理 Q4 PHYSICS, APPLIED Journal of Low Temperature Physics Pub Date : 2024-10-17 DOI:10.1007/s10909-024-03219-6
Nico Sprinkart, Elke Scheer, Angelo Di Bernardo
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Abstract

The Berry phase is a fundamental concept in quantum mechanics with profound implications for understanding topological properties of quantum systems. This tutorial provides a comprehensive introduction to the Berry phase, beginning with the essential mathematical framework required to grasp its significance. We explore the intrinsic link between the emergence of a non-trivial Berry phase and the presence of topological characteristics in quantum systems, showing the connection between the Berry phase and the band structure as well as the phase’s gauge-invariant nature during cyclic evolutions. The tutorial delves into various topological effects arising from the Berry phase, such as the quantum, anomalous, and spin Hall effects, which exemplify how these quantum phases manifest in observable phenomena. We then extend our discussion to cover the transport properties of topological insulators, elucidating their unique behaviour rooted in the Berry phase physics. This tutorial aims at equipping its readers with a robust understanding of the basic theory underlying the Berry phase and of its pivotal role in the realm of topological quantum phenomena.

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教程:从拓扑学到霍尔效应--贝里相物理学的启示
贝里相是量子力学中的一个基本概念,对理解量子系统的拓扑特性有着深远的影响。本教程全面介绍了贝里相,从掌握其意义所需的基本数学框架开始。我们探讨了非琐碎贝里相的出现与量子系统中存在拓扑特性之间的内在联系,展示了贝里相与带状结构之间的联系,以及该相在循环演化过程中的规整不变性。教程深入探讨了贝里相产生的各种拓扑效应,如量子效应、反常效应和自旋霍尔效应,这些效应体现了这些量子相在可观测现象中的表现形式。然后,我们将讨论扩展到拓扑绝缘体的传输特性,阐明它们植根于贝里相物理学的独特行为。本教程旨在让读者充分了解贝里相的基础理论及其在拓扑量子现象领域中的关键作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Low Temperature Physics
Journal of Low Temperature Physics 物理-物理:凝聚态物理
CiteScore
3.30
自引率
25.00%
发文量
245
审稿时长
1 months
期刊介绍: The Journal of Low Temperature Physics publishes original papers and review articles on all areas of low temperature physics and cryogenics, including theoretical and experimental contributions. Subject areas include: Quantum solids, liquids and gases; Superfluidity; Superconductivity; Condensed matter physics; Experimental techniques; The Journal encourages the submission of Rapid Communications and Special Issues.
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