Topological features of Bloch impedance

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY EPL Pub Date : 2023-09-29 DOI:10.1209/0295-5075/acfe93

Igor Tsukerman, Vadim A. Markel

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Abstract

Abstract The bulk-boundary correspondence (b-bc) principle states that the presence and number of evanescent bandgap modes at an interface between two periodic media depend on the topological invariants (Chern numbers in 2D or Zak phases in 1D) of propagating modes at completely different frequencies in all Bloch bands below that bandgap. The objective of this letter is to explain, on physical grounds, this connection between modes with completely different characteristics.We assume periodic lossless 1D structures and lattice cells with mirror symmetry; in this case the Zak phase is unambiguously defined.The letter presents a systematic study of the behavior of electromagnetic Bloch impedance, defined as the ratio of electrical and magnetic fields in a Bloch wave at the boundary of a lattice cell. The impedance-centric view confers transparent physical meaning on the bulk-boundary correspondence principle. Borrowing from the semiconductor terminology, we classify the bandgaps as p - and n -type at the Γ and X points, depending on whether the Bloch impedance has a pole ( p ) or a null ( n ) at the bottom of that gap. An interface mode exists only for pn -junctions per our definition. We expect these ideas to be extendable to problems in higher dimensions, with a variety of emerging applications.

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布洛赫阻抗的拓扑特征

体边界对应(b-bc)原理指出，在两个周期介质之间的界面上，消失的带隙模式的存在和数量取决于该带隙以下所有Bloch带中完全不同频率的传播模式的拓扑不变量(二维的Chern数或一维的Zak相)。这封信的目的是在物理基础上解释具有完全不同特性的模式之间的这种联系。我们假设周期性无损的一维结构和具有镜像对称性的晶格单元;在这种情况下，Zak相位是明确定义的。这封信提出了对电磁布洛赫阻抗行为的系统研究，定义为在晶格单元边界的布洛赫波中电场和磁场的比率。以阻抗为中心的观点赋予体边界对应原理透明的物理意义。借用半导体术语，我们在Γ和X点将带隙分类为p型和n型，这取决于布洛赫阻抗在该带隙的底部是否具有极(p)或零(n)。根据我们的定义，接口模式只存在于pn -结中。我们希望这些想法可以扩展到更高维度的问题，并具有各种新兴的应用。

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

EPL 物理-物理：综合

CiteScore

3.30

自引率

5.60%

发文量

332

审稿时长

1.9 months

期刊介绍： General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.