Flat band localization due to self-localized orbital

Abstract

We discover a new wave localization mechanism in a periodic wave system, which can produce a novel type of flat band and is distinct from the known localization mechanisms, i.e., Anderson localization and flat band lattices. The first example we give is a designed electron waveguide (EWG) on 2DEG with special periodic confinement potential. Numerical calculations show that, with proper confinement geometry, electrons can be completely localized in an open waveguide. We interpret this flat band localization (FBL) phenomenon by introducing the concept of self-localized orbitals. Essentially, each unit cell of the waveguide is equivalent to an artificial atom, where the self-localized orbital is a special eigenstate with unique spatial distribution. These self-localized orbitals form the flat bands in the waveguide. Such self-localized orbital induced FBL is a general phenomenon of wave motion, which can arise in any wave systems with carefully engineered boundary conditions. We then design a metallic waveguide (MWG) array to illustrate that similar FBL can be readily realized and observed with electromagnetic waves.

Graphical abstract

Keywords

flat band localization / self-localized orbital / electron waveguide

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[37] See Supplemental Material I for the calculations about the EWGs.

[38] See Supplemental Material II for the Fermi level in EWG.

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[43] See Supplemental Material VII for this self-localized orbits.

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Conflicts of interest

There are no conflicts to declare.

Electronic supplementary materials

The online version contains supplementary material available at https://doi.org/10.1007/s11467-023-1306-2 and https://journal.hep.com.cn/fop/EN/10.1007/s11467-023-1306-2.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874160, 12141401, and 11534001), the National Key Research and Development Program of China (No. 2017YFA0403501), and the Fundamental Research Funds for the Central Universities (HUST: 2017KFYXJJ027).

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