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Transformation of the Topological Phase and the Edge Modes of Double-Bilayer Bismuthene with Inter-Bilayer Spacing

1
Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China
2
College of Electronic, Communication and Physics, Shandong University of Science and Technology, Qingdao 266590, China
3
Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801-3080, USA
4
Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, 104 South Goodwin Avenue, Urbana, IL 61801-2902, USA
5
Department of Physics, National Taiwan University, Taipei 10617, Taiwan
*
Author to whom correspondence should be addressed.
Crystals 2019, 9(5), 266; https://doi.org/10.3390/cryst9050266
Received: 4 April 2019 / Revised: 18 May 2019 / Accepted: 20 May 2019 / Published: 22 May 2019
(This article belongs to the Special Issue Recent Advances in Novel Topological Materials)
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Abstract

The transformations of the topological phase and the edge modes of a double-bilayer bismuthene were investigated with first-principles calculations and Green’s function as the inter-bilayer spacing increased from 0 Å to 10 Å. At a critical spacing of 2 Å, a topological phase transition from a topological insulator to a band insulator resulting from a band inversion between the highest valence band and the second lowest conduction band, was observed, and this was understood based on the particular orbital characters of the band inversion involved states. The edge modes of double-bilayer bismuthene survived the phase transition. When d was 2 Å < d < 4 Å, the interaction between the edge modes of two separated bismuthene bilayers induced an anti-crossing gap and resulted in a trivial band connection. At and beyond 4 Å, the two bilayers behavior decoupled entirely. The results demonstrate the transformability of the topological phase and the edge modes with the inter-bilayer spacing in double-bilayer bismuthene, which may be useful for spintronic applications. View Full-Text
Keywords: double-bilayer bismuthene; topological phase transition; edge modes; inter-bilayer spacing; first-principles calculations double-bilayer bismuthene; topological phase transition; edge modes; inter-bilayer spacing; first-principles calculations
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Hu, H.; Shi, Z.; Wang, P.; Zhou, W.; Chiang, T.-C.; Wang, X. Transformation of the Topological Phase and the Edge Modes of Double-Bilayer Bismuthene with Inter-Bilayer Spacing. Crystals 2019, 9, 266.

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