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Title: Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z 2 Invariants, and Junction States

Abstract

Graphene nanoribbons (GNRs) have recently been shown by Cao, Zhao, and Louie [Cao, T.; Zhao, F.; Louie, S. G. Phys. Rev. Lett.2017, 119, 076401] to possess distinct topological phases in general, characterized by a 2 invariant. Cove-edged and chevron GNRs moreover are chemically and structurally diverse, quasi-one-dimensional (1D) nanostructures whose structure and electronic properties can be rationally controlled by bottom-up synthesis from precursor molecules. We derive the value of the topological invariant of the different types of cove-edged and chevron GNRs, and we investigate the electronic properties of various junctions formed by these GNRs, as well as such GNRs with the more common armchair or zigzag GNRs. We study the topological junction states at the interface of two topologically distinct segments. For an isolated GNR having two ends of different terminations, topological end states are shown to develop only at the topologically nontrivial end. Our work extends the explicit categorization of topological invariants of GNRs beyond the previously demonstrated armchair GNRs and provides new design rules for novel GNR junctions as well as future GNR-based nanoelectronic devices.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2];  [3]; ORCiD logo [2]
  1. Pohang Univ. of Science and Technology, Pohang, Kyungbuk (Korea). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division; Univ. of California, Berkeley, CA (United States). Dept. of Physics
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division; Univ. of California, Berkeley, CA (United States). Dept. of Physics
  3. Pohang Univ. of Science and Technology, Pohang, Kyungbuk (Korea). Dept. of Physics
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE
OSTI Identifier:
1543687
Resource Type:
Accepted Manuscript
Journal Name:
Nano Letters
Additional Journal Information:
Journal Volume: 18; Journal Issue: 11; Journal ID: ISSN 1530-6984
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Chemistry; Science & Technology - Other Topics; Materials Science; Physics

Citation Formats

Lee, Yea-Lee, Zhao, Fangzhou, Cao, Ting, Ihm, Jisoon, and Louie, Steven G. Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z 2 Invariants, and Junction States. United States: N. p., 2018. Web. https://doi.org/10.1021/acs.nanolett.8b03416.
Lee, Yea-Lee, Zhao, Fangzhou, Cao, Ting, Ihm, Jisoon, & Louie, Steven G. Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z 2 Invariants, and Junction States. United States. https://doi.org/10.1021/acs.nanolett.8b03416
Lee, Yea-Lee, Zhao, Fangzhou, Cao, Ting, Ihm, Jisoon, and Louie, Steven G. Tue . "Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z 2 Invariants, and Junction States". United States. https://doi.org/10.1021/acs.nanolett.8b03416. https://www.osti.gov/servlets/purl/1543687.
@article{osti_1543687,
title = {Topological Phases in Cove-Edged and Chevron Graphene Nanoribbons: Geometric Structures, Z 2 Invariants, and Junction States},
author = {Lee, Yea-Lee and Zhao, Fangzhou and Cao, Ting and Ihm, Jisoon and Louie, Steven G.},
abstractNote = {Graphene nanoribbons (GNRs) have recently been shown by Cao, Zhao, and Louie [Cao, T.; Zhao, F.; Louie, S. G. Phys. Rev. Lett.2017, 119, 076401] to possess distinct topological phases in general, characterized by a 2 invariant. Cove-edged and chevron GNRs moreover are chemically and structurally diverse, quasi-one-dimensional (1D) nanostructures whose structure and electronic properties can be rationally controlled by bottom-up synthesis from precursor molecules. We derive the value of the topological invariant of the different types of cove-edged and chevron GNRs, and we investigate the electronic properties of various junctions formed by these GNRs, as well as such GNRs with the more common armchair or zigzag GNRs. We study the topological junction states at the interface of two topologically distinct segments. For an isolated GNR having two ends of different terminations, topological end states are shown to develop only at the topologically nontrivial end. Our work extends the explicit categorization of topological invariants of GNRs beyond the previously demonstrated armchair GNRs and provides new design rules for novel GNR junctions as well as future GNR-based nanoelectronic devices.},
doi = {10.1021/acs.nanolett.8b03416},
journal = {Nano Letters},
number = 11,
volume = 18,
place = {United States},
year = {2018},
month = {9}
}

Journal Article:
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Cited by: 9 works
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Figures / Tables:

Figure 1 Figure 1: Schematic structures (top panels) and band structures calculated using DFT-LSDA (bottom panels) of short period cove-edged GNRs of (a) N = 5 (odd), (b) N = 6 (even) with symmetric edges (aligned facing vacancies), and (c) N = 6 (even) with asymmetric edges (misaligned facing vacancies) across themore » ribbon. The cove-edged GNRs are periodic along the x direction, and the side view in (a) illustrates the structural deformation along the direction perpendicular to the GNR plane. The unit cell of each GNR studied is shown by the black bracket. The gray and silver balls denote carbon and hydrogen atoms, respectively. The pink and blue areas denote edge carbon rings tilting upward and downward from the ribbon plane, respectively. (d) DFT-LSDA band gap of the three types of cove-edged GNRs in (a)-(c). For N = asymmetric-even cove-edged GNRs, the DFT-LSDA band gap is close to 0. (e) Wannier centers of the $π$-electron Wannier functions of an N = 5 cove-edged GNR are denoted by red dots in the unit cell.« less

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