Energy gaps of atomically precise armchair graphene sidewall nanoribbons

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Energy gaps of atomically precise armchair graphene sidewall nanoribbons

Wen-Xiao Wang, Mei Zhou, Xinqi Li, Si-Yu Li, Xiaosong Wu, Wenhui Duan, and Lin He

Phys. Rev. B 93, 241403(R) – Published 9 June 2016

Abstract

Theoretically, it has been demonstrated that armchair Graphene nanoribbons (GNRs) can be divided into three families, i.e., $N_{a} = 3 p, N_{a} = 3 p + 1$ , and $N_{a} = 3 p + 2$ (here $N_{a}$ is the number of dimer lines across the ribbon width and $p$ is an integer), according to their electronic structures, and the energy gaps for the three families are quite different even with the same $p$ . However, a systematic experimental verification of this fundamental prediction is still lacking, owing to very limited atomic-level control of the width of the armchair GNRs investigated. Here, we studied electronic structures of the armchair GNRs with atomically well-defined widths ranging from $N_{a} = 6$ to $N_{a} = 26$ by using a scanning tunneling microscope. Our result demonstrated explicitly that all the studied armchair GNRs exhibit semiconducting gaps and, more importantly, the observed gaps as a function of $N_{a}$ are well grouped into the three categories, as predicted by density-functional theory calculations. Such a result indicated that the electronic properties of the armchair GNRs can be tuned dramatically by simply adding or cutting one carbon dimer line along the ribbon width.

Received 3 February 2016
Revised 8 May 2016

DOI:https://doi.org/10.1103/PhysRevB.93.241403

Physics Subject Headings (PhySH)

Band gap

Graphene Nanoribbon

Scanning techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wen-Xiao Wang¹, Mei Zhou², Xinqi Li³, Si-Yu Li¹, Xiaosong Wu³, Wenhui Duan², and Lin He^1,*

¹Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, 100875, People's Republic of China
²State Key Laboratory of Low-Dimensional Quantum Physics and Collaborative Innovation Center of Quantum Matter, Department of Physics, Tsinghua University, Beijing, 100084, People's Republic of China
³State Key Laboratory for Artificial Microsctructure and Mesoscopic Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

^*helin@bnu.edu.cn

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Issue

Vol. 93, Iss. 24 — 15 June 2016

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Images

Figure 1
Geometry and electronic structure of armchair GNRs. (a) Schematic of a $N_{a} = 15$ armchair GNR with the edge dangling σ bonds passivated by hydrogen atoms (gray balls). Black dashed frame indicates the supercell in the calculation. (b) Band structures of $N_{a}$ armchair GNRs with $N_{a} = 3 p, 3 p + 1$ , and $3 p + 2$ (here $p = 5)$ obtained by first-principles calculations. The colored areas indicate the energy bandgaps of the three different families of the armchair GNRs. Obviously, the $N_{a} = 3 p + 2$ armchair GNR exhibits a much smaller bandgap.
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Figure 2
Structures of graphene and GNRs on C-face terraces of SiC surface. (a) Schematic structure of graphene monolayer on C-face terraces of SiC surface. There are three different regions exhibiting quite different electronic properties. (b) A representative STM image of a graphene sheet on a C-face terrace of SiC surface $(V_{sample} = - 0.9 V, I = 0.28 nA)$ . The inset shows an atomic-resolution STM image of the graphene sheet. (c) STS spectra, i.e., dI/dV-V curves, taken at the position in panel (b) under zero and 4 T magnetic fields. For clarity, the curves are offset on the $y$ axis and Landau level indices of massless Dirac fermions are marked. (d) A typical STM image $(V_{sample} = 0.8 V, I = 0.3 nA)$ showing a graphene sheet across several adjacent C-face nanoterraces of SiC surface. The atomic-resolution STM image of an armchair GNR on a C-face nanoterrace is shown in panel (e). The atomic structure of graphene is overlaid onto the STM image to determine the number of carbon dimer lines along the ribbon width. (f) A profile line across the GNR width.
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Figure 3
STS spectra of armchair GNRs with different widths on C-face nanoterraces of SiC surface. Representative spectra of different armchair GNRs belonging to the (a) $N_{a} = 3 p$ , (b) $N_{a} = 3 p + 1$ , and (c) $N_{a} = 3 p + 2$ families. The corresponding atomic-resolution STM images of these armchair GNRs are shown in the insets. The edges of the energy bandgap of the STS spectra are marked by two arrows. The peaks in the spectra are the van Hove singularities induced by 1D electron confinement.
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Figure 4
Spatially resolved band gaps of three armchair GNRs by tunnelling spectroscopy. (a) Left: Atomic resolution STM image of an armchair GNR with $N_{a} = 3 p + 2 = 8$ . Right: Intensity plot of dI/dV spectra taken along the armchair GNR. The armchair GNR exhibits a constant bandgap along it. (b) Left: Atomic resolution STM image of an armchair GNR showing a transition of widths from $N_{a} = 3 p = 15$ (top) to $N_{a} = 3 p + 1 = 16$ (bottom). Right: Intensity plot of dI/dV spectra taken along the armchair GNR exhibiting a variation of the gaps from about 428 to 661 meV along it. (c) Left: Atomic resolution STM image of an armchair GNR showing a transition of widths from $N_{a} = 3 p + 2 = 11$ (top) to $N_{a} = 3 p = 12$ (bottom). Right: Intensity plot of dI/dV spectra taken along the armchair GNR exhibiting a large variation of the gaps from about 150 to about 445 meV along it. The edges of bandgap are highlighted with blue lines in the spectra maps.
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Figure 5
The measured bandgap of the armchair GNRs as a function of widths. The measured energy bandgaps can be grouped into three categories. The theoretical data points taken from Ref. [3] are also given for comparison. The solid lines are calculated according to Eq. (1) of Ref. [3].
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