Tuning structures and electronic spectra of graphene layers with tilt grain boundaries

Long-Jing Yin, Jia-Bin Qiao, Wen-Xiao Wang, Zhao-Dong Chu, Kai Fen Zhang, Rui-Fen Dou, Chun Lei Gao, Jin-Feng Jia, Jia-Cai Nie, and Lin He

Phys. Rev. B 89, 205410 – Published 8 May 2014

Abstract

Despite the fact that structures and properties of tilt grain boundaries of graphite surface and graphene have been extensively studied, their effect on the structures and electronic spectra of graphene layers has not been fully addressed. Here we study effects of one-dimensional tilt grain boundaries on structures and electronic spectra of graphene multilayers by scanning tunneling microscopy and spectroscopy. A tilt grain boundary of a top graphene sheet in graphene multilayers leads to a twist between consecutive layers and generates superstructures (Moiré patterns) on one side of the boundary. Our results demonstrate that the twisting changes the electronic spectra of Bernal graphene bilayer and graphene trilayers dramatically. We also study quantum-confined twisted graphene bilayer generated between two adjacent tilt grain boundaries and find that the band structure of such a system is still valid even when the number of superstructures is reduced to two in one direction. It implies that the electronic structure of this system is driven by the physics of a single Moiré spot.

Received 9 December 2013
Revised 25 April 2014

DOI:https://doi.org/10.1103/PhysRevB.89.205410

Authors & Affiliations

Long-Jing Yin^1,*, Jia-Bin Qiao^1,*, Wen-Xiao Wang¹, Zhao-Dong Chu¹, Kai Fen Zhang², Rui-Fen Dou^1,†, Chun Lei Gao², Jin-Feng Jia², Jia-Cai Nie¹, and Lin He^1,†

¹Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
²Department of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China

^*These authors contributed equally to this paper.
^†Corresponding authors: helin@bnu.edu.cn, rfdou@bnu.edu.cn

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Vol. 89, Iss. 20 — 15 May 2014

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Images

Figure 1
(a) Schematic structure of a unique graphene bilayer, in which one side of the grain boundary is Bernal graphene bilayer and the opposite side is twisted graphene bilayer with a period of Moiré pattern $D$ . The period of superstructures $P_{B}$ along the boundaries depends on the twisted angle θ and α, the orientation of the boundary in respect to the graphene lattice. In panel (a), $α = 30^{\circ} \pm θ / 2$ , $P_{B} = D$ . (b)–(e) STM images of graphene layers on graphite surface. Moiré pattern with different periods appears on one side of the tilt grain boundary. All the grain boundaries show 1D superlattices with $P_{B} \approx D$ . (b) $D = 4.7$ nm, $θ = 3 . 0^{\circ}$ ; (c) $D = 7.2$ nm, $θ = 2 . 0^{\circ}$ ; (d) $D = 17.0$ nm, $θ = 0 . 83^{\circ}$ ; (e) $D = 28.2$ nm, $θ = 0 . 50^{\circ}$ .
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Figure 2
(a) Value of $P_{B}$ as a function of 1/θ. The solid red circles are the average experimentally measured values obtained from several tens of samples. The black dashed line is plotted according $P_{B} = a / θ$ . (b) The $Δ E_{VHS}$ as a function of θ. The red solid circles are the average experimentally measured values obtained in twisted graphene bilayer on graphite surface. The black solid squares are the experimental results taken from the CVD-grown graphene sheet deposited on graphite, as reported in Ref. [25]. The dashed line is a guide to the eyes.
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Figure 3
(a) STM image of graphene layers on graphite surface with two sets of superlattices showing a region of higher contrast (left) and a region of lower contrast (right). The left tilt grain boundary is on the top graphene layer; the right one is on the second layer. (b) Zoom-in topography of the white frame in (a). The white line shows no atomic mismatch between the two regions of superlattice, indicating that the surface graphene layer is continuous for both regions. The inset shows Fourier transforms of panel (b). (c) Zoom-in topography of the black frame in (a) with atomic resolution. The blue and red lines give one direction of the atomic lattice of graphene grains connected by the left tilt boundary. The angle between these directions is measured to be $\sim 2 . 2^{\circ}$ . (d), (e) Schematic pictures of the structure in panel (a). (f)–(i) dI/dV-V curves measured on different positions of panel (a). The spectra have been vertically offset for clarity.
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Figure 4
(a) Dispersion of low-energy states for $θ = 2 . 2^{\circ}$ , $t_{θ} = 156$ meV, in a twisted graphene bilayer. Two saddle points form at $k_{y} = 0$ between the two Dirac cones. (b) Electronic spectra of low-energy states for $θ = 2 . 2^{\circ}$ , $t_{θ} = 156$ meV, in a twisted graphene trilayer (the top layer and the second layer is AB stacking and there is a stacking fault with $θ \approx 2 . 2^{\circ}$ between the third layer and the second layer). (c) A section view of the band structures with $k_{x} = 0$ in panel (a) (solid curve) and (b) (dashed curve). (d) DOS of the bilayer in panel (a) (solid curve) and the trilayer in panel (b) (dashed curve) with two VHSs. Both are calculated numerically according to the well-known formula $\frac{S}{4 π^{2}} \oint \frac{1}{|\nabla_{k} E (\vec{k})|} d k$ .
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