Superlattice-induced minigaps in graphene band structure due to underlying one-dimensional nanostructuration

A. Celis, M. N. Nair, M. Sicot, F. Nicolas, S. Kubsky, D. Malterre, A. Taleb-Ibrahimi, and A. Tejeda

Phys. Rev. B 97, 195410 – Published 8 May 2018

Abstract

We have studied the influence of one-dimensional periodic nanostructured substrates on graphene band structure. One-monolayer-thick graphene is extremely sensitive to periodic terrace arrays, as demonstrated on two different nanostructured substrates, namely Ir(332) and multivicinal curved Pt(111). Photoemission shows the presence of minigaps related to the spatial periodicity. The potential barrier strength of the one-dimensional periodic nanostructuration can be tailored with the step-edge type and the nature of the substrate. The minigap opening further demonstrates the presence of backward scattered electronic waves on the surface and the absence of Klein tunneling on the substrate, probably due to the fast variation of the potential, of a spatial extent of the order of the lattice parameter of graphene.

Received 22 December 2017
Revised 12 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.195410

Physics Subject Headings (PhySH)

Band gap

Graphene

Angle-resolved photoemission spectroscopy Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Celis¹, M. N. Nair^2,1, M. Sicot³, F. Nicolas², S. Kubsky², D. Malterre³, A. Taleb-Ibrahimi², and A. Tejeda^1,2,*

¹Laboratoire de Physique des Solides, CNRS, Université Paris–Sud, Université Paris–Saclay, 91405 Orsay, France
²Synchrotron SOLEIL, Saint-Aubin, 91192 Gif-sur-Yvette, France
³Institut Jean Lamour, UMR 7198 CNRS, Université de Lorraine, 54506 Vandoeuvre lès Nancy, France

^*antonio.tejeda@u-psud.fr

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Vol. 97, Iss. 19 — 15 May 2018

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Images

Figure 1
(a) Scheme of a curved multivicinal Pt(111) crystal. (b) Step-edge structure of a noble metal with step edges running along the $[10 \bar{1}]$ direction. Step edges have square (triangular) atomic disposition in the $A (B)$ step edges. (c) Three-dimensional representation of an STM image of graphene on the multivicinal Pt(111) crystal at a vicinal angle of $\sim - 7 deg$ and $3.5 \pm 0.5$ nm width facets (100 mV, 2.8 nA). The original surface relaxes into (111) terraces $(T)$ and step bunching areas (SB). (d) STM image of graphene on Ir(332) (0.9 V, 0.5 nA). (e) Zoom on a $T$ -SB boundary. The border width is of the order of the lattice parameter of graphene. Some hexagons are superimposed to indicate the continuity of graphene across the boundary. (f) Representation of the superperiodic structure (top) and energetic representation of the potential (bottom). $L$ is the width of the $T$ and SB regions, $b$ is the varying potential region a few Å wide, and $U_{0}$ is the potential barrier.
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Figure 2
Electronic structure of graphene on Ir(332). (a) Isoenergetic map of the band structure at $- 330$ meV. The Brillouin zones associated with the different graphene rotations are shown by the dotted lines. “Ir” labels the substrate spectral features [38]. $d I^{2} / d^{2} E$ maps of the dispersion relations $E (k)$ along the directions (b) perpendicular and (c) parallel to the steps [see the continuous lines in (a)]. The insets show the experimental geometry. $S 1, S 2$ , and $I$ are substrate-related features. The graphene dispersion exhibits minigaps of $\sim 400$ meV $(E_{g})$ perpendicularly to the steps, while no band-gap opening is appreciated in the parallel direction.
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Figure 3
LEED pattern of Ir(332) at 148 eV showing the $G_{1 \times 1}$ vector of the Ir(111) substrate and the $G$ vector due to the facet periodicity. This $G$ vector allows us to determine the spatial periodicity. In this case it is L = 1. $8 \pm 0.2$ nm along the $[1 \bar{2} 1]$ direction.
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Figure 4
Electronic structure of graphene on multivicinal Pt(111). $d I^{2} / d^{2} E$ maps of the dispersion relations $E (k)$ for different facet size and orientation angle with respect to the (111) direction: (a) $3.2 \pm 0.1$ nm and $- 5 . 5^{\circ}$ , (b) $3.5 \pm 0.1$ nm and $- 2^{\circ}$ , and (c) $3.5 \pm 0.1$ nm and $+ 2^{\circ}$ . The Dirac Hamiltonian model is shown as continuous lines, corresponding to a periodicity and potential strength of (a) 3.2 nm and 3.35 eV Å, (b) 3.5 nm and 2.8 eV Å, and (c) 3.5 nm and 1.8 eV Å. The vertical dashed lines indicate the $k$ location of the band-gap opening $(k_{0})$ . (d) Spectra of the original photoemission intensity around $k_{0}$ , integrating in a $k$ range of 0.1 Å $^{- 1}$ . Gaps are indicated by arrows. The Fermi level corresponds to 0 eV.
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Figure 5
Energy distribution curves of photoemission intensity. (a) EDCs for graphene on Ir(332). Black markers show the graphene dispersion and green markers show the iridium states $I, S 1$ , and $S 2$ . The arrows indicate the minigaps. (b) EDCs for graphene on multivicinal Pt corresponding to Fig. 3.
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Figure 6
Comparison between gap openings due to moiré and a one-dimensional periodicity. Simulation of gap openings in the one-dimensional periodicity of Fig. 2 (blue) and on the moiré of a Ir(111) surface (red). The minigaps due to Ir(111) moiré do not correspond to the gaps by nanostructuration as they appear at different $k$ locations.
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