Electron Interference in Ballistic Graphene Nanoconstrictions

Jens Baringhaus, Mikkel Settnes, Johannes Aprojanz, Stephen R. Power, Antti-Pekka Jauho, and Christoph Tegenkamp

Phys. Rev. Lett. 116, 186602 – Published 5 May 2016

Abstract

We realize nanometer size constrictions in ballistic graphene nanoribbons grown on sidewalls of SiC mesa structures. The high quality of our devices allows the observation of a number of electronic quantum interference phenomena. The transmissions of Fabry-Perot-like resonances are probed by in situ transport measurements at various temperatures. The energies of the resonances are determined by the size of the constrictions, which can be controlled precisely using STM lithography. The temperature and size dependence of the measured conductances are in quantitative agreement with tight-binding calculations. The fact that these interference effects are visible even at room temperature makes the reported devices attractive as building blocks for future carbon based electronics.

Received 6 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.186602

Physics Subject Headings (PhySH)

Ballistic transport

Graphene

Electron diffraction Scanning electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jens Baringhaus¹, Mikkel Settnes³, Johannes Aprojanz¹, Stephen R. Power³, Antti-Pekka Jauho³, and Christoph Tegenkamp^1,2,*

¹Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany
²Laboratory of Nano and Quantum Engineering (LNQE), Leibniz Universität Hannover, Schneiderberg 39, 30167 Hannover, Germany
³Center for Nanostructured Graphene (CNG), DTU Nanotech, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark

^*tegenkamp@fkp.uni-hannover.de

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Vol. 116, Iss. 18 — 6 May 2016

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Images

Figure 1
Synthesis of sidewall GNCs by STM lithography. First, a reference two-point-probe measurement is performed on the pristine sidewall GNR to ensure the presence of a ballistic channel. The GNC is subsequently defined into the GNR via local etching by means of a STM tip. A second two-point measurement probes the transport properties of the GNC.
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Figure 2
STM study of a sidewall GNC. (a) Schematic view of the graphene structure on the SiC mesa sidewall after synthesis of a narrow constriction with STM lithography. (b) STM images of the top, center, and bottom part of the cut (tip voltage for imaging $V_{t} = 3 V$ , tunneling current $I_{t} = 1 nA$ ). In the bottom frame, the presence of a GNC is confirmed. The red and black dots in the middle frame indicate the locations at which spectroscopy was performed, panel (d). (c) Atomically resolved STM topograph of the graphene lattice in the vicinity of the cut [see blue rectangle in (b)] ( $V_{t} = 200 mV$ , $I_{t} = 100 pA$ ). (d) $d I_{t} / d V_{t}$ spectroscopy of the GNC. Red curve: spectrum acquired directly on the cut [open-feedback parameters (setpoint): $V_{t} = 0.2 V$ , $I_{t} = 0.2 nA$ , modulation voltage $V_{rms} = 15 mV$ ]. Black curve: spectrum acquired in the vicinity of the cut on the unpatterned graphene lattice ( $V_{t} = 0.4 V$ , $I_{t} = 0.4 nA$ , modulation voltage $V_{rms} = 20 mV$ ).
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Figure 3
Electronic transport across GNCs. (a) $I V$ curves across a GNC with length $L = 6 nm$ and width $W = 2 nm$ for temperatures between $T = 28$ and 300 K. The solid lines indicate corresponding fits to the Kaiser expression [40]. The violet curve is the $I V$ curve of the pristine ribbon, prior to STM lithography. (b) Differential conductance of the $I V$ curve shown in (a). Conductance peaks $G_{P}$ at voltage $V_{P}$ are clearly visible for the complete temperature range. The violet curve is the differential conductance of the pristine ribbon. (c) Peak conductances $G_{P}$ and peak voltages $V_{P}$ extracted from differential conductance curves. The peak conductance is exponentially decreasing with increasing temperature while the voltage position of the peak remains constant. (d) Differential conductance across a GNC measured with two different contact spacings $d = 500 nm$ and $5 μ m$ . The inset depicts the arrangement of the probes on both sides of the constriction.
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Figure 4
Theoretical transport characteristics of GNCs and comparison with the experiment. (a) Theoretical differential conductance of a GNC of dimension $L \approx 1 nm$ and $W \approx 1.7 nm$ for different temperatures. (b) Voltage position of the conductance peaks plotted against the length $L$ of the constriction. The solid black line indicates the energy of the ground state in the standard particle-in-a-box picture. Inset: measured conductance at $T = 298 K$ for constriction lengths $L \approx 6 nm$ (black) and $L \approx 1.5 nm$ (red). Note the different voltage scales for the two curves.
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