Evidence of electronic cloaking from chiral electron transport in bilayer graphene nanostructures

Kyunghoon Lee, Seunghyun Lee, Yun Suk Eo, Cagliyan Kurdak, and Zhaohui Zhong

Phys. Rev. B 94, 205418 – Published 14 November 2016

Abstract

The coupling of charge carrier motion and pseudospin via chirality for massless Dirac fermions in monolayer graphene has generated dramatic consequences, such as the unusual quantum Hall effect and Klein tunneling. In bilayer graphene, charge carriers are massive Dirac fermions with a finite density of states at zero energy. Because of their non-relativistic nature, massive Dirac fermions can provide an even better test bed with which to clarify the importance of chirality in transport measurement than massless Dirac fermions in monolayer graphene. Here, we report an electronic cloaking effect as a manifestation of chirality by probing phase coherent transport in chemical-vapor-deposited bilayer graphene. Conductance oscillations with different periodicities were observed on extremely narrow bilayer graphene heterojunctions through electrostatic gating. Using a Fourier analysis technique, we identified the origin of each individual interference pattern. Importantly, the electron waves on the two sides of the potential barrier can be coupled through the evanescent waves inside the barrier, making the confined states underneath the barrier invisible to electrons. These findings provide direct evidence for the electronic cloaking effect and hold promise for the realization of pseudospintronics based on bilayer graphene.

Received 24 April 2016

DOI:https://doi.org/10.1103/PhysRevB.94.205418

Physics Subject Headings (PhySH)

Cloaking

Bilayer films Graphene

Chemical vapor deposition

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Kyunghoon Lee^1,2, Seunghyun Lee^1,3, Yun Suk Eo⁴, Cagliyan Kurdak⁴, and Zhaohui Zhong^1,*

¹Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA
²Department of Electrical Engineering and Computer Science, University of California, Berkeley, California 94720, USA
³Department of Electronics and Radio Engineering, Kyung Hee University, Gyeonggi 446-701, South Korea
⁴Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

^*zzhong@umich.edu

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Vol. 94, Iss. 20 — 15 November 2016

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Images

Figure 1
(a) Schematic diagram of a dual-gated BLG device. (b) False-color scanning electron microscopy image of three BLG devices having different channel lengths (200, 50, and 100 nm from left to right). Source/drain electrodes, BLG, and top-gate electrodes are represented by blue, green, and yellow color, respectively. The scale bar is 200 nm. (c) Schematic showing Fabry-Perot resonance in monopolar regime due to reflection at the source and drain contact. (d) Schematic illustration of electronic cloaking resonance in BLG arising from decoupling of orthogonal pseudospins in bipolar regime (green color). Blue- and yellow-colored trajectories show resonance of confined states by potential barrier.
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Figure 2
Fabry-Perot resonance in back-gated BLG devices. (a), (b), and (c), Two-dimensional color plot of differential conductance versus V and $V_{BG}$ for BLG device with channel length of (a) 55 nm, (b) 118 nm, and (c) 160 nm. The channel width is 500 nm for all three devices, and all data are taken at 6 K. For each image, a smooth background was subtracted to highlight the Fabry-Perot oscillation patterns. Quasiperiodic crisscrossing dark (bright) lines correspond to conductance dips (peaks). The dotted yellow lines are guides to the eye, and the red arrows indicate the bias voltage oscillation period ( $V_{C}$ ). (d) $e V_{C}$ measured from three devices plotted against device physical channel length. The results are also compared with theoretical length-dependent resonance periods for single-layer graphene with linear dispersion (red curve) and BLG with parabolic dispersion (blue curve).
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Figure 3
Electronic cloaking effect in dual-gated BLG device. (a) Two-dimensional resistance map as a function of $V_{TG}$ and $V_{BG}$ from a 150 nm BLG device. (b) and (c) To extract oscillation components controlled by both $V_{TG}$ and $V_{BG}$ , and controlled only by $V_{BG}$ separately, inverse Fourier transform with masking technique was performed on the 2D resistance map in (a). The two fringing patterns along the (b) $N_{T}$ (black solid line) and (c) $N_{B}$ directions (white solid line) were obtained, respectively. (d) Two-dimensional resistance map is recovered with clearer oscillation patterns by adding two fringing patterns, (b) and (c). Top insets in (b), (c), (d) show representative trajectories for each resonance condition. Observed Fabry-Perot conductance oscillations are represented by yellow, green, and blue lines, respectively in (b), (c), (d), corresponding to massive Dirac fermion trajectories with the same colors shown in the insets. (e), (f), (g) The Fourier transform spectra for (b), (c), and (d), respectively. The Fourier transforms were performed along the gray dashed line ( $V_{TG} = - 2.1 V$ ) in the highlighted dashed square regions. Note that weak higher harmonics are also observed, corresponding to multiple rotating trajectories within the defined cavities. The inset in (f) shows false-color SEM image of a device with top gate (blue), source-drain electrodes (yellow), and BLG (dark purple). The scale bar is 100 nm. The schematic view of resonant cavity lengths with trajectories is drawn for corresponding FFT results in the inset in (g).
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