Quantum Hall effect in monolayer-bilayer graphene planar junctions

Jifa Tian, Yongjin Jiang, Isaac Childres, Helin Cao, Jiangping Hu, and Yong P. Chen

Phys. Rev. B 88, 125410 – Published 6 September 2013

Abstract

The Hall resistance of a homogeneous electron system is well known to be antisymmetric with respect to the magnetic field and the sign of charge carriers. We have observed that such symmetries no longer hold in planar hybrid structures consisting of partly single layer graphene (SLG) and partly bilayer graphene (BLG) in the quantum Hall (QH) regime. In particular, the Hall resistance across the SLG and BLG interface is observed to exhibit quantized plateaus that switch between those characteristic of SLG QH states and BLG QH states when either the sign of the charge carriers (controlled by a back gate) or the direction of the magnetic field is reversed. Simultaneously reversing both the carrier type and the magnetic field gives rise to the same quantized Hall resistances. The observed SLG-BLG interface QH states, with characteristic asymmetries with respect to the signs of carriers and magnetic field, are determined only by the chirality of the QH edge states and can be explained by a Landauer-Büttiker analysis applied to such graphene hybrid structures involving two regions of different Landau level structures.

Received 25 March 2013

DOI:https://doi.org/10.1103/PhysRevB.88.125410

Authors & Affiliations

Jifa Tian^1,2,*, Yongjin Jiang^1,3, Isaac Childres^1,2, Helin Cao^1,2, Jiangping Hu¹, and Yong P. Chen^1,2,4,†

¹Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
²Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
³Center for Statistical and Theoretical Condensed Matter Physics, and Department of Physics, Zhejiang Normal University, Jinhua 321004, People's Republic of China
⁴School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA

^*Email address: tian5@purdue.edu
^†Email address: yongchen@purdue.edu

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Issue

Vol. 88, Iss. 12 — 15 September 2013

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Images

Figure 1
(a) Optical image of a SLG and BLG hybrid structure (exfoliated from graphite). (b) Representative Raman spectra of the SLG and BLG parts in device 1. The wavelength of the Raman excitation laser is 532 nm. The power of the laser is ∼200 μW incident on the sample. The field effect curves ( $R$ vs $V_{g}$ ) are measured from the SLG ( $R_{1 x x}$ ) and BLG ( $R_{2 x x}$ ) parts for (c) device 1 and (d) device 2.Reuse & Permissions
Figure 2
(a) Optical image of device 1. The contours for the regions corresponding to SLG and BLG are highlighted by white dotted and blue dashed lines, respectively. The widths of all electrodes are 1 μm. (b) Schematic 3D structure of the device, indicating electrical connections for various resistance measurements. The positive $B$ direction (black arrow) points upward. (c) Hall resistances ( $R_{1 x y}$ , $R_{2 x y}$ , and $R_{12 x y}$ ) and longitudinal resistances ( $R_{1 x x}$ , $R_{2 x x}$ , and $R_{12 x x}$ ), as functions of $V_{g}$ at $B$ = $+$ 15 T and $T$ = 0.5 K. (d) $R_{1 x y}$ , $R_{2 x y}$ , and $R_{12 x y}$ , as well as $R_{1 x x}$ , $R_{2 x x}$ , and $R_{12 x x}$ , as functions of the $B$ at 0.5 K and $V_{g}$ = 0 V. In (c) and (d), QH plateaus associated with SLG or BLG QH states are labeled by arrows, and their quantum numbers $(m$ , related to the plateau values $R_{x y} = h$ /( $m e^{2}))$ are green or purple, respectively. The edge state chirality, CW or ACW, has been labeled near the representative QH plateaus observed in $R_{12 x y}$ in both (c) and (d).Reuse & Permissions
Figure 3
(a) Optical image of device 2. The widths of all electrodes are 1 μm. (b) Schematic 3D structure of the device with the corresponding electrical connections. (c) $R_{12 x y}$ (between electrodes $c$ and $b$ ) as a function of $V_{g}$ at $B$ = $-$ 18 T and $B$ = $+$ 18 T (blue and black curves, respectively). (d) $R_{12 x y}$ as a function of the $B$ at $V_{g}$ = 0 and 30 V (blue and black curve, respectively). In (c) and (d), QH plateaus corresponding to values associated with SLG or BLG QH states are labeled by arrows, and their quantum numbers are green or purple, respectively.Reuse & Permissions
Figure 4
Schematic of the edge state currents with (a) CW and (b) ACW circulation in both region 1 (white) and region 2 (purple). (c) Schematic illustration of the QHE in SLG, BLG, and the SLG-BLG interface. The QHE $R_{x y}$ of either SLG (solid line) or BLG (dashed line) is related to the corresponding number ( $m$ ) of edge states in SLG or BLG by $m$ = ( $h$ / $e^{2}$ )/ $R_{x y}$ , where $h$ / $e^{2}$ the resistance quantum. The calculated interface QHE $R_{x y}$ takes the SLG or BLG values depending on the pair of electrodes used and the edge state chirality. While it is well known that 1/ $R_{x y}$ shows a jump of 4 $e^{2}$ / $h$ for SLG and 8 $e^{2}$ / $h$ for BLG at ν = 0 (within a single-particle physics picture), the jump for the SLG-BLG interface is 6 $e^{2}$ / $h$ .Reuse & Permissions

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