Aharonov-Bohm effect in the magnetoresistance of a multiwalled carbon nanotube with tunneling contacts

We study the magnetoresistance (MR) of a multiwalled carbon nanotube (MWNT) as a function of the angle $\left({\theta }_{\mathit{tilt}}\right)$ between the external field $\left(B_{\mathit{ext}}\right)$ and the MWNT axis. With $B_{\mathit{ext}}$ oriented along the nanotube axis, its MR exhibits two symmetric (with respect to zero field) sharp minima that shift to higher $B_{\mathit{ext}}$ as this field is rotated away from the axis. We suggest that these minima are associated with a cancellation of the nanotube effective flux as predicted by Nakanishi and Ando [J. Phys. Soc. Jpn. 74, 3027 (2005)].

Figure 1

(Color online) (a) $R_{2\mathrm{T}}\left(T\right)$ for the CNT device. Red circles (gray), measured with constant drive current of $3.3\mathrm{nA}$. Blue circles (dark gray), measured with a constant voltage of $500\mathrm{mV}$. These data were extracted from our $T$-dependent MR measurements. Upper inset: AFM image of the CNT device showing its contacts and the periodic gate array. Lower inset: Magnetic-force microscopy image of a test pattern of an array of five nanomagnets. Bright and dark regions show magnetic poles and the single-domain nature of the nanomagnets. (b) Source-drain current-voltage characteristic of the CNT device at $4.2\mathrm{K}$. Inset: AFM image of the CNT device in close-up. (c) MR measurement of the CNT device at $4.2\mathrm{K}$. Results for sweeps in opposite directions are indicated.

Figure 2

(Color online) (a) Evolution of the MR as a function of ${\theta }_{\mathit{tilt}}$. Arrows denote a central peak that is invariant to the change of ${\theta }_{\mathit{tilt}}$. (b) Red (gray) data indicate the value of the external magnetic field at which the symmetric MR dips are observed, while blue (dark gray) data indicate the corresponding value of the field component along the nanotube length $\left(B_{\mathit{ext}}\cos {\theta }_{\mathit{tilt}}\right)$.

Figure 3

(Color online) (a) Variation of $R_{2\mathrm{T}}$ as a function of magnetic field and back-gate voltage for ${\theta }_{\mathit{tilt}}=0°$ at $4.2\mathrm{K}$. (b) The variation of $B_{\mathit{\text{dip}}}$ as function of back-gate voltage.

Figure 4

(Color online) (a) Schematic illustration of different trajectories that could contribute to a weak-localization process as ${\theta }_{\mathit{tilt}}$ is varied. Arrows indicate the direction of $B_{\mathit{ext}}$. (b) The MR (circles) for ${\theta }_{\mathit{tilt}}=90°$ at $4.2\mathrm{K}$ with a best fit to Eq. (1) (solid line). (c) Relative MR at three different temperatures. $R_{2\mathrm{T}}(B=0)=1.64$, 1.61, and $0.90\mathrm{M}\Omega$ at 4.2 (gray), $20\mathrm{K}$ (black), and $100\mathrm{K}$ (dark gray), respectively