Figure 1

(a) Scanning electron microscopy (SEM) image of sample $B$: individual MWNTs are deposited on a prestructured Al gate electrode and contacted by four Au fingers, which are deposited on top of the tube. The electrode spacing is 300 nm. Only the two inner electrodes are used. A second tube is located at the right outermost contact. (b) Conductance of sample $A$ at 300 K as a function of gate voltage with an ac bias of $2\mu \mathrm{V}$. The estimated position of the charge neutrality point (CNP) corresponds to the minimum of $G$ and is indicated by the gray line. (c) Same as in Fig. 1b, but for 10 K, 1 K, and 30 mK (top to bottom). For the 10 K curve, both the positions of the CNP (gray line) and the regions of quenched magnetoconductance (black lines) as observed in Fig. 2 are indicated.Reuse & Permissions

Figure 2

(a) Color coded conductance $G$ of sample $A$ as a function of gate voltage $U$ and perpendicular magnetic field at a temperature of 10 K. (b) Color plot of the deviation of $G$ from the zero-field conductance $G(U,B)-G(U,0)$. White arrows indicate the regions of quenched magnetoconductance. (c) Reproduction of the magnetoconductance by 1D weak localization fits. The parameters $L_{\phi }$ and $G(B=0)$ are used as obtained by fitting the data on Fig. 2a. (d) Phase coherence length $L_{\phi }$ vs gate voltage as obtained from the fit. The positions of the charge neutrality point (red line) and the regions of quenched magnetoconductance (black lines) are indicated. (e) Elastic mean-free path (black) and number of transport channels per spin direction (gray) as a function of gate voltage. (f) Color coded differential conductance of sample $A$ as a function of $U$ and dc bias voltage $V$ at $T=10\mathrm{K}$. (g) Exponent $\alpha$ vs $U$ as obtained from fitting a power law $V^{\alpha }$ to $G(U,V)$ in the range $eV\gg k_{\mathrm{B}}T$. Right: scale conversion of the gate voltage into a (nonlinear) energy scale as described in the text.Reuse & Permissions

Figure 3

(a) Calculated $\pi$-orbital DOS for a $(140,140)$ armchair nanotube of diameter of 19 nm (dotted) as a function of energy. Number of excess electrons $N(E)$ (gray) as obtained from the integration of the DOS from 0 to $E$. The subband spacing for this diameter is 66 meV. (b) Measured values $U^{*}$ of quenched MC vs calculated numbers $\Delta N^{*}$ of electrons at subband onsets for sample $A$ (circles, diameter 19 nm) and $B$ (triangles, diameter 14 nm). The lines correspond to linear fits of the data. The slopes of the lines correspond to gate capacitances per length of $300a\mathrm{F}/\mu \mathrm{m}$ and $330a\mathrm{F}/\mu \mathrm{m}$ for samples $A$ and $B$, respectively.Reuse & Permissions

Figure 4

(a) Averaged magnetoconductance of sample $A$ (circles) at temperatures of 60 K, 10 K, 3 K, and 1 K (top to bottom) and fits of 1D weak localization behavior (lines) with scaling factors $A=0.61$, 0.48, 0.35, and 0.22 (top to bottom) as described in the text. (b) Double-logarithmic plot of the temperature dependence of the phase coherence length $L_{\phi }$ as obtained from the weak localization fit (black dots). The line corresponds to a power law fit with an exponent $-0.31$.Reuse & Permissions