Large oscillating nonlocal voltage in multiterminal single-wall carbon nanotube devices

We report on the observation of a nonlocal voltage in a ballistic (quasi)-one-dimensional conductor, realized by a single-wall carbon nanotube with four contacts. The contacts divide the tube into three quantum dots, which we control by the back-gate voltage $V_g$. We measure a large oscillating nonlocal voltage $V_{\mathrm{nl}}$ as a function of $V_g$. Though a resistor model that includes the impedance of the voltmeter can account for a nonlocal voltage including change of sign, it fails to describe the magnitude properly. The large amplitude of $V_{\mathrm{nl}}$ is due to quantum interference effects and can be understood within the scattering approach of electron transport.

Figure 1

(a) A SEM image of a device. The metallic single-wall CNT is contacted with two ferromagnetic (F) and two normal contacts (N), which together divide the tube into three equidistant segments ($L\approx 500$ nm) which act as QDs. (b) Two-terminal magnetoresistance signal (F-F). (c,d) Schematics of the measurement setup for the local two-terminal (c) and nonlocal four-terminal (d) measurement.

Figure 2

(a)–(c) Linear conductance $G$ of each segment of the device as a function of gate voltage $V_g$. The inset of (c) shows a gray-scale plot of $dI∕d{V}_0$ as function of $V_g$ and source-drain bias $V_{\mathrm{sd}}$ in the same $V_g$ range. (d) Nonlocal voltage measured across terminals 3 and 4 (full curve) and the current injected across terminals 1 and 2 (dashed).

Figure 3

Nonlocal measurement as a function of gate voltage $V_g$ of another device. (a) The current $I$ between terminals 1-2 (dashed) is plotted together with the nonlocal voltage $V_{\mathrm{nl}}$ between terminals 3-4 (solid). (b) Calculated nonlocal resistance $R=V_{\mathrm{nl}}∕I$.

Figure 4

(a) Resistor model for metal-CNT contacts. The three resistors in each shaded region model the property of the contact, whereas $R_{34}$, for example, describes the intratube resistance in between contacts $3$ and $4$. Two limiting cases are shown in (b) and (c): In (b), the contacts are weakly coupled to the CNT, whereas they split the CNT into segments due to their strong coupling in (c). (d) shows the quantum description, using three-port scattering matrices $S_j$ (triangles) in each node. Note that there is an additional input resistance $R_I$ (not shown) in both electrometers measuring $V_3$ and $V_4$.

Figure 5

Measurements of the two-terminal conductance $G_{42}$ between terminals 2 and 4 while terminal 3 is floating (line) and while it is grounded (dashed line). The inset depicts transmission through the CNT in both cases.