Four-probe measurements of carbon nanotubes with narrow metal contacts

We find that electrons in single-wall carbon nanotubes may propagate substantial distances (tens of nanometers) under metal contacts. We perform four-probe transport measurements of the nanotube conductance and observe significant deviations from the standard Kirchhoff’s circuit rules. Most noticeably, injecting current between two neighboring contacts on one end of the nanotube induces a nonzero voltage difference between two contacts on the other end.

Figure 1

(Color online) Top: the schematic and the scanning electron micrograph of the sample. White bar: $1\mu \mathrm{m}$. Main panel, top curves: differential resistances of the three nanotube segments measured by a two-probe method between pairs of contacts $AB$, $BC$, and $CD$. Middle curves: the three-terminal contact resistances $R_{i,g,v,f}$ and $R_{f,v,g,i}$ (see clarification in the text). Bottom: $R_{i,g,g,v}$ data (dots) and the fit described in the text. $T=1.3\mathrm{K}$.

Figure 2

(Color online) Differential resistance of the middle segment measured by a two-probe method (solid line) and by a four-probe method (dash-dotted line). Dashed line: $R_{BC}^{\left(2\right)}-R_{BC}^{\left(4\right)}-R_{i,g,v,f}-R_{f,v,g,i}$. $T=1.3\mathrm{K}$.

Figure 3

(Color online) Nonlocal four-probe resistance measurements $R_{i,g,v-,v+}$ (see schematic) and $R_{v+,v-,g,i}$ as a function of magnetic field parallel to the nanotube. $T=1.3\mathrm{K}$.

Figure 4

(Color online) Various signals discussed in the paper measured at the temperature of $70\mathrm{K}$. Top three curves $(R\gtrsim 10\mathrm{k}\Omega )$: segment resistances. Next lower curves $R\gtrsim 1\mathrm{k}\Omega$: three-terminal resistances. Scattered squares with overlayed curve $(R\sim 100\Omega )$: $R_{i,g,g,v}$ measurement and the corresponding fit. Lowest curve: nonlocal four-probe resistance. Note that the NL4P signal changes sign at $V_{\mathit{\text{gate}}}\approx 5.6\mathrm{V}$.

Figure 5

(Color online) Nonlocal four-probe resistance as a function of gate voltage at several temperatures. The modulations of the NL4P signal decay rapidly with temperature. However, a nonzero signal is still left at the highest temperature.