Tomonaga-Luttinger Liquid Features in Ballistic Single-Walled Carbon Nanotubes: Conductance and Shot Noise

We study the electrical transport properties of well-contacted ballistic single-walled carbon nanotubes in a three-terminal configuration at low temperatures. We observe signatures of strong electron-electron interactions: the conductance exhibits bias-voltage-dependent amplitudes of quantum interference oscillation, and both the current noise and Fano factor manifest bias-voltage-dependent power-law scalings. We analyze our data within the Tomonaga-Luttinger liquid model using the nonequilibrium Keldysh formalism and find qualitative and quantitative agreement between experiment and theory.

Figure 1

Illustration of a three-terminal SWNT device with a interaction parameter $g$ ($g=1$ in the metal electrodes and $g<1$ in the SWNT). Inset: atomic force microscope image of a device.

Figure 2

Graphs of $dI/d{V}_{\mathrm{ds}}$ in units of $2G_{\mathrm{Q}}$. (a) Density plot in $V_{\mathrm{ds}}$ and $V_{\mathrm{g}}$. (b) Theoretical $dI/d{V}_{\mathrm{ds}}$ in $V_{\mathrm{ds}}$ at a given $V_{\mathrm{g}}$ for $g=1$ (blue) and $g=0.25$ (red) with $U_1=0.14$ and $U_2=0.1$ at $T=4\mathrm{K}$. (c) Three experimental traces at $V_{\mathrm{g}}=-9\mathrm{V}$ (top), $V_{\mathrm{g}}=-8.3\mathrm{V}$ (middle), and $V_{\mathrm{g}}=-7.7\mathrm{V}$ (bottom). (d) Theoretical traces at $T=4\mathrm{K}$ for $U_2=-0.1$ (top), $U_2=0$ (middle), and $U_2=0.1$ (bottom) with $U_1=0.14$.

Figure 3

Shot noise power spectral density vs $V_{\mathrm{ds}}$ for the LED/PD pair ($S_{\mathrm{PD}}$, triangle) and the SWNT ($S_{\mathrm{SWNT}}$, dot) at $V_{\mathrm{g}}=-7.9\mathrm{V}$. The slopes of $S_{\mathrm{PD}}$ and $S_{\mathrm{SWNT}}$ are 1 and 0.64, from which the inferred $g$ value for SWNT is 0.16.

Figure 4

Fano factor ($F$) vs $V_{\mathrm{ds}}$ at $V_{\mathrm{g}}=-7.9\mathrm{V}$. The theoretical $F$ curves for $g=1$ (yellow) and $g=0.25$ (red) at $T=4\mathrm{K}$ are drawn with $U_1=0.14$ and $U_2=0.1$ after subtracting thermal noise $4k_{\mathrm{B}}T(dI/d{V}_{\mathrm{ds}})$. The power exponent and the inferred $g$ values from experiments are $\alpha \sim -0.35$ (blue line) and $g=0.18$. The theoretical $g=1$ (yellow) plot gives $\alpha \sim 0$ as expected.