Shot Noise with Interaction Effects in Single-Walled Carbon Nanotubes

We have measured shot noise in single-walled carbon nanotubes with good contacts at 4.2 K at low frequencies ($f=600–850\mathrm{MHz}$). We find a strong modulation of shot noise over the Fabry-Perot pattern; in terms of the differential Fano factor the variation ranges over 0.4–1.2. The shot noise variation, in combination with differential conductance, is analyzed using two (spin-degenerate) modes with different, energy-dependent transmission coefficients. Deviations from the predictions from Landauer-Buttiker formalism are assigned to electron-electron interactions.

Figure 1

Differential conductance $G_d$ on the plane spanned by bias voltage $V$ and gate voltage $V_g$. The scale bar is given on the right in units of $e^2/h(=G_0/2)$.

Figure 2

Excess noise $S(I)-S(0)$ vs bias voltage $V>0$ (○) and $V<0$ (●) at $V_g=0.04\mathrm{V}$. Red curve illustrates an evaluation of Eq. (4) using $F=0.65$ and the experimentally determined value $R(0)/(V/I)$. The dashed line refers to exponent $\beta =1$. The bottom inset displays the data on linear scale (in $A^2/\mathrm{Hz}$). The inset on top displays the electrical equivalent model employed to calculate the coupling of the current fluctuations as well as the corrections due to nonlinearities.

Figure 3

Differential Fano factor $F_d$ on $V_g$ vs $V$ plane. The scale bar is given on the right.

Figure 4

Plots obtained using data of Figs. 1, 3 at $V=-6.2\mathrm{mV}$. (a) Average differential Fano factor $\tilde{F}=\frac{1}{I}{\int }_0^I{F}_{d}dI$ (●) and differential Fano factor $F_d=\frac{1}{2e}\frac{dS}{dI}$ (△) as a function of $V_g$. (b) $\tilde{F}$ vs total conductance $G=I/V$ plotted parametrically by varying $V_g$. (c) $F_d$ vs $G_d$ plotted parametrically by varying $V_g$; $F_d$ varies in a clockwise manner with growing $V_g$. For the overlayed curves, see text.