Electron injection in a nanotube with leads: Finite-frequency noise correlations and anomalous charges

The nonequilibrium transport properties of a carbon nanotube which is connected to Fermi liquid leads, where electrons are injected in the bulk, are computed. A previous work which considered an infinite nanotube showed that the zero-frequency noise correlations, measured at opposite ends of the nanotube, could be used to extract the anomalous charges of the chiral excitations which propagate in the nanotube. Here, the presence of the leads has the effect that such noise cross correlations vanish at zero frequency. Nevertheless, information concerning the anomalous charges can be recovered when considering the spectral density of noise correlations at finite frequencies, which is computed perturbatively in the tunneling amplitude. The spectrum of the noise cross correlations is shown to depend crucially on the ratio of the time of flight of quasiparticles traveling in the nanotube to the “voltage” time which defines the width of the quasiparticle wave packets injected when an electron tunnels. Potential applications toward the measurement of such anomalous charges in nonchiral Luttinger liquids (nanotubes or semiconductor quantum wires) are discussed.

Figure 1

Nanotube connected to leads, with electrons injected in the bulk via a STM.

Figure 2

Entanglement of quasiparticle excitations in an infinite Luttinger liquid.

Figure 3

1D model for noninteracting leads: the Luttinger liquid parameter varies over distance.

Figure 4

Finite frequency noise autocorrelation for an infinite nanotube, in the noninteracting case ($K_{c+}=1$ dashed lines), as well as in the case of repulsive interactions ($K_{c+}=\frac{1}{3}$, full line). The noise is normalized to the zero-frequency value. In the case of $K_{c+}=\frac{1}{3}$, the cross correlations $-S_{x,-x}$ have the same dependence on $\omega$.

Figure 5

Finite frequency noise correlations for a nanotube connected to leads. (a) Case where ${\tau }_{\mathrm{L}}=14{\tau }_{\mathrm{V}}$; (b) case where ${\tau }_{\mathrm{L}}={\tau }_{\mathrm{V}}$. The noise is normalized according to the frequency-independent prefactor of Eq. (36).