Transport through single-wall metallic carbon nanotubes in the cotunneling regime

Using the real-time diagrammatic technique and taking into account both the sequential and cotunneling processes, we analyze the transport properties of single-wall metallic carbon nanotubes coupled to nonmagnetic and ferromagnetic leads in the full range of parameters. In particular, considering the two different shell filling schemes of the nanotubes, we discuss the behavior of the differential conductance, the tunnel magnetoresistance, and the shot noise. We show that in the Coulomb diamonds corresponding to even occupations, the shot noise becomes super-Poissonian due to bunching of fast tunneling processes resulting from the dynamical channel blockade, whereas in the other diamonds the noise is roughly Poissonian, in qualitative agreement with recent experiments. The tunnel magnetoresistance is very sensitive to the number of electrons in the nanotube and exhibits a distinctively different behavior depending on the shell filling sequence of the nanotube.

Figure 1

(Color online) (a) Differential conductance and (b) Fano factor as a function of bias and gate voltages. The parameters are $\Delta =8.4\text{meV}$, $U/\Delta =0.26$, $J/\Delta =0.12$, $\delta U/\Delta =0.04$, $\delta /\Delta =0.27$, $k_{B}T/\Delta =0.035$, $p_L=p_R=0$, $x=0.14$, and $\Gamma =0.2\text{meV}$.

Figure 2

(Color online) Bias dependence of the current, the differential conductance, and the Fano factor for [(a)–(c)] $V_g=-0.2666\text{V}$ and [(d)–(f)] $V_g=-0.1202\text{V}$ (see the dashed lines in Fig. 1). The dashed lines show the first-order calculation. The parameters are the same as in Fig. 1.

Figure 3

(Color online) (a) Tunnel magnetoresistance and Fano factor in the (b) parallel and (c) antiparallel configurations as a function of bias and gate voltages. The parameters are as in Fig. 1 with $p_L=p_R=0.5$.

Figure 4

(Color online) Bias dependence of the current, the differential conductance, the TMR, and the Fano factor in the parallel (solid line) and antiparallel (dashed line) configurations for [(a)-(d)] $V_g=-0.2666\text{V}$ and [(e)-(h)] $V_g=-0.1202\text{V}$ (see the dashed lines in Fig. 3). The parameters are the same as in Fig. 3.

Figure 5

(Color online) (a) Tunnel magnetoresistance and (b) Fano factor in the parallel configuration as a function of bias and gate voltages. The parameters are the same as in Fig. 3 with $\delta /\Delta =0.1$.

Figure 6

(Color online) Bias dependence of the current, the differential conductance, the TMR, and the Fano factor in the parallel (solid line) and antiparallel (dashed line) configuration for [(a)-(d)] $V_g=-0.2544\text{V}$ and [(e)-(h)] $V_g=-0.108\text{V}$, corresponding to the dashed lines in Fig. 5. The parameters are the same as in Fig. 5.