Theory of shot noise in single-walled metallic carbon nanotubes weakly coupled to nonmagnetic and ferromagnetic leads

We present a theoretical study of shot noise in single-walled metallic carbon nanotubes weakly coupled to either nonmagnetic or ferromagnetic leads. Using the real-time diagrammatic technique, we calculate the current, Fano factor, and tunnel magnetoresistance in the sequential tunneling regime. It is shown that the differential conductance displays characteristic fourfold periodicity, indicating single-electron charging. Such a periodicity is also visible in tunnel magnetoresistance of the system as well as in the Fano factor. The present studies elucidate the impact of ferromagnetic (vs nonmagnetic) contacts on the transport characteristics under consideration.

Figure 1

Linear conductance as a function of the gate voltage. The parameters are $\Delta =8.4\mathrm{meV}$, $U∕\Delta =0.26$, $J∕\Delta =0.12$, $\delta U∕\Delta =0.04$, $\delta ∕\Delta =0.27$, $k_{B}T∕\Delta =0.025$, $p_L=p_R=0$, $x=0.14$, and $\Gamma =0.2\mathrm{meV}$.

Figure 2

(Color online) Differential conductance as a function of bias and gate voltages. The parameters are the same as in Fig. 1.

Figure 3

Fano factor as a function of gate voltage for several values of bias voltage $V$. The parameters are the same as in Fig. 1.

Figure 4

Bias dependence of the current [(a) and (d)], differential conductance [(b) and (e)] and the Fano factor [(c) and (f)] for $V_g=-0.2666\mathrm{V}$ (left panel) and for $V_g=-0.1202\mathrm{V}$ (right panel). The parameters are the same as in Fig. 1.

Figure 5

The Fano factor, calculated using the total noise (solid line) and the excess noise (dashed line), as a function of the bias voltage for $V_g=-0.1202\mathrm{V}$. The parameters are the same as in Fig. 1.

Figure 6

(Color online) Differential conductance in the parallel (a) and antiparallel (b) magnetic configurations and tunnel magnetoresistance (c) as a function of bias and gate voltages. The parameters are the same as in Fig. 1, except that $p_L=p_R=0.4$.

Figure 7

Tunnel magnetoresistance as a function of gate voltage for several values of the bias voltage. The parameters are the same as in Fig. 1 with $p_L=p_R=0.4$. Tunnel magnetoresistance in the linear response is given by $\mathrm{TMR}=p_L{p}_R∕(1-p_L{p}_R)$.

Figure 8

(Color online) The Fano factor in the parallel (solid) and antiparallel (dashed) magnetic configurations as a function of gate voltage for several values of the bias voltage. The parameters are the same as in Fig. 1 with $p_L=p_R=0.4$.

Figure 9

(Color online) Bias dependence of the current [(a) and (e)], differential conductance [(b) and (f)], TMR [(c) and (g)], and Fano factor [(d) and (h)] for $V_g=-0.2666\mathrm{V}$ (left column) and for $V_g=-0.1202\mathrm{V}$ (right column), and $p_L=p_R=0.4$. The solid (dashed) lines in (a) and (e), (b) and (f), and (d) and (h) correspond to the parallel (antiparallel) magnetic configuration. The other parameters are the same as in Fig. 1.