Spin current and shot noise in single-molecule quantum dots with a phonon mode

In this paper, we investigate the spin-current and its shot-noise spectrum in a single-molecule quantum dot coupled with a local phonon mode. We pay special attention to the effect of the phonon on the quantum transport property. The spin-polarization-dependent current is generated by a rotating magnetic field applied in the quantum dot. Our results show the remarkable influence of phonon mode on the zero-frequency shot noise. The electron-phonon interaction leads to sideband peaks that are located exactly on the integer number of the phonon frequency, and moreover, the peak height is sensitive to the electron-phonon coupling.

Figure 1

Schematic diagram of a molecule quantum-dot system.

Figure 2

(a) The spin current $I_s$ vs the parameter $r$ ($\Gamma =0.04$, $V_g=0$, $g={0.5}^2$, and $\theta =88°$, with frequencies of the magnetic field $w=0.05$, 0.25, 0.7, and 1.5) for the two cases with (solid line) and without (dashed line) the phonon mode for comparison. (b) The spin current $I_s$ as a function of the gate voltage $V_g$ ($\Gamma =0.04$, $g={0.6}^2$, $w=0.1$, and $\theta =88°$, with the parameters $r=0.02$, 0.04, 0.06, and 0.08) for the two cases with (solid line) and without (dashed line) the phonon mode for comparison. (c) The spin current $I_s∕w$ vs the frequency $w$ of the rotating magnetic field, with $\Gamma =0.04$, $V_g=0$, $r=0.08$, and $\theta =88°$ for various coupling constants $g=0$ (solid curve), $g={0.3}^2$ (dotted curve), $g={0.5}^2$ (dashed curve), and $g={0.7}^2$ (dashed-dotted curve). (d) The spin current $I_s$ as a function of the coupling constant $g$.

Figure 3

(a) The cross-correlation shot noise as a function of the parameter $r$ (solid line, with phonon mode, dashed line, without phonon mode). (b) The cross-correlation shot noise as a function of the gate voltage $V_g$ (solid line, with phonon mode; dashed line, without phonon mode). (c) The cross-correlation shot noise $S_{LR}∕w$ vs the frequency $w$ for different coupling constants $g=0$ (solid curve), $g={0.3}^2$ (dotted curve), $g={0.5}^2$ (dashed curve), and $g={0.7}^2$ (dashed-dotted curve), with $\Gamma =0.04$, $V_g=0$, $r=0.08$, and $\theta =88°$.

Figure 4

(a) The autocorrelation shot noise vs the gate voltage $V_g$, with $r=0.02$, 0.06, 0.1, and 0.2 (solid line, with phonon mode, dashed line, without phonon mode). (b) The autocorrelation shot noise vs the frequency $w$ with the same parameters as in Fig. 2c for various coupling constants $g=0$ (solid curve), $g={0.3}^2$ (dotted curve), $g={0.5}^2$ (dashed curve), and $g={0.7}^2$ (dashed-dotted curve).