Nonthermal broadening in the conductance of double quantum dot structures

We study the transport properties of a double quantum dot (DQD) molecule at zero and at finite temperature. The properties of the zero-temperature conductance depend on whether the level attraction between the symmetric and antisymmetric states of the DQD, produced by the coupling to the leads, exceeds or not the interdot tunneling. For finite temperature, we find a remarkable nonthermal broadening effect of the conductance resonance when the energy levels of the individual dots are detuned.

Figure 1

(Color online) Double quantum dot coupled to left (L) and right (R) leads with interdot coupling $t_c$.

Figure 2

(Color online) Zero-temperature conductance at $E=E_F$ as a function of ${\tilde{\epsilon }}_1$, ${\tilde{\epsilon }}_2$ for $t_c⪢\Lambda$. For details, see text.

Figure 3

(Color online) Zero-temperature conductance at $E=E_F$ as a function of ${\tilde{\epsilon }}_1$, ${\tilde{\epsilon }}_2$ for $t_c⪡\Lambda$. For details, see text.

Figure 4

(a) Conductance for $t_c⪢\Lambda$ along the $\overline{\epsilon }$ axis using Eq. (1) (solid line). The approximation given by Eq. (8) is shown with dashed lines. We used $t_c∕\overline{\Gamma }=7$ and $\Delta \Gamma ∕\overline{\Gamma }=0.5$. (b) The transmission for $t_c=\sqrt{{\Gamma }_L{\Gamma }_R}<\Lambda$ given by Eq. (9). The parameters are $t_c∕\overline{\Gamma }=0.954$ and $\Delta \Gamma ∕\overline{\Gamma }=0.3$. For details, see text.

Figure 5

(a) Local DOS ${\rho }_1\left(E\right)$ for $t_c∕\overline{\Gamma }=2$, $\Delta \Gamma =0$ (solid line), and ${\rho }_1\left(E\right)$, ${\rho }_2\left(E\right)$ for $\Delta \Gamma ∕\overline{\Gamma }=0.6$ (dashed and dotted lines, respectively). (b) Local DOS ${\rho }_1\left(E\right)$, ${\rho }_2\left(E\right)$ (solid and dashed lines, respectively) for $\Delta \Gamma ∕\overline{\Gamma }=0.6$, $t_c∕\overline{\Gamma }=0.1$, and (c) for $t_c∕\overline{\Gamma }=0.5$. (d) ${\rho }_1\left(E\right)$ for $\Delta \epsilon ∕\overline{\Gamma }=0.5$, $t_c∕\overline{\Gamma }=0.1$ (solid line) and $t_c∕\overline{\Gamma }=2.0$ (dashed line).

Figure 6

(Color online) Conductance (in units of $2e^2∕h$) as a function of $\overline{\epsilon }$ for two different temperatures: $k_{B}T∕\overline{\Gamma }=1,2.5$ [black and red (gray) lines, respectively]. Curves with solid lines show the exact result of Eq. (4); the curves with dashed lines are calculated using Eq. (17).

Figure 7

(Color online) Conductance (in units of $2e^2∕h$) as a function of ${\tilde{\epsilon }}_1$ for ${\tilde{\epsilon }}_2=E_F$ fixed using four different temperatures: $k_{B}T∕\overline{\Gamma }=0,0.5,1.0,2.0$ (solid, dashed, dotted, and dashed-dotted lines, respectively).

Figure 8

(Color online) FWHM as a function of temperature along the $\Delta \epsilon$ axis. The black curve shows the numerically obtained FWHM using Eq. (4); the green (light gray) curve is the function given by Eq. (18). We used $t_c∕\Gamma =0.5$.

Figure 9

(Color online) Conductance as a function of $\overline{\epsilon }$ for three different temperatures: $k_{B}T∕\overline{\Gamma }=0,1,8$ (solid, dashed, and dotted lines, respectively). The ratio of $t_c$ and $\overline{\Gamma }$ is $t_c∕\overline{\Gamma }=10$, while $\Delta \Gamma =0$.

Figure 10

(Color online) Conductance as a function of $\overline{\epsilon }$ around the energy of the symmetric state ${\epsilon }_{-}$ if $t_c⪢k_{B}T⪢\overline{\Gamma }$. The exact result of Eq. (4) is shown with solid line, the approximation of Eq. (22) with dotted line, and the formula given by Eq. (24) with dashed line. Parameters: $k_{B}T∕\overline{\Gamma }=8$, $t_c∕k_{B}T=5$, $\Delta {\Gamma }_L=0$.

Figure 11

(Color online) The conductance as a function of $\Delta \epsilon$ for three different temperatures: $k_{B}T∕\Gamma =1,5,10$ (solid, dashed, and dotted lines, respectively) and fixed ${\tilde{\epsilon }}_1={\epsilon }_{-}$ (a). The numerically calculated FWHM using Eq. (4) as a function of temperature (b). We used $\Delta \Gamma =0$ and $t_c∕\Gamma =20$.

Figure 12

The two integration contours to calculate the integral in Eq. (3). Filled circles denote the second order poles of $-\frac{\partial f_0\left(E\right)}{\partial E}$; open circles show the poles of $T_{dd}\left(E\right)$.