Thermopower signatures and spectroscopy of the canyon of conductance suppression

Interference effects in quantum dots between different transport channels can lead to a strong suppression of conductance, which cuts like a canyon through the common conductance plot [Phys. Rev. Lett. 104, 186804 (2010)]. In the present work we consider the thermoelectric transport properties of the canyon of conductance suppression using the second-order von Neumann approach. We observe a characteristic signal for the zeros of the thermopower. This demonstrates that thermoelectric measurements are an interesting complimentary tool to study complex phenomena for transport through confined systems.

Figure 1

Schematic of the system: A quantum dot with single particle levels $E_1$ and $E_{1^{\prime }}$ coupled to the leads via tunneling barriers. The leads have a temperature difference $\mathrm{\Delta }T$ which can give rise to a current flowing through the dot.

Figure 2

The thermopower $S$ (left column) and conductance $G$ (right column) as a function of the detuning $\mathrm{\Delta }E$ and gate voltage $V_g$ in the noninteracting case $U=0$. The asymmetry values are $a=1,1/2,1/4,0$ for (a) to (d), respectively. For the contour plots the temperature is set to $k_{\mathrm{B}}T=0.5\mathrm{\Gamma }$ and $\pm$ denotes the sign of the thermopower for these contour plots. The dashed (blue) curves depict zeros of thermopower, given by Eqs. (20), for the case of a small temperature $\mathrm{\Gamma }\gg k_{\mathrm{B}}T\to 0$. (e) A cut of the contour plots at the detuning $\mathrm{\Delta }E=-8.5\mathrm{\Gamma }$.

Figure 3

Same as Fig. 2 just for the case where the tunneling amplitudes have the same sign. The dashed (blue) curves depict zeros of thermopower, given by Eqs. (21).

Figure 4

The thermopower $S$ and conductance $G$ evolution as a function of increasing charging energy for symmetric coupling configuration $a=1$. The charging energy values are $U=0,5\mathrm{\Gamma },10\mathrm{\Gamma }$ for (a) to (c), respectively. For the 2vN thermopower calculations we have set $k_{\mathrm{B}}\mathrm{\Delta }T=0.1\mathrm{\Gamma },k_{\mathrm{B}}\overline{T}=\mathrm{\Gamma }$ and for conductance calculations we have set $k_{\mathrm{B}}\mathrm{\Delta }T=0,k_{\mathrm{B}}\overline{T}=\mathrm{\Gamma },V=0.1\mathrm{\Gamma }$. Also a finite bandwidth $D=20\mathrm{\Gamma }$ is used. The dashed (green) lines denote the bare resonances given by Eq. (25). The dashed (red) lines show a region of detuning, where the thermopower is not defined because of the zero conductance.

Figure 5

The thermopower $S$ and conductance $G$ evolution as a function of increasing charging energy for asymmetric coupling configuration $a=1/2$. The charging energy values are $U=0,2.5\mathrm{\Gamma },5\mathrm{\Gamma },7.5\mathrm{\Gamma },10\mathrm{\Gamma }$ for (a) to (e), respectively. Other parameter values are as in Fig. 4.

Figure 6

The thermopower $S$ and conductance $G$ evolution as a function of increasing charging energy for the same sign tunneling amplitudes Eq. (16) and asymmetric coupling configuration $a=1/2$. The charging energy values are $U=0,2.5\mathrm{\Gamma },5\mathrm{\Gamma },7.5\mathrm{\Gamma },10\mathrm{\Gamma }$ for (a) to (e), respectively. Other parameter values are as in Fig. 4. The (red) horseshoe patches denote the region of parameters, where our numerical procedure for solving the 2vN equations does not converge.

Figure 7

The thermopower $S$ (first column) calculated for canyon of conductance $G$ suppression (second column) discussed in Ref. [53]. The charging energy values are $U=2\mathrm{\Gamma }$ and $U=5\mathrm{\Gamma }$ for (a) and (b), respectively. Note that here the parametrization $t_{\mathrm{L}1}=-\sqrt{0.3}{t}_0,t_{\mathrm{R}1}=\sqrt{0.1}{t}_0,t_{\mathrm{L}{1}^{\prime }}=t_0,t_{\mathrm{R}{1}^{\prime }}=\sqrt{0.4}{t}_0$, with $t_0=\sqrt{\mathrm{\Gamma }/\left(2\pi {\nu }_F\right)}$, for tunneling amplitudes is used. Other parameter values are as in Fig. 4.