Enhanced thermoelectric response in the fractional quantum Hall effect

We study the linear thermoelectric response of a quantum dot embedded in a constriction of a quantum Hall bar with fractional filling factors $\nu =1/m$ within Laughlin series. We calculate the figure of merit $ZT$ for the maximum efficiency at a fixed temperature difference. We find a significant enhancement of this quantity in the fractional filling in relation to the integer-filling case, which is a direct consequence of the fractionalization of the electron in the fractional quantum Hall state. We present simple theoretical expressions for the Onsager coefficients at low temperatures, which explicitly show that $ZT$ and the Seebeck coefficient increase with $m$.

Figure 1

Sketch of the setup. A quantum Hall bar is biased by a difference of temperature $\mathrm{\Delta }T=T_L-T_R$ and a voltage $V=({\mu }_R-{\mu }_L)/e$. Charge and thermal transport is induced through a quantum dot generated by constrictions that generate regions of the sample with filling factors ${\nu }_L$ and ${\nu }_R$. The spectrum of the quantum dot can be manipulated with a gate voltage $V_g$.

Figure 2

Onsager coefficients at the temperature $T=\gamma$, as functions of the gate voltage for a quantum dot with two energy levels. Solid, dashed, and dashed-dotted lines correspond to $\tilde{m}=m_L+m_R=2,4,6$, respectively. The integer-filling case corresponds to $\tilde{m}=2$. The level spacing is $\mathrm{\Delta }=30\gamma$. The chemical potential is set at $\mu =0$.

Figure 3

Electrical and thermal conductances, $G$ and $\kappa$, respectively, and Seebeck coefficient $S$ of a single-level quantum dot, as functions of the gate voltage. Other details are the same as in Fig. 2.

Figure 4

Figure of merit $ZT$ as a function of the temperature $T$ and the energy of the QD level ${\varepsilon }_d$ (right panel). Plots at fixed temperatures are shown in the left panels. Other details are the same as in Fig. 2.