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Thermoelectric properties of finite two-dimensional quantum dot arrays with band-like electronic states

The thermal power ($PF=S^2G_e$) depends on the Seebeck coefficient ($S$) and electron conductance ($G_e$). The enhancement of $G_e$ will unavoidably suppress $S$ because they are closely related. As a consequence, the optimization of $PF$ is extremely difficult. Here, we theoretically investigated the thermoelectric properties of two-dimensional quantum dot (QD) arrays with carriers injected from electrodes. The Lorenz number of 2D QD arrays in the resonant tunneling procedure satisfies the Wiedemann-Franz law, which confirms the formation of minibands. When the miniband center is far away from the Fermi level of the electrodes, the electron transport is in the thermionic-assisted tunneling procedure (TATP). In this regime, $G_e$ in band-like situation and $S$ in atom-like situation can happen simultaneously. We have demonstrated that the enhancement of $G_e$ with an increasing number of electronic states will not suppress $S$ in the TATP.