Thermopower of a single-electron transistor in the regime of strong inelastic cotunneling

We study Coulomb blockade oscillations of thermoelectric coefficients of a single-electron transistor based on a quantum dot strongly coupled to one of the leads by a quantum point contact. At temperatures below the charging energy $E_C$ the transport of electrons is dominated by strong inelastic cotunneling. In this regime we find analytic expressions for the thermopower as a function of temperature T and the reflection amplitude r in the contact. In the case when the electron spins are polarized by a strong external magnetic field, the thermopower shows sinusoidal oscillations as a function of the gate voltage with the amplitude of the order of $e^{-1}|r|{(T/E}_C).\mathrm{}$ We obtain qualitatively different results in the absence of the magnetic field. At temperatures between $E_C$ and $E_C|r{|}^2$ the thermopower oscillations are sinusoidal with the amplitude of order $e^{-1}|r{|}^2\ln {(E}_C/T).\mathrm{}$ On the other hand, at $T\ll E_C|r{|}^2$ we find nonsinusoidal oscillations of the thermopower with the amplitude $\sim e^{-1}|r|\sqrt{{T/E}_C}\ln {(E}_C/T).\mathrm{}$