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 $e^{-1}\mathrm{\mid }r\mathrm{\mid }\frac{T}{E_C}$. We obtain qualitatively different results in the absence of the magnetic field. At temperatures between $E_C$ and $E_C\mathrm{\mid }r{\mathrm{\mid }}^2$ the thermopower oscillations are sinusoidal with the amplitude of order $e^{-1}\mathrm{\mid }r{\mathrm{\mid }}^2\ln \frac{E_C}{T}$. On the other hand, at $T\ll E_C\mathrm{\mid }r{\mathrm{\mid }}^2$ we find non-sinusoidal oscillations of the thermopower with the amplitude $\sim e^{-1}\mathrm{\mid }r\mathrm{\mid }\sqrt{T\mathrm{/}{E}_C}\ln (E_C\mathrm{/}T)$.