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 thermopoweras a function of temperature $T$ and the reflection amplitude $r$ in the contact. In the case when the electron spins are plarized 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 $e^{-1} |r| frac{T}{E_C}$. 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 $e^{-1} |r|^2 ln frac{E_C}{T}$. On the other hand, at $ T E_C |r|^2$ we find non-sinusoidal oscillations of the thermopower with the amplitude $~ e^{-1} |r| sqrt{T/E_C} ln (E_C/T)$.