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). 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|²ln(E_C/T). On the other hand, at T≪E_C|r|² we find nonsinusoidal oscillations of the thermopower with the amplitude ∼e^-1|r|√T/E_Cln(E_C/T).