  The experimental unexpected large Seebeck coefficient in SrTiO3 (STO) cannot
be reproduced theoretically by the conventional Bloch-Boltzmann transport with
electron-phonon coupling calculated perturbatively, indicating a failure of
Fermi liquid picture in STO and ill-treatment of polaronic states. Starting
from many-body interaction picture, the polaronic states can be precisely
described by the method of cumulant expansion of retarded Green's function. By
applying Kubo-Greenwood method, we found that the mysterious Seebeck
coefficient can be fully described by a combination of polarons and Fermi
liquid. The coexistence of two types of quasi-particles are attributed to the
multi-band nature of t2g orbitals. Polarons are formed from the one with
heavier electronic effective mass, while the one with lighter effective mass is
renormalized into Fermi liquid quasi-particles. Our method provides a practical
way to study the effect of strong electron-phonon coupling on transport
properties from first principles.
