  We study the thermoelectric transport coefficients of a one-dimensional (1D)
electron waveguide connected to one and then two off-channel cavities, in the
presence of dephasing phonons. The model system is that of a linear chain
described as a 1D lattice. For simplicity we consider single-mode cavities,
which may be tuned with external gates. While the presence of only one
off-channel cavity yields a nearly symmetric transmission profile, which is
canceled around the cavity mode, an additional cavity modifies this profile
strongly and results in an asymmetric shape characterized by oscillations. In
both cases, we consider electron-phonon interactions in our calculations and
analyze their effects on the transmission function around the Fermi energy.
Knowledge of the energy-dependent transmission function allows the numerical
computation of thermoelectric transport coefficients, including the
thermopower. In the presence of a second off-channel cavity, the sign of the
thermopower depends on the relative position of this cavity energy level with
respect to the Fermi energy: the thermopower is positive when low-energy
electrons in the vicinity of the Fermi level are not transmitted, and becomes
negative when the higher-energy electrons are not transmitted.
