Holstein phonons and magnetic fields synergistically tune thermoelectric performance in dice lattices

In this study, we investigate the transport and thermoelectric properties of a doped dice lattice subjected to electron-phonon coupling via Einstein phonons and an external perpendicular magnetic field. The electronic band structure is modeled using the Holstein Hamiltonian augmented with a Zeeman interaction term. Employing a one-loop approximation for the electronic self-energy within a full-band framework, we derive the interacting Green's functions to examine the temperature-dependent electrical and thermal conductivities, as well as the energy-dependent density of states (DOS). Particular attention is given to the behaviors of the Seebeck coefficient, power factor, figure of merit, and Lorenz number. Our findings reveal that increasing the magnetic field diminishes the DOS at the Fermi energy, enhancing the semiconductor-like characteristics of the system. Furthermore, activating electron-phonon coupling results in a notable reduction of the DOS at zero energy. These results underscore the pivotal influence of electron-phonon interactions and magnetic fields in modulating the electronic and thermoelectric attributes of two-dimensional dice lattices, providing valuable insights for the design of advanced thermoelectric materials and devices.