A driven fractal network: Possible route to efficient thermoelectric application

An essential attribute of many fractal structures is self-similarity. A Sierpinski gasket (SPG) triangle is a promising example of a fractal lattice that exhibits localized energy eigenstates. In the present work, for the first time we establish that a mixture of both extended and localized energy eigenstates can be generated yeilding mobility edges at multiple energies in presence of a time-periodic driving field. We obtain several compelling features by studying the transmission and energy eigenvalue spectra. As a possible application of our new findings, different thermoelectric properties are discussed, such as electrical conductance, thermopower, thermal conductance due to electrons and phonons. We show that our proposed method indeed exhibits highly favorable thermoelectric performance. The time-periodic driving field is assumed through an arbitrarily polarized light, and its effect is incorporated via Floquet-Bloch ansatz. All transport phenomena are worked out using Green's function formalism following the Landauer-B\"{u}ttiker prescription.