Thermoelectricity in massive-massless complex graphene structures

Abstract The advance in the growing techniques allow the creation of novel nanodevices based on nanostructured materials. In the present work, we study the thermoelectric effects via the transport properties of Dirac particles in gapped graphene structures using a complex configuration formed by adjacent massive and massless regions. In our mathematical model the transmission, the conductance at zero temperature, and the Seebeck coefficient are determined using the transfer matrix approach, the Landauer-Buttiker formalism, and the Cluter-Mott formula, respectively. We show that in a complex thermoelectric system the self-similar conductance and Seebeck coefficient patterns are displayed. Furthermore, these patterns can be replicated for different structural parameters under the appropriate scaling equations. Finally, we have deduced a general scaling expression for the conductance and Seebeck coefficient. So, this type of complex massive and massless regions can be a way to unveil another exotic phenomenon in graphene such as the self-similar quantum transport.