Coexistence of linear and non-linear thermoelectricity in graphene-superconductor tunnel junctions

We theoretically analyze the electronic transport properties of a monolayer graphene/insulator/superconductor (GIS) tunnel junction subject to a temperature gradient. For intrinsic graphene, the system shows always dissipative charge transport even in the presence of an electronic temperature difference between the two leads. Differently, the GIS produces a thermoelectric response when the graphene electrochemical potential is lifted to energies comparable to the zero-temperature gap of the superconductor, i.e., the system is particle–hole asymmetric. Indeed, the thermally biased GIS system is able to produce both a short-circuit Peltier current and an open-circuit Seebeck voltage. This thermoelectric effect is made of a linear conventional component, due to the intrinsic particle–hole asymmetry of the system, and a non-linear contribution, due to a further spontaneous particle–hole symmetry breaking. In most of the thermal and charge configurations of the GIS system, the linear component prevails. Concluding, the GIS system could be employed in the design of thermometers, electromagnetic radiation sensors, and heat engines with profound influence in superconducting quantum technologies.