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 ( G I S ) 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 G I S 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 G I S 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 G I S system, the linear component prevails. Concluding, the G I S system could be employed in the design of thermometers, electromagnetic radiation sensors, and heat engines with profound influence in superconducting quantum technologies.