Anomalous Seebeck effect and counterpropagating ballistic currents in graphene

The Seebeck effect consists in the induction of a voltage drop due to the temperature difference in a conductor. In the middle of the 19th century, Kelvin proposed a relation between the Seebeck coefficient and the derivative of the chemical potential over temperature in the broken circuit regime. This relation appears to be nearly universal as it equally well applies to metals, semimetals, and semiconductors. We show that it may fail, however, in graphene, due to the nonlocality effects in the ballistic electronic transport regime. The correction to Kelvin's formula emerges due to the coexistence of counterpropagating nondissipative currents of cold and hot electrons. The external magnetic field normal to the graphene sample allows separating hot and cold currents in real space. The developed formalism may help interpreting the recent experimental data on ballistic edge currents in graphene bilayers in the quantum Hall regime [J. Barrier et al., Nature (London) 628, 741 (2024)].