Geometric oscillations of local Hall and Nernst effects in ballistic graphene at weak magnetic fields

Abstract

We predict a novel class of magnetotransport oscillations in ballistic graphene specific for a ring-shape geometry. Using the B\"uttiker-Landauer formalism, we analytically obtain the local Hall and Nernst coefficients in the weak-field ballistic regime. These coefficients exhibit pronounced oscillations as functions of both the magnetic field and the angular positions of the measurement probes. The oscillations originate from the discrete set of skipping orbits that geometrically connect the contacts, with resonances occurring when the angular separation between contacts times the radius of the disk equals an integer number of cyclotron diameters. Unlike conventional quantum oscillations in conductivity, this effect is robust at room temperature and can dominate local thermoelectric signals. This geometric control of ballistic flow provides a platform for studying electron hydrodynamics and engineering phase-coherent devices, with potential applications in sensitive terahertz detectors and thermal management systems.