On-demand Higher-Harmonic Generation Through Nonlinear Hall Effects in Curved Nanomembranes

The high-order Hall effects, which go beyond the ordinary, unlock morepossibilities of electronic transport properties and functionalities. Pioneerworks focus on the manufacture of complex nanostructures with low latticesymmetry to produce them. In this paper, we theoretically show that suchhigh-order Hall effects can alternatively be generated by curving a conductingnanomembrane which is highly tunable and also enables anisotropy. Its Hallresponse can be tuned from first to fourth order by simply varying thedirection and magnitude of the applied magnetic field. The dominant Hallcurrent frequency can also be altered from zero to double, or even four timesthat of the applied alternating electric field. This phenomenon is criticallydependent on the occurrence of high-order snake orbits associated with theeffective magnetic-field dipoles and quadruples induced by the curved geometry.Our results offer pathways for spatially engineering magnetotransport, currentrectification, and frequency multiplication in the bent conductingnanomembrane.