  The high-order Hall effects, which go beyond the ordinary, unlock more
possibilities of electronic transport properties and functionalities. Pioneer
works focus on the manufacture of complex nanostructures with low lattice
symmetry to produce them. In this paper, we theoretically show that such
high-order Hall effects can alternatively be generated by curving a conducting
nanomembrane which is highly tunable and also enables anisotropy. Its Hall
response can be tuned from first to fourth order by simply varying the
direction and magnitude of the applied magnetic field. The dominant Hall
current frequency can also be altered from zero to double, or even four times
that of the applied alternating electric field. This phenomenon is critically
dependent on the occurrence of high-order snake orbits associated with the
effective magnetic-field dipoles and quadruples induced by the curved geometry.
Our results offer pathways for spatially engineering magnetotransport, current
rectification, and frequency multiplication in the bent conducting
nanomembrane.
