Multiterminal Nonlinear Transports in Mesoscopic Systems

Recently, the nonreciprocal and nonlinear transports were widely explored in various multiterminal mesoscopic systems, such as quantum anomalous Hall systems. However, the current theoretical understanding of nonreciprocal and nonlinear transports is mostly based on two-terminal theories between source and drain leads. In this work, we develop a new method to study nonreciprocal transport in multiterminal devices based on the nonlinear Landauer-B\"uttiker formalism. Using this method, we find a new way to generate nonreciprocal transport in multiterminal leads cases even in ballistic and noninteracting limits. The additional leads play a role of dissipation or non-hermitian potential, which interrupts the phase coherence of scattering states between source and drain leads. We apply our theory to three terminal Rashba device, observing the magnetochiral anisotropy effects that is consistent with experiments. We also apply our theory to calculate the nonlinear Hall effect in a four terminal systems and we find second order nonlinear Hall effect in time-reversal invariant system. Our theory paves the way for the study of nonreciprocal and nonlinear phenomena in multiterminal mesoscopic systems.