Non-linear Transport in Non-centrosymmetric Systems: From Fundamentals to Applications

Ohm's law has been a cornerstone of electronics since its experimental discovery. This law establishes that in a conductive system, the voltage is directly proportional to the current. Even when time-reversal symmetry is disrupted, leading to the emergence of magnetoresistance and Hall effects, the linear relationship between voltage and current remains intact. However, recent experiments have demonstrated a breakdown of Ohm's law in non-centrosymmetric structures. In these systems, non-linear transport effects are permitted with quadratic scaling between voltages and currents. Here, we review the main demonstrations of non-linear transport in non-centrosymmetric systems, analyzing the connection between non-linear behavior and the system's symmetry. Additionally, we delve into the microscopic mechanisms driving these effects, such as Berry curvature dipole and Berry connection polarizability. Finally, we highlight potential applications of non-linear transport in spintronics and energy harvesting.