Weak-value amplification for the optical signature of topological phase transitions

We show that weak measurements can be used to measure the tiny signature of topological phase transitions.The signature is an in-plane photonic spin Hall effect,which can be described as a consequence of a Berry phase.It is also parallel to the propagation direction of a light beam.The imaginary part of the weak value can be used to analyze ultrasmall longitudinal phase shifts in different topological phases.These optical signatures are related to the Chern number and bandgaps;we also use a preselection and postselection technique on the spin state to enhance the original signature.The weak amplification technique offers a potential way to determine the spin and valley properties of charge carriers,Chern numbers,and topological phases by direct optical measurement.