Probing Fermi surface topology by ultrafast pump pulse dynamics

We present a dynamical approach to detect changes in Fermi surface topology in a two-band model. Specifically, we show that the system's response to a low intensity light pulse can precisely identify topological Lifshitz transitions. At a suitable frequency, the light resonantly couples valence and conduction electrons, leading to an oscillation in the interband coherence term. This, in turn, generate a persistent oscillatory current which survives even after the end of the pulse. Notably, the relative amplitude of the oscillatory current during the pulse with that of the post-pulse reaches a minimum when the Fermi energy aligns with the saddle point, providing a robust framework for dynamically identifying Lifshitz transitions.