Fidelity susceptibility and topological phase transition of a two-dimensional spin-orbit-coupled Fermi superfluid

We investigate the fidelity susceptibility (FS) of a two-dimensional spin-orbit-coupled (SOC) Fermi superfluid and the topological phase transition driven by a Zeeman field in the perspective of its ground state wave function. Without Zeeman coupling, FS shows additional features characterizing the BCS-BEC crossover induced by SOC. In the presence of a Zeeman field, the topological phase transition is explored using both FS and the topological invariant. In particular, we obtain the analytical result of the topological invariant which explicitly demonstrates that the topological phase transition corresponds to a sudden change of the ground state wave function. Consequently, FS diverges at the phase transition point with its critical behavior being X proportional to ln vertical bar h-h(c vertical bar) . Based on this observation, we conclude that the topological phase transition can be detected by measuring the momentum distribution in cold atom experiments.