Optical spin transport theory of spin-1/2 topological Fermi superfluids

We theoretically investigate optical (frequency-dependent) bulk spin transport properties in a spin-1/2 topological Fermi superfluid. We specifically consider a one-dimensional system with an interspin p-wave interaction, which can be realized in ultracold-atom experiments. Developing the BCS-Leggett theory to describe the BCS to Bose-Einstein condensate (BEC) evolution and the Z(2) topological phase transition in this system, we show how the spin transport reflects these many-body aspects. We find that the optical spin conductivity, which is a small AC response of a spin current, shows the spin-gapped spectrum in the wide parameter region and the gap closes at the Z(2) topological phase transition point. Moreover, the validity of the low-energy effective model of the Majorana zero mode is discussed along the BCS-BEC evolution in connection with the scale invariance at p-wave unitarity.