From 2D semimetal to topological Fulde-Ferrell superfluid in fermionic ultracold atoms

The intriguing topological phenomena have been observed in different condensed matter systems including topological insulators and topological supercondutors. In the light of this, the ultracold spin-orbit coupled Fermi gases became a excellent platform to investigate the phenomenon difficult to observe otherwise owing to its high experimental controllability. Since recent experiments have been able to realize two-dimensional spin-orbit coupling, the studies concerning topological superfluid are promising. In this work, we propose a generic theory to determine whether a time-reversal symmetry breaking system is topological or not after considering a superconducting pairing, by knowing the properties of the Fermi surfaces and the low lying states. Then we also propose an easily acheived experimental model that contains a novel 2D spin-orbit coupling for cold atoms to demonstrate the generic theory and to provide a possible realisation of a gapped topological Flude-Ferrell superflud, characterized by Cooper's pairs with finite center-of-mass momenta, with large topological regions. The Berezinskii Kosterlitz-Thouless transition in this system is also investigated in this work.