Since the early days of Bardeen-Cooper-Schrieffer theory, it has been predicted that a sufficiently large supercurrent can close the energy gap in a superconductor and creates gapless Bogoliubov quasiparticles through the Doppler shift of quasiparticle energy due to the Cooper pair momentum. In such gapless superconducting state, zero-energy quasiparticles reside on a segment of the normal state Fermi surface, while its remaining part is still gapped. In this talk I will discuss the recent discovery of such segmented Fermi surface in Bi2Te3 thin films proximitized by the superconductor NbSe2. The observation is based on quasiparticle interference technique and supported by extensive numerical modelling. I will then describe how the segmented Fermi surface can be used to induce a topological phase transition and create Majorana zero modes in quantum confined regions. Our results reveal the strong impact of finite Cooper pair momentum on the quasiparticle spectrum, and thus pave the way for further studies of states such as pair density wave and FFLO in unconventional superconductors.
