  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 this
gapless superconducting state, zero-energy quasiparticles reside on a segment
of the normal state Fermi surface, while its remaining part is still gapped.
The finite density of states of field-induced quasiparticles, known as the
Volovik effect, has been observed in tunneling and specific heat measurements
on d- and s-wave superconductors. However, the segmented Fermi surface of a
finite-momentum state carrying a supercurrent has never been detected directly.
Here we use quasiparticle interference (QPI) technique to image
field-controlled Fermi surface of Bi$_2$Te$_3$ thin films proximitized by the
superconductor NbSe$_2$. By applying a small in-plane magnetic field, a
screening supercurrent is induced which leads to finite-momentum pairing on
topological surface states of Bi$_2$Te$_3$. Our measurements and analysis
reveal the strong impact of finite Cooper pair momentum on the quasiparticle
spectrum, and thus pave the way for STM study of pair density wave and FFLO
states in unconventional superconductors.
