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A sufficiently large supercurrent can close the energy gap in a superconductor and create gapless quasiparticles through the Doppler shift of quasiparticle energy caused by finite Cooper pair momentum. In this gapless superconducting state, zero-energy quasiparticles reside on a segment of the normal-state Fermi surface, whereas the remaining Fermi surface is still gapped. We use quasiparticle interference to image the field-controlled Fermi surface of bismuth telluride (Bi2Te3) thin films under proximity effect from the superconductor niobium diselenide (NbSe2). A small applied in-plane magnetic field induces a screening supercurrent, which leads to finite-momentum pairing on the topological surface states of Bi2Te3. We identify distinct interference patterns that indicate a gapless superconducting state with a segmented Fermi surface. Our results reveal the strong impact of finite Cooper pair momentum on the quasiparticle spectrum. [ABSTRACT FROM AUTHOR]

We have fabricated ultra-thin lead films on silicon substrates with atomic-scale control of the thickness over a macroscopic area. We observed oscillatory behavior of the superconducting transition temperature when the film thickness was increased by one atomic layer at a time. This oscillating behavior was shown to be a manifestation of the Fabry-Pérot interference modes of electron de Broglie waves (quantum well states) in the films, which modulate the electron density of states near the Fermi level and the electronphonon coupling, which are the two factors that control superconductivity transitions. This result suggests the possibility of modifying superconductivity and other physical properties of a thin film by exploiting well-controlled and thickness-dependent quantum size effects. [ABSTRACT FROM AUTHOR]