Quantum Oscillation and Topology Change of the Uncondensed Landau Fermi Surface in Superconducting CeCoIn_{5}.

Metals typically have multiple Fermi-surface sheets, and when they enter the superconducting state, some electrons on these sheets may remain uncondensed, or their superconducting pairs can be rapidly destroyed by a magnetic field. Detecting uncondensed electrons within the superconducting state provides key information about the underlying electronic structure; however, this task remains a significant experimental challenge. Here we demonstrate quantum oscillations from the uncondensed electrons in the heavy-fermion superconductor CeCoIn_{5}, observed through thermal conductivity measurements with a magnetic field rotating within the tetragonal a-b plane. We detect a fine structure in thermal conductivity characterized by multiple small resonances (oscillations) in a rotating magnetic field. Remarkably, the phase of these resonances shifted by as much as π for a field above 9.7 T where spin-density wave (SDW) order emerges and coexists with superconductivity. This approximate π-phase shift in resonance can be naturally interpreted as a Berry-phase evolution associated with an SDW-induced reconstruction of the uncondensed Fermi surface, within the superconducting state. Our work strongly supports the existence of uncondensed electrons in the superconducting state of CeCoIn_{5}, thus resolving a long-standing debate on this issue.