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 ${\text{CeCoIn}}_5$, observed through thermal conductivity measurements with a magnetic field rotating within the tetragonal $a\text{−}b$ 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 $\pi$ for a field above 9.7 T where spin-density wave (SDW) order emerges and coexists with superconductivity. This approximate $\pi$-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 ${\text{CeCoIn}}_5$, thus resolving a long-standing debate on this issue.

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• Density of states
• Electronic structure of atoms & molecules
• Methods in superconductivity
• Superconductors
• Thermodynamics
• Heavy-fermion systems
• Strongly correlated systems
• Superconductivity
• Unconventional superconductors