Observation of strong electron pairing on bands without Fermi surfaces in LiFe_1-x Co_xAs

In conventional BCS superconductors, the quantum condensation of superconducting electron pairs is understood as a Fermi surface instability, in which the low-energy electrons are paired by attractive interactions. Whether this explanation is still valid in high-T_c superconductors such as cuprates and iron-based superconductors remains an open question. In particular, a fundamentally different picture of the electron pairs, which are believed to be formed locally by repulsive interactions, may prevail. Here we report a high-resolution angle-resolved photoemission spectroscopy study on LiFe_1-x Co_xAs. We reveal a large and robust superconducting gap on a band sinking below the Fermi level on Co substitution. The observed Fermi-surface-free superconducting order is also the largest over the momentum space, which rules out a proximity effect origin and indicates that the order parameter is not tied to the Fermi surface as a result of a surface instability.