The thermal conductivity kappa of the layered s-wave superconductor NbSe_2 was measured down to T_c/100 throughout the vortex state. With increasing field, we identify two regimes: one with localized states at fields very near H_c1 and one with highly delocalized quasiparticle excitations at higher fields. The two associated length scales are naturally explained as multi-band superconductivity, with distinct small and large superconducting gaps on different sheets of the Fermi surface. This behavior is compared to that of the multi-band superconductor MgB_2 and the conventional superconductor V_3Si.
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