Quasiparticle transport in the vortex state of an s-wave superconductor at T -> 0 was investigated by measuring the thermal conductivity of LuNi_2B_2C down to 70 mK in a magnetic field perpendicular to the heat current. In zero field, there is no electronic conduction, as expected for a superconducting gap without nodes. However, as soon as vortices enter the sample quasiparticles are seen to conduct remarkably well, even better than they would in a typical d-wave superconductor. This is in stark conflict with the widely held view that quasiparticle states in s-wave superconductors just above H_{c1} should be localized and bound to the vortex core.
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