  Transport critical current, Ic, is usually defined in terms of a threshold
electric field criterion, Ec, with the convention Ec = 1 microVolt/cm, chosen
somewhat arbitrarily to provide "reasonably small" electric power dissipation
in practical devices. Thus Ic is not fundamentally determined. However,
recently it was shown, that the self-field critical current of thin-film
superconductors is indeed a fundamental property governed only by the London
penetration depth. Here we reconsider the definition of critical current and
resolve the apparent contradiction. We measure the field distribution across
the width of 2G high-Tc superconducting tapes as the transport current is
increased to Ic. We identify a threshold current, Ic_surfB, at which two
physical events occur simultaneously: (i) an abrupt crossover from non-linear
to linear dependence of the local surface magnetic flux density, Bsurf, as a
function of transport current measured at any point on the superconductor
surface. This effect was not reported previously. (ii) the appearance of a
non-zero electric field, just above of the sensitivity of measuring system. In
the present examples Ic_surfB is 10-15% lower than Ic_E determined by the Ec
criterion. We propose the transition of Bsurf(I) from non-linear to linear as
the most reliable and more fundamental technique for measuring transport
critical currents.
