The evolution of the superconducting properties of the carbon-doped MgB2 superconductors, MgB(2-x)Cx (x= 0.02, 0.04, 0.06) have been investigated by the transverse-field muon spin rotation (TF-muSR) technique. The low-temperature depolarisation rate, sigma(0) at 0.6 T which is proportional to the second moment of the field distribution of the vortex lattice decreases monotonically with increasing electron doping and decreasing Tc. In addition, the temperature dependence of sigma(T) has been analysed in terms of a two-gap model. The size of the two superconducting gaps decreases linearly as the carbon content increases, while the doping effect is more pronounced for the smaller gap related to the 3D pi-sheets of the Fermi surface.
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