Josephson Current through a Metallic Carbon Nanotube in the Conductance-Quantization Regime

Abstract

DC Josephson current through a metallic carbon nanotube with N conducting channels is studied at temperature T when the potential range of scatterers is larger than the lattice constant. With increasing length of the carbon nanotube, its conductance approaches the quantized value G₀=4e²⁄h irrespective of N. Our attention is focused on the T-dependence of the Josephson critical current I_c in this conductance-quantization regime. The thermal length ξ_T, which characterizes I_c(T), is calculated by combining the Matsubara technique and the random-matrix approach. It is shown that ξ_T=hv_F⁄(2πNk_BT) (v_F: the Fermi velocity). This indicates that I_c(T) depends on N, in contrast to the conductance which is given by G₀ irrespective of N.