Fig. 2: The diode efficiency, η = (Jc+ − Jc−)/(Jc+ + Jc−), obtained by numerically solving for the critical currents Jc± with Eq. (7).

a The dependence on the magnetic flux (ϕ0 = h/2e is the flux quantum). The solid curves are for various values of the nanotube radius R, normalized so that r = R/l0, where \({l}_{0}=\hslash /\sqrt{2{m}_{0}{T}_{c}}\). The dashed curve is the approximate result given by Eq. (8) with r = 30. b Dependence on the angle θ which corresponds to the chiral structure of the nanotube. c The temperature dependence. The parameters are m0 = 1, m1 = 2, ζ2m2 → ∞, ζ0/Tc = 10, ζ1/Tc = 20, r = 2, θ = 0.6π, ϕ/ϕ0 = 0.3 and T/Tc = 0.9 for all the results unless specified otherwise.