The nonlinear C R is the fingerprint of a JJ, which relates the supercurrent I ( ) to the phase (inset). For tunnel JJs, the C R has been considered to be purely sinusoidal (dashed grey line; equation ( 1 )), with the maximum given by the critical current I c . However, as we show in this work, even in tunnel JJs, the underlying microscopic complexity of the charge transport can manifest in the contribution of higher harmonics to the C R. As an example, the red line shows a C R consistent with measured data (CD1 of the KIT sample), which includes the harmonics expected from a mesoscopic model assuming an inhomogeneous AlO x barrier. The shaded red area shows the difference from the purely sinusoidal C R. We provide C Rs for all other measured samples in Supplementary Fig. 7 .
