Theoretical Prediction of the Fractional ac Josephson Effect in p- and d-Wave Superconductors

For certain orientations of Josephson junctions between two p _x-wave or two d-wave superconductors, the sub-gap Andreev states produce a 4π-periodic relation between the Josephson current/and the phase difference φ:I ∝ sin(φ/2). Consequently, the ac Josephson current has the fractional frequency eV/hℏ, where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current is carried by single electrons, rather than by Cooper pairs.