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Several recent experiments revealed a change of the sign of the firstharmonic in the current-phase relation of Josephson junctions (JJ) based onnovel superconductors, e.g., d-wave based or JJ with ferromagnetic barrier. Inthis situation the role of the second harmonic becomes dominant and itdetermines the scenario of a 0-pi transition. We discuss different mechanismsof the second harmonic generation and its sign. If the second harmonic isnegative the 0-pi transition becomes continuous and the realization of theso-called varphi junction is possible. We study the unusual properties of sucha novel JJ and analyze the possible experimental techniques for theirobservation.

Josephson junctions with negative second harmonic in the current-phase relation: properties of novel varphi-junctions