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We show that the two-band nature of noncentrosymmetric superconductors leadsnaturally to an anomalous Josephson current appearing at zero phase differencein a clean noncentrosymmetric superconductor/ferromagnet/noncentrosymmetricsuperconductor junction. The two-band nature provides two sets of Andreev boundstates which carry two supercurrents with different amplitudes. When themagnetization direction of the ferromagnet is suitably chosen, twosupercurrents experience opposite phase shifts from the conventional sinusoidalcurrent-phase relation. Then the total Josephson current results in acontinuously tunable ground-state phase difference by adjusting the ferromagnetparameters and the triplet-singlet ratio of noncentrosymmetric superconductors.The physics picture and analytical results are given on the basis of the$s$+$p$ wave, while the numerical results are reported on both $s$+$p$ and$d$+$p$ waves. For the $d$+$p$ wave, we find novel states in which thesupercurrents are totally carried by continuous propagating states instead ofdiscrete Andreev bound states. Instead of carrying supercurrent, the Andreevbound states which here only appear above the Fermi energy block thesupercurrent flowing along the opposite direction. These novel states advancethe understaning of the relation between Andreev bound states and the Josephsoncurrent. And the ground-state phase difference serves as a tool to determinethe triplet-singlet ratio of noncentrosymmetric superconductors.

Anomalous Josephson Effect in magnetic Josephson junctions with noncentrosymmetric superconductors