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Tunneling amplitude through magnetic breakdown (MB) gap is considered for twobands Fermi surfaces illustrated in many organic metals. In particular, theS-matrix associated to the wave-function transmission through the MB gap forthe relevant class of differential equations is the main object allowing thedetermination of tunneling probabilities and phases. The calculatedtransmission coefficients include a field-dependent Onsager phase. As a result,quantum oscillations are not periodic in 1/B for finite magnetic breakdown gap.Exact and approximate methods are proposed for computing ratio amplitudes ofthe wave-function in interacting two-band models.

Transmission and tunneling probability in two-band metals: influence of magnetic breakdown on the Onsager phase of quantum oscillations