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

Tunneling amplitude through magnetic breakdown (MB) gap is considered for two bands Fermi surfaces illustrated in many organic metals. In particular, the S-matrix associated to the wave-function transmission through the MB gap for the relevant class of differential equations is the main object allowing the determination of tunneling probabilities and phases. The calculated transmission 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 of the wave-function in interacting two-band models.