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Josephson current through a Luttinger liquid (LL) under a magnetic field istheoretically studied. We derive an analytical expression of Josephson currentfor clean interfaces, by using quasiclassical Green's function and functionalbosonization procedure. We show that critical currents can be renormalized byelectron-electron interactions at perfect transparency when LL is adiabaticallyconnected with superconductors. We also find that a generation of $\pi$-state,due to spin-dependent energy shift in Andreev bound states (ABS), is prohibitedeven at zero temperature when the strength of repulsive interactions reachessome critical value. The suppression of $\pi$-state is caused by the low energyfluctuations propagating in LL, and making the Zeeman splitting in ABS blurred.Comment: 5 pages, 4figure

physical review. b, condensed matter and materials physics

Josephson<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>π</mml:mi></mml:mrow></mml:math>state in superconductor–Luttinger liquid hybrid systems

Josephsonπstate in superconductor–Luttinger liquid hybrid systems