Decoherence effect on Fano line shapes in double quantum dots coupled between normal and superconducting leads

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We investigate the Fano-type spectroscopic line shapes of the T-shape double quantum dot coupled between the conducting and superconducting electrodes and analyze their stability on a decoherence. Because of the proximity effect the quantum interference patterns appear simultaneously at $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\varepsilon}}_{2}$, where ${\ensuremath{\varepsilon}}_{2}$ is an energy of the side-attached quantum dot. We find that decoherence gradually suppresses both such interferometric structures. We also show that at low temperatures another tiny Fano-type structure can be induced upon forming the Kondo state on the side-coupled quantum dot due to its coupling to the floating lead.