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Statistical correlations of currents flowing via proximized quantum dot

Statistical properties of the electron transport flowing through nanostructures are strongly influenced by the interactions, geometry of the system and/or by type of the external electrodes. These factors affect not only the average current induced in the system but also contribute to fluctuations in the flux of charges and their correlations. Due to possible applications of the hybrid nano-systems, containing one or more superconducting electrodes, a detailed understanding of the flow of charge and its fluctuations seems to be of primary importance. Coulomb repulsion between electrons usually strongly affect the current-current correlation function. In this work we study the correlations in the charge flow through such interacting quantum dot contacted to one superconducting and two normal electrodes. This set-up allows for analysis of the Andreev scattering events in the correlations of currents flowing between external electrodes and, in particular, gives access to cross-correlations between currents from/to different normal electrodes. Our approach relies on the master equation technique, which properly captures the Coulomb interactions. We study the finite frequency correlations and find the relaxation processes, related to the high frequency charge and low frequency polarisation fluctuations. The multiterminal structure of here studied single electron device allows to analyze a competition between the intra- and inter-channel correlations. In the appropriate limit of the interacting quantum dot embedded between two normal electrodes our calculations quantitatively describe the recent experimental data on the frequency dependent correlations. This shows a promising potential of the method for description of the hybrid systems with superconducting electrode(s).