Nowadays electronic circuits are operating with a huge number of charges and the nearest goal is thus the realization of integrated circuits at a single-electron level. In order to create such circuits one requires technology for transporting elementary charges between different functional parts of the circuit and for manipulating them in a very controlled way. Coherent operation of single electrons in solid-state devices is also extremely important for transferring quantum information through corresponding networks connecting quantum processors.
In this work, we analyze theoretically coherent charge and heat transport across a nanoscale Y-shaped beam splitter with normal (N) and superconducting (S) electronic conductors, an essential component in future quantum schemes. Generalizing our previous results for a two-electrode hybrid sample  we have developed appropriate boundary conditions taking into account Andreev backscattering effect at the N/S interface and calculated current-vs-voltage and conductance-vs-voltage characteristics for different configurations of current (output) and voltage (input) leads as well as for different vertex scattering strengths. To understand the role of inelastic phase coherence-destroying processes, the Büttiker probe formalism has been extended by incorporating incoherent elastic and inelastic effects into the fully coherent scheme .
Next, we have applied our approach to the phase manipulation of the electronic thermal conductivity in three-arm splitters and discuss possibility of realizing phase-coherent caloritronic devices with superconducting branches. We argue that superconducting phase coherencecan offer unprecedented thermal management of heat flows at the nanoscale.
M. Belogolovskii is deeply grateful to the Slovak Academic Information Agency for the support of his stay at the Comenius University in Bratislava.
Belogolovskii M., Grajcar M., Kúš P., Plecenik A., Beňačka Š., Seidel, P.Phase-coherent charge transport in superconducting heterocontacts// Phys. Rev. B.-1999.-59, N 14.-P. 9617-9626.