Controllable odd-frequency Cooper pairs in multisuperconductor Josephson junctions

We consider Josephson junctions formed by multiple superconductors with distinct phases and explore the formation of nonlocal or intersuperconductor pair correlations. We find that the multiple superconductor nature offers an additional degree of freedom that broadens the classification of pair symmetries, enabling nonlocal even- and odd-frequency pairings that can be highly controlled by the superconducting phases and the energy of the superconductors. Specially, when the phase difference between two superconductors is <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>π</a:mi></a:math>, their associated nonlocal odd-frequency pairing is the only type of intersuperconductor pair correlations. Finally, we show that these nonlocal odd-frequency Cooper pairs dominate the nonlocal conductance via crossed Andreev reflections, which constitutes a direct evidence of odd-frequency pairing.