Fractional transconductance in a chain of Josephson junctions

Many robust physical phenomena in quantum physics are based on topological invariants, which are intriguing geometrical properties of quantum states. A prime example is the 2D quantum Hall effect with its quantized quantum Hall conductance in units of e²/h protected by the respective 2D topology. A comparable effect in superconducting systems is the appearance of a quantized transconductance in units of 4e²/h for topological Andreev bound states in multiterminal Josephson junctions [1].

In this work, we theoretically demonstrate how a fractional quantized transconductance can be observed in a chain of Josephson junctions. The fractional properties in this setup can be controlled by an offset flux that leads to the appearance of fractional plateaus in the transconductance for finite voltages. These plateaus can be interpreted as a fractional pumping of a Cooper pair in the chain. Finally, we demonstrate the robustness of the effect taking into account disorder along the chain.

[1] Riwar et al., Nat. Commun. 7, 11167 (2016).