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Journal of Experimental and Theoretical Physics Letters

Quantum Coulomb Drag for Cooper Pairs

A. Latysev, A. G. Semenov, Andrei D. Zaikin

Published Dec 1, 2025• 0 citations
Publisher

Abstract

We demonstrate that the system of two connected in series resistively shunted Josephson nanojunctions may exhibit a novel quantum Coulomb drag effect mediated by cotunneling of Cooper pairs. In the Coulomb blockade regime, one of the junctions can develop a non-vanishing electric current while an external voltage bias is applied to another one. This phenomenon results from a non-trivial interplay between macroscopic quantum coherence, dissipation, and electron–electron interactions and can be directly tested in future experiments.

DOI
10.1134/s0021364025609583

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We demonstrate that the system of two connected in series resistively shunted Josephson nanojunctions may exhibit a novel quantum Coulomb drag effect mediated by cotunneling of Cooper pairs. In the Coulomb blockade regime, one of the junctions can develop a non-vanishing electric current while an external voltage bias is applied to another one. This phenomenon results from a non-trivial interplay between macroscopic quantum coherence, dissipation, and electron–electron interactions and can be directly tested in future experiments.
We predict two novel quantum drag effects which can occur in macroscopically quantum coherent Josephson circuits. We demonstrate that biasing one resistively shunted Josephson junction by an external current one can induce a nonzero voltage drop across another such junction capacitively coupled to the first one. This quantum Coulomb drag is caused by cotunneling of magnetic flux quanta across both junctions which remain in the "superconducting" regime. Likewise, Cooper pair cotunneling across a pair of connected in series Josephson junctions in the "insulating" regime is responsible for another-dual-quantum Coulomb drag effect.
We investigate nonequilibrium transport through superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite-gap effects, and to account for both quasiparticle and Cooper-pair tunneling. With focus on the weak-tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. For the particular case of a strongly interacting quantum dot sandwiched between two superconductors, we identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current, and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of $0\ensuremath{-}\ensuremath{\pi}$ transitions. The latter signal the interplay between strong interactions and tunneling at finite bias.
We investigate non-equilibrium transport through interacting superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite gap effects, and to account for both quasiparticle and Cooper pair tunneling. With focus on the weak tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. We identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of 0-πtransitions. The latter signal the interplay between strong interactions and tunneling at finite bias.
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The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.