Particle conserving approach to ac-dc driven interacting quantum dots with superconducting leads

Julian, Siegl,; Picó-Cortés, Jordi; Grifoni, Milena

doi:10.1103/physrevb.107.115405

Cited by 5 publications

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“…A key remaining open question is thus whether for finite superconducting gap described by the approaches of Ref. [34] or [39] a more general duality relation can be found. The continued interest in (time-)controlled proximized nanoelectronic systems [60][61][62][63][64] provides a strong experimental impetus for such work.…”

Section: Discussionmentioning

confidence: 99%

“…Master equations governing proximized interacting quantum dots were microscopically derived using the established real-time approach [34,35] for the large-gap limit [36,37] and for a finite gap [21,38] including coherences in the energy-basis, see also recent work [39]. The time-dependent state of the proximized dot was obtained analytically in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor

2023

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We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -covering both the repulsive and attractive case- proximized by contact with a large-gap superconductor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analytically in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.

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