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In [1-5] has been investigated a relativistic relation between the Josephson energy and the transport current has been verified. This was further generalized in [6], by including the influence of external charges associated with Wannier-type semiconductor qubits coupled to a Josephson junction. The resulting modification of the Andreev bound states reflects the coupling between the superconducting condensate and the quantum dynamics of the Wannier qubits [7]. Within this framework, we investigate further generalization, i.e. an external magnetic field is swicthed in. A generalized form of the Cooper-pair quasiparticle appears, too. The analysis indicates the emergence of a superposition of effective masses in the generalized superconducting quasiparticle, whose properties can be electrically tuned via the charge states of the nearby Wannier qubits with computational methodology specified in [5-6].
References
[1]. G.Schon, V.Ambegaokar, U.Eckern , Quantum dynamics of a superconducting tunnel junction, Phys. Rev. B 30, 6419, 1984,
[2]. J.M.Martinis, M.H.Devoret, J.Clarke, Quantum Josephson junction circuits and the dawn of artificial atoms. Nat. Phys. 16, 234–237, 2020.
[3]. S.Matsuo et al. , Phase engineering of anomalous Josephson effect derived from Andreev molecules, Sci. Adv.9, 2023.
[4]. S.Crowe, S.Evans, A.Smolyaninov. Analysis of polymerized superconducting circuits, Arxiv: 2509.1801, 2025.
[5]. K.Pomorski, A.Bednorz, Justification of the canonical quantization of the Josephson effect and its modifications due to high capacitance energy, J.Phys. A: Math. Theor., 49, 125002, 2016.
[6]. K.Pomorski, P.Peczkowski, R.B.Staszewski, Analytical solutions for N interacting electron system confined in graph of coupled electrostatic semiconductor and superconducting quantum dots in tight-binding model, Vol.109, 103117, Cryogenics, 2020.
[7].K.Pomorski, Electrostatically interacting Wannier qubits in curved space, Materials, 17, 2024.