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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2509.17517 |
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| _version_ | 1866917446216056832 |
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| author | Wang, Yiyan Li, Cong Dong, Bing |
| author_facet | Wang, Yiyan Li, Cong Dong, Bing |
| contents | In this work, we study a Josephson junction with parallel-connected quantum dots (QDs) threaded by a magnetic flux in the central region. We discretize the superconducting (SC) electrode into three discrete energy levels and modify the tunneling coefficients to construct a finite-dimensional surrogate Hamiltonian. By directly diagonalizing this Hamiltonian, we compute the physical quantities of the system. Additionally, we employ a low-energy effective model to gain deeper physical insight. Our findings reveal that when only one QD exhibits Coulomb interaction, the system undergoes a phase transition between singlet and doublet states. The magnetic flux has a minor influence on the singlet state but significantly affects the doublet state. When both QDs have interactions, the system undergoes two phase transitions as the SC phase difference increases: the ground state evolves from a doublet to a singlet and finally into a triplet state at $ϕ= π$. Increasing the magnetic flux suppresses the doublet and triplet phases, eventually stabilizing the singlet state. In this regime, enhancing the interaction strength does not induce a singlet-doublet transition but instead drives a transition between upper and lower singlet states, leading to a critical current peak as $U$ increases. Finally, we examine the case where the tunneling coefficient $Γ$ exceeds the SC pairing potential $Δ$. Here, doublet states dominate, and the system only exhibits a phase transition between doublet and triplet states when $ϕ_B = 0$. In the presence of a magnetic flux, the three states converge, resulting in a triple point in the ($ϕ$, $ϕ_B$) parameter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic flux controlled current phase relationship in double Quantum Dot Josephson junction Wang, Yiyan Li, Cong Dong, Bing Mesoscale and Nanoscale Physics Superconductivity In this work, we study a Josephson junction with parallel-connected quantum dots (QDs) threaded by a magnetic flux in the central region. We discretize the superconducting (SC) electrode into three discrete energy levels and modify the tunneling coefficients to construct a finite-dimensional surrogate Hamiltonian. By directly diagonalizing this Hamiltonian, we compute the physical quantities of the system. Additionally, we employ a low-energy effective model to gain deeper physical insight. Our findings reveal that when only one QD exhibits Coulomb interaction, the system undergoes a phase transition between singlet and doublet states. The magnetic flux has a minor influence on the singlet state but significantly affects the doublet state. When both QDs have interactions, the system undergoes two phase transitions as the SC phase difference increases: the ground state evolves from a doublet to a singlet and finally into a triplet state at $ϕ= π$. Increasing the magnetic flux suppresses the doublet and triplet phases, eventually stabilizing the singlet state. In this regime, enhancing the interaction strength does not induce a singlet-doublet transition but instead drives a transition between upper and lower singlet states, leading to a critical current peak as $U$ increases. Finally, we examine the case where the tunneling coefficient $Γ$ exceeds the SC pairing potential $Δ$. Here, doublet states dominate, and the system only exhibits a phase transition between doublet and triplet states when $ϕ_B = 0$. In the presence of a magnetic flux, the three states converge, resulting in a triple point in the ($ϕ$, $ϕ_B$) parameter space. |
| title | Magnetic flux controlled current phase relationship in double Quantum Dot Josephson junction |
| topic | Mesoscale and Nanoscale Physics Superconductivity |
| url | https://arxiv.org/abs/2509.17517 |