JB
Jasper Brookman
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Master thesis
(2025)
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Jasper Brookman, A.R. Akhmerov, A.L. Rigotti Manesco, R.J.Z. Zijderveld, A.R. Akhmerov, S. Goswami, C.K. Andersen
Understanding the ground-state properties of many-body systems is a computational challenge in condensed-matter physics. MeanFi is a Python package that performs self-consistent Hartree-Fock calculations on non-superconducting tight-binding models and aims to find the ground state solution of a Hamiltonian with density-density interactions. This thesis presents how this package is generalized to also perform these calculations for superconducting tight-binding models. First, a complete derivation of the mean-field expansion is given by applying Wick’s contractions and the mean-field approximation. This expansion is then transformed into the Bogoliubov-de Gennes basis to explicitly include superconducting terms in the Hamiltonian. Second, the self-consistency criterion is adapted by constraining the solution space by enforcing symmetries on the solution by using Qsymm. Third, finite-temperature calculations are added to the algorithm and the total charge of the system replaces the electron filling-factor that was used in MeanFi, introducing a minimization problem to the algorithm. Last, the updated algorithm is applied to a 1D-Hubbard model with attractive interactions and the resulting superconducting gap as a function of temperature matches theoretical predictions from BCS-theory.
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Understanding the ground-state properties of many-body systems is a computational challenge in condensed-matter physics. MeanFi is a Python package that performs self-consistent Hartree-Fock calculations on non-superconducting tight-binding models and aims to find the ground state solution of a Hamiltonian with density-density interactions. This thesis presents how this package is generalized to also perform these calculations for superconducting tight-binding models. First, a complete derivation of the mean-field expansion is given by applying Wick’s contractions and the mean-field approximation. This expansion is then transformed into the Bogoliubov-de Gennes basis to explicitly include superconducting terms in the Hamiltonian. Second, the self-consistency criterion is adapted by constraining the solution space by enforcing symmetries on the solution by using Qsymm. Third, finite-temperature calculations are added to the algorithm and the total charge of the system replaces the electron filling-factor that was used in MeanFi, introducing a minimization problem to the algorithm. Last, the updated algorithm is applied to a 1D-Hubbard model with attractive interactions and the resulting superconducting gap as a function of temperature matches theoretical predictions from BCS-theory.
Conventional semiconductor diodes dissipate energy in the form of heat when current passes through them. This is unwanted in, for example, cryogenic environments. Using a superconducting diode could mitigate this problem. These have been made by using special materials or combining multiple different circuit elements. We provide a systematic method of designing a tunable superconducting diode using a circuit of solely Josephson tunnel junctions. We show that even for a small number of Josephson junctions a strong diode effect can be achieved and that this method is stable under manufacturing tolerances. This method involves solving computationally inexpensive linear least squares problems to tune the Josephson energies of the junctions used.
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Conventional semiconductor diodes dissipate energy in the form of heat when current passes through them. This is unwanted in, for example, cryogenic environments. Using a superconducting diode could mitigate this problem. These have been made by using special materials or combining multiple different circuit elements. We provide a systematic method of designing a tunable superconducting diode using a circuit of solely Josephson tunnel junctions. We show that even for a small number of Josephson junctions a strong diode effect can be achieved and that this method is stable under manufacturing tolerances. This method involves solving computationally inexpensive linear least squares problems to tune the Josephson energies of the junctions used.