Greedy optimization of the geometry of Majorana Josephson junctions
arXiv:2205.05689 · doi:10.21468/SciPostPhys.14.3.047
Abstract
Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the topological gap, the question of how to construct optimal geometries remains unexplored. We introduce a greedy numerical algorithm to optimize the shape of Majorana junctions. The core of the algorithm relies on perturbation theory and is embarrassingly parallel, which allows it to explore the design space efficiently. By introducing stochastic variations in the junction Hamiltonian, we avoid overfitting geometries to specific system parameters. Furthermore, we constrain the optimizer to produce smooth geometries by applying image filtering and fabrication resolution constraints. We run the algorithm in various setups and find that it reliably produces geometries with increased topological gaps over large parameter ranges. The results are robust to variations in the optimization starting point and the presence of disorder, which suggests the optimizer is capable of finding global maxima.
arXiv comment12 pages, 6 figures
References in corpus (31)
- Unpaired Majorana fermions in quantum wires
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Helical liquids and Majorana bound states in quantum wires
- New directions in the pursuit of Majorana fermions in solid state systems
- Search for Majorana fermions in superconductors
- Kwant: a software package for quantum transport
- Realizing Majorana zero modes in superconductor-semiconductor heterostructures
- Introduction to topological superconductivity and Majorana fermions
- Evidence of topological superconductivity in planar Josephson junctions
- Topological Superconductivity in a Phase-Controlled Josephson Junction
- Topological Superconductivity in a Planar Josephson Junction
- Two-dimensional platform for networks of Majorana bound states
- Next steps of quantum transport in Majorana nanowire devices
- Effects of gate-induced electric fields on semiconductor Majorana nanowires
- Topological Insulators by Topology Optimization
- Hybridization at superconductor-semiconductor interfaces
- Robust topology optimization of three-dimensional photonic-crystal band-gap structures
- Orbital effect of magnetic field on the Majorana phase diagram
- Angle dependence of Andreev scattering at semiconductor-superconductor interfaces
- Ballistic superconductivity and tunable -junctions in InSb quantum wells
- Enhanced proximity effect in zigzag-shaped Majorana Josephson junctions
- Band Gap Optimization of Two-Dimensional Photonic Crystals Using Semidefinite Programming and Subspace Methods
- Doppler Shift in Andreev Reflection from a Moving Superconducting Condensate in Nb/InAs Josephson Junctions
- Phase-induced topological superconductivity in a planar heterostructure
- Enhanced topological superconductivity in spatially modulated planar Josephson junctions
- Supercurrent-induced Majorana bound states in a planar geometry
- Rapid Exploration of Topological Band Structures using Deep Learning
- Optimized micromagnet geometries for Majorana zero modes in low g-factor materials
- Enhanced topological protection in planar quasi-one-dimensional channels with periodically-modulated width
- Majorana bound state engineering via efficient real-space parameter optimization
- Inverse Design of a Graphene-Based Quantum Transducer via Neuroevolution
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- Unconventional Supersymmetry via the Dressing Field Method
- Multiple Majorana bound states and their resilience against disorder in planar Josephson junctions
- Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization