Josephson effect in a fractal geometry
arXiv:2404.01373 · doi:10.1063/5.0211437
Abstract
The Josephson effect is a hallmark signature of the superconducting state, which, however, has been sparsely explored in non-crystalline superconducting materials. Motivated by this, we consider a Josephson junction consisting of two superconductors with a fractal metallic interlayer, which is patterned as a Sierpiński carpet by removing atomic sites in a self-similar and scale-invariant manner. We here show that the fractal geometry has direct observable consequences on the Josephson effect. In particular, we demonstrate that the form of the supercurrent-magnetic field relation as the fractal generation number increases can be directly related to the self-similar fractal geometry of the normal metallic layer. Furthermore, the maxima of the corresponding diffraction pattern directly encode the self-repeating fractal structure in the course of fractal generation, implying that the corresponding magnetic length directly probes the shortest length scale in the given fractal generation. Our results should motivate future experimental efforts to verify these predictions in designer quantum materials and motivate future pursuits regarding fractal-based SQUID devices.
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References in corpus (14)
- Design and characterization of electronic fractals
- Fractal superconductivity near localization threshold
- Photonic Floquet topological insulators in a fractal lattice
- Inner Skin Effects on Non-Hermitian Topological Fractals
- Topological states on fractal lattices
- Higher-order topological phases on fractal lattices
- Topology in the Sierpiński-Hofstadter problem
- The existence of robust edge currents in Sierpinsky Fractals
- Hall conductivity of Sierpinski carpet
- Anyons and Fractional Quantum Hall Effect in Fractal Dimensions
- Topological Random Fractals
- Noncrystalline topological superconductors
- Dimensional crossover and hidden incommensurability in Josephson junction arrays of periodically repeated Sierpinski gaskets
- Ginzburg Landau theory of superconductivity at fractal dimensions