Anomalous fractal scaling in two-dimensional electric networks
Abstract Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a two-dimensional L C circuit network. We find this anomalous impe...
| Main Authors: | , , , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-06-01
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| Series: | Communications Physics |
| Online Access: | https://doi.org/10.1038/s42005-023-01266-1 |
| Summary: | Abstract Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a two-dimensional L C circuit network. We find this anomalous impedance contribution to sensitively depend on the number of nodes N in a curious erratic manner and experimentally demonstrate its robustness against perturbations from the contact and parasitic impedance of individual components. This impedance anomaly is traced back to a generalized resonance condition reminiscent of Harper’s equation for electronic lattice transport in a magnetic field, even though our circuit network does not involve magnetic translation symmetry. It exhibits an emergent fractal parametric structure of anomalous impedance peaks for different N that cannot be reconciled with a continuum theory and does not correspond to regular waveguide resonant behavior. This anomalous fractal scaling extends to the transport properties of generic systems described by a network Laplacian whenever a resonance frequency scale is simultaneously present. |
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| ISSN: | 2399-3650 |