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arXiv · 2401.16014

Resonant helical multi-edge transport in Sierpi\'nski carpets

M. A. Toloza Sandoval·A. L. Araújo·F. Crasto de Lima·A. Fazzio
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Abstract

In recent years, synthesis and experimental research of fractalized materials has evolved in a paradigmatic crossover with topological phases of matter. We present here a theoretical investigation of the helical edge transport in Sierpinski carpets (SCs), combining the Bernevig-Hughes-Zhang (BHZ) model and the Landauer approach. Starting from a pristine two-dimensional topological insulator (2DTI), according to the BHZ model, our results reveal resonant transport modes when the SC fractal generation reaches the same scale as the space discretization; these modes are analyzed within a contour plot mapping of the local spin-polarized currents, shown spanned and assisted by inner-edge channels. From such a deeply fractalized SC building block, we introduce a rich tapestry formed by superior SC hierarchies, enlightening intricate patterns and unique fingerprints that offer valuable insights into how helical edge transport occurs in these fractal dimensions.

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M. A. Toloza Sandoval, A. L. Araújo, F. Crasto de Lima, A. Fazzio. 2024-01-29. Resonant helical multi-edge transport in Sierpi\'nski carpets. https://doi.org/10.1016/j.physe.2024.116097

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