# Random edge states on a finite lattice

Source: [Random edge states on a finite lattice](<https://www.sota2.com/research/paper/68fa36451e209131ce8a8969>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T21:45:05.211Z

Authors: K. Ziegler

Published: 2017-08-28T15:56:17.000Z

## Abstract

A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong influence on the electromagnetic field and its polarization inside the sample. The creation of edge states through a randomly fluctuating sign of the Dirac mass defeats Anderson localization and allows the electromagnetic field to distribute over the entire sample. The width of the distribution increases with an increasing gap due to increasing sharpness of the edge states. These results are compared with those of a random one-band Helmholtz equation. In contrast to the Dirac model, the one-band model displays a clear signature of Anderson localization.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1708.08388>)

[PDF](<https://arxiv.org/pdf/1708.08388.pdf>)