Invisible defects in complex crystals

TL;DR

This paper demonstrates how to create invisible localized defects in complex crystals using supersymmetric transformations, resulting in defects that do not affect the crystal's observable properties like energy spectrum and scattering.

Contribution

It introduces a novel method to engineer invisible defects in crystals via supersymmetric transformations, expanding the understanding of defect manipulation in solid-state physics.

Findings

Invisible defects do not alter the energy spectrum.

Bragg scattering remains unaffected by the defects.

The method is exemplified with Mathieu potential synthesis.

Abstract

We show that invisible localized defects, i.e. defects that can not be detected by an outside observer, can be realized in a crystal with an engineered imaginary potential at the defect site. The invisible defects are synthesized by means of supersymmetric (Darboux) transformations of an ordinary crystal using band-edge wave functions to construct the superpotential. The complex crystal has an entire real-valued energy spectrum and Bragg scattering is not influenced by the defects. An example of complex crystal synthesis is presented for the Mathieu potential.