| Summary: | © 2019 IOP Publishing Ltd. A dislocation, just like a phonon, is a type of atomic lattice displacement but subject to an extra topological constraint. However, unlike the phonon which has been quantized for decades, the dislocation has long remained classical. This article is a comprehensive review of the recent progress on quantized dislocations, aka the 'dislon' theory. Since the dislon utilizes quantum field theory to solve materials defects problems, we adopt a pedagogical approach to facilitate understanding for both materials science and condensed matter communities. After introducing a few preliminary concepts of dislocations, we focus on the necessity and pathways of dislocation's quantization in great detail, followed by the interaction mechanism between the dislon and materials electronic and phononic degrees of freedom. We emphasize the formality, the new phenomena, and the predictive power. Imagine the leap from classical lattice wave to quantized phonon; the dislon theory may open up vast opportunities to compute dislocated materials at a full quantum many-body level.
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