Theory of Electron-Phonon-Dislon Interacting System - Toward a Quantized Theory of Dislocations

We provide a comprehensive theoretical framework to study how crystal dislocations influence the functional properties of materials, based on the idea of quantized dislocation, namely a dislon. In contrast to previous work on dislons which focused on exotic phenomenology, here we focus on the theoretical structure and computational power. We first provide a pedagogical introduction of the necessity and benefits taking the dislon approach, that why the dislon Hamiltonian takes its current form. Then we study the electron-dislocation and phonon-dislocation scattering problems, using the dislon formalism. Both the effective electron and phonon theories are derived, from which the role of dislocations on electronic and phononic transport properties is computed. Comparing with the traditional dislocation scattering studies which are intrinsically single-particle, low-order perturbation and classical quenched defect in nature, the dislon theory not only allows easy incorporation of quantum many-body effects such as electron correlation, electron-phonon interaction and higher-order scattering events, but also allows proper consideration of dislocations long-range strain field and the dynamic aspects on equal footing. This means that instead of developing individual model for a specific dislocation scattering problem, the dislon theory allows for the calculation of electronic structure and electrical transport, thermal transport, optical and superconducting properties, etc., under one unified theory. Furthermore, the dislon theory has another advantage over empirical models in that it requires no fitting parameters. The dislon theory could serve as a major computational tool to understand the role of dislocations on multiple materials functional properties at an unprecedented level of clarity, and may have wide applications in dislocated energy materials.

The Non-Perturbative Quantum Nature of the Dislocation-Phonon Interaction

Despite the long history of dislocation-phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and the nature of dislocation-phonon resonance. Here by introducing a fully quantized dislocation field, the dislon[1], a phonon is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime that is reducible to classical results. A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. In particular, a renormalized phonon naturally resolves the decades-long debate between dynamic and static dislocation-phonon scattering approaches.