We provide a comprehensive theoretical framework to study how crystal dislocations influence the functional properties of materials, based on the idea of a quantized dislocation, namely a 'dislon'. In contrast to previous work on dislons which focused on exotic phenomenology, here we focus on their theoretical structure and computational power. We first provide a pedagogical introduction that explains the necessity and benefits of taking the dislon approach and 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. Compared with traditional dislocation scattering studies, which are intrinsically single-particle, loworder 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 the dislocation's long-range strain field and dynamic aspects on equal footing for arbitrary types of straight-line dislocations. This means that instead of developing individual models for specific dislocation scattering problems, 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.
List of symbols in alphabetical orderA s Classical electron-dislon scattering amplitude A(k 1 , k 2 , k 3 ) Anharmonic coupling constant b k Phonon annihilation operator + b k Phonon creation operator b, b Phonon fields in coherent state form b Burgers vector c ijkl Stiffness tensor OPEN ACCESS RECEIVED R j 0 Atomic coordinate of j th atom in a perfect crystal S Action S Energy flow operator T Dislocation kinetic energy Recently, some of us started to develop a theory based on the quantization of a dislocation and introduced the 'dislon' as the basic quanta of a quantized dislocation for arbitrary types of dislocation lines, including both edge and screw dislocations. Starting from a one-dimensional quantization approach [25, 36, 77], we treated electron [25] and phonon [36] scattering with an individual dislocation, and single electron-interacting dislocation pair scattering [77]. Later, we generalized the one-dimensional approach to a full three-dimensional quantization [76], but focused on the electron-dislocation superconductivity.In this study, we generalize the dislon theory in 3D to include electron...