  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 dislocation's 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.
