Oscillatory deviations from Matthiessen's rule due to interacting dislocations.

We theoretically examine the validity of Matthiessen's rule caused by strong dislocation-dislocation interaction using a fully quantized dislocation field, where its degree of deviation is quantified at arbitrary electron energy, dislocation-electron and dislocation-dislocation distances and interaction strengths. Contrary to intuition, we show that the electron relaxation rate deviates from the Matthiessen's rule in an oscillatory way as a function of inter-dislocation distance, instead of monotonically. In addition, we show quantitatively that the deviation is larger in a material with lower mass density, higher Poisson ratio and higher elastic moduli. This study could serve as a computational tool to investigate the electronic behavior of a highly-dislocated system at a full quantum field theoretical level.