Three-dimensional non-Bosonic non-Fermionic quasiparticle through a quantized topological defect of crystal dislocation

It is a fundamental postulate that quasiparticles in 3D space obey either Bosonic or Fermionic statistics, satisfying either canonical commutation or anti-commutation relation. However, under certain constraints, such as the 2D dimensional constraint, canonical quantization algebra is allowed to break down, and quasiparticles can obey other statistics, such as anyonic statistics. In this study, we show that dislons- the quasiparticles in 3D due to quantized displacement field of a dislocation- can also obey neither Bosonic nor Fermionic statistics due to the topological constraint of the dislocation. With this theory, an effective electron field theory based on the electron-dislon interaction is obtained, which consists of two types of interactions. One classical-type of interaction is reducible to the well-known deformation potential scattering, and the other quantum-type of interaction indicates an effective attraction between electrons. The role of dislocations in superconductivity is clarified as the competition between the classical and quantum interactions, showing excellent agreement with experiments.