Abstract
This work presents a method of grouping the electron spinors and the phonon modes of metal oxide crystals such as vanadium dioxide into an SU(2) gauge theory. The gauge “charge” is the electron spin, which is assumed to couple to the transverse acoustic phonons on the basis of spin ordering phenomena in {text{M}}_{{1}}- and {text{M}}_{{2}}-{text{VO}}_{{2}}, while the longitudinal mode is neutral. A generalization of the Peierls Mechanism is presented based on the discrete gauge invariance of crystals and the corresponding Ward-Takahashi identity. The introduction of a band index results in violation of this discrete Ward-Takahashi identity for interband transitions, resulting in scattering from the longitudinal component. Thus both the spinors and the bosons acquire mass and an electronic band gap and optical phonon modes result: a symmetry-breaking metal-insulator transition, which can manifest concurrent spin-ordering.
Highlights
This work presents a method of grouping the electron spinors and the phonon modes of metal oxide crystals such as vanadium dioxide into an SU(2) gauge theory
There currently exist a number of seemingly intractable problems in Condensed Matter physics
Postulating that the observation of spin and charge ordering appearing coincident with different crystal structure distortions allows an SU(2) Yang-Mills theory of electron-phonon interactions in vanadium dioxide to be formulated
Summary
This work presents a method of grouping the electron spinors and the phonon modes of metal oxide crystals such as vanadium dioxide into an SU(2) gauge theory. The introduction of a band index results in violation of this discrete WardTakahashi identity for interband transitions, resulting in scattering from the longitudinal component Both the spinors and the bosons acquire mass and an electronic band gap and optical phonon modes result: a symmetry-breaking metal-insulator transition, which can manifest concurrent spin-ordering. The reader is directed to Liu et al.[15] for a thorough review There is both experimental and theoretical support for the involvement of phonons in the transition, with diffuse X-ray scattering[16] and more recently inelastic X-ray scattering[17] suggesting softening at the tetragonal R-point occurring, which aligns with the symmetry-breaking of the transformation. In reality both are intertwined, which has been termed “correlation assisted Peierls” process or “Peierls-Mott” insulating behaviour by some[18,19]
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