Fermionic Band Dispersions and an Evidence of Cooperon Excitations in a Spin-$1/2$ Trimer Chain

Abstract

We obtain the solution of the Hamiltonian of an antiferromagnetically coupled spin-$1/2$ trimer chain in terms of three bands that host three different species of fermions. While the lowest two bands correspond to spin-$1/2$ fermions, the fermions in the highest band are of spin-$3/2$. Because the bands are for different species of fermions, the particle-hole excitation channel across the bands is closed. However, fractionalized excitations as spin-$1/2$ and spin-$3/2$ fermions in pairs open a cooperon channel of excitations in Raman scattering. The background spectral intensity profile obtained by Raman scattering measurements in Na${}_2$Cu${}_3$Ge${}_4$O${}_{12}$ having a trimer chain consisting of spin-$1/2$ Cu ions, has comprehensively been shown to be consistent with these excitations.

The manuscript has been withdrawn because the theoretical and experimental parts will be submitted separately with a more detailed analysis