Fractionalized Charge Excitations in a Spin Liquid on Partially Filled Pyrochlore Lattices

We study the Mott transition from a metal to cluster Mott insulators in the $1/4$- and $1/8$-filled pyrochlore lattice systems. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or “photons” that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in x-ray scattering experiments. Various other experimental signatures of the exotic cluster Mott insulator are discussed in light of candidate materials with partially filled bands on the pyrochlore lattice.

Figure 1

The ring hopping processes of charge rotors around a hexagon in the CMI, for the $\frac{1}{4}$- and $\frac{1}{8}$-filled cases shown in (a) and (b) . As shown in (c) , $\mathbf{r}$ and ${\mathbf{r}}^{\prime }$ are located on the center of the tetrahedra and form a dual diamond lattice. We use $\mathbf{r},{\mathbf{r}}^{\prime }$ ($i,j$) to label the diamond (pyrochlore) lattice sites. In (c), $\mathbf{r}\in \mathrm{A}$ diamond sublattice and ${\mathbf{e}}_{\mu }$ are four vectors connecting A sublattice sites to the four neighboring B sublattice sites. In (d) , the electron charge fractionalization in the FCL/QSL phase is illustrated. The two end charge defects are connected by a fictitious string. The phase diagram at the $\frac{1}{4}$- or $\frac{1}{8}$-filling is plotted in (e) . Here, $(V/t{)}_c=1.65(0.98)$ for the $\frac{1}{4}$ ($\frac{1}{8}$)-filling in the mean-field theory. There are only two phases: a Fermi liquid metal and a CMI (FCL/QSL).