We study a two-dimensional system of spin-polarized fermions on the kagome lattice at filling fraction $f=1/3$ interacting through a nearest-neighbor interaction $V$. Above a critical interaction strength $V_c$ a charge-density wave with a broken $Z_3$ symmetry is stabilized. Using the unrestricted mean-field approximation, we present several arguments showing that elementary topological point defects in the order parameter bind a fractional charge. Our analysis makes use of two appealing properties of the model: (i) For weak interaction, the low-energy degrees of freedom are described by Dirac fermions coupled to a complex-valued mass field (order parameter). (ii) The nearest-neighbor interaction is geometrically frustrated at filling $f=1/3$. Both properties offer a route to fractionalization and yield a consistent value $\pm 1/2$ for the fractional charge as long as the symmetry between the up and the down triangles of the kagome lattice is preserved. If this symmetry is violated, the value of the bound charge varies continuously with the strength of the symmetry-breaking term in the model. In addition, we have numerically computed the confining potential between two fractionally charged defects. We find that it grows linearly at large distances but can show a minimum at a finite separation for intermediate interactions. This indicates that the polaron state, formed upon doping the charge-density wave, can be viewed as a bound state of two defects.

• Received 9 January 2011

DOI:https://doi.org/10.1103/PhysRevB.83.165118