We followed the Shastry-Shraiman formulation of Raman scattering in Hubbard systems and considered the Raman intensity profile in the spin-$\frac{1}{2}$ “perfect” kagome lattice herbertsmithite ${\text{ZnCu}}_3{\left(\text{OH}\right)}_6{\text{Cl}}_2$, assuming the ground state is well-described by the U(1) Dirac spin-liquid state. In the derivation of the Raman $T$ matrix, we found that the spin-chirality term appears in the $A_{2g}$ channel in the kagome lattice at the $t^4/{\left({\omega }_i-U\right)}^3$ order, but (contrary to the claims by Shastry and Shraiman) vanishes in the square lattice to that order. In the ensuing calculations on the spin-$\frac{1}{2}$ kagome lattice, we found that the Raman intensity profile in the $E_g$ channel is invariant under an arbitrary rotation in the kagome plane, and that in all ($A_{1g}$, $E_g$, and $A_{2g}$) symmetry channels the Raman intensity profile contains broad continua that display power-law behaviors at low energy, with exponent approximately equal to 1 in the $A_{2g}$ channel and exponent approximately equal to 3 in the $E_g$ and the $A_{1g}$ channels. For the $A_{2g}$ channel, the Raman profile also contains a characteristic $1/\omega$ singularity, which arose in our model from an excitation of the emergent U(1) gauge field.

• Received 4 November 2009

DOI:https://doi.org/10.1103/PhysRevB.81.024414