Raman signature of the U(1) Dirac spin-liquid state in the spin-1/2 kagome system

We followed the Shastry-Shraiman formulation of Raman scattering in Hubbard systems and considered the Raman intensity profile in the spin-1/2 "perfect" kagome lattice herbertsmithite ZnCu3(OH )(6)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(2)g channel in the kagome lattice at the t(4)/(omega(i)-U)(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-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.