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

Abstract

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 ZnCu[subscript 3](OH)[subscript 6]Cl[subscript 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[subscript 2g] channel in the kagome lattice at the t4/(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 Eg channel is invariant under an arbitrary rotation in the kagome plane, and that in all (A[subscript 1g], E[subscript g], and A[subscript 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[subscript 2g] channel and exponent approximately equal to 3 in the E[subscript g] and the A[subscript 1g] channels. For the A[subscript 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.