Discovery of Berezinskii-Kosterlitz-Thouless Correlations in the Quantum Kagome Compound Cs_{2}Cu_{3}SnF_{12}.

We investigate the microscopic properties of the kagome compound Cs_{2}Cu_{3}SnF_{12} using ^{63,65}Cu nuclear quadrupolar resonance. Analysis of the local hyperfine fields below the Néel temperature T_{N}=20  K indicates a spin structure consistent with P2_{1}/n symmetry of negative vector chirality. Measurements of the spin-lattice relaxation rate T_{1}^{-1} reveal signatures of a gapless ground state and two-dimensional Berezinskii-Kosterlitz-Thouless-type correlations above T_{N}, extending over a broad temperature range of approximately 130 K in zero magnetic field. Within the same temperature range, the observed increase in the nuclear quadrupolar resonance linewidth is consistent with short-range chiral order recently identified by neutron scattering. Our results establish Cs_{2}Cu_{3}SnF_{12} as a unique quantum kagome system exhibiting Berezinskii-Kosterlitz-Thouless behavior.