Nuclear quadrupole resonance measurements were performed on the heavy fermion superconductor Ce2PdIn8. Above the Kondo coherence temperature T_coh simeq 30K, the spin-lattice relaxation rate 1/T_1 is temperature independent, whereas at lower temperatures, down to the onset of superconductivity at T_c = 0.64K, it is nearly proportional to T^{1/2}. Below T_c, 1/T_1 shows no coherence peak and decreases as T^3 down to 75mK. All these findings indicate that Ce2PdIn8 is close to the antiferromagnetic quantum critical point, and the superconducting state has an unconventional character with line nodes in the superconducting gap.
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