We present NMR measurements of the layered nitride superconductor Li_xZrNCl. The nuclear spin-lattice relaxation rate, 1/T_1, shows that the coherence peak is strongly suppressed in Li_xZrNCl in contrast to conventional BCS superconductors. In the lightly-doped region close to the insulating state, the system shows a gap-like behavior, i.e., pseudogap, that is characterized by a reduction in the magnitude of the Knight shift and 1/T_1T. A higher superconducting (SC) transition temperature, T_c, is achieved by coexisting with the pseudogap state. These unusual behaviors, which deviate from the ordinary BCS framework, are the key ingredients to understanding the SC mechanism of Li_xZrNCl.
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