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A charge-density wave (CDW) state has a broken symmetry described by acomplex order parameter with an amplitude and a phase. The conventional view,based on clean, weak-coupling systems, is that a finite amplitude andlong-range phase coherence set in simultaneously at the CDW transitiontemperature T$_{cdw}$. Here we investigate, using photoemission, X-rayscattering and scanning tunneling microscopy, the canonical CDW compound2H-NbSe$_2$ intercalated with Mn and Co, and show that the conventional view isuntenable. We find that, either at high temperature or at large intercalation,CDW order becomes short-ranged with a well-defined amplitude that impacts theelectronic dispersion, giving rise to an energy gap. The phase transition atT$_{cdw}$ marks the onset of long-range order with global phase coherence,leading to sharp electronic excitations. Our observations emphasize theimportance of phase fluctuations in strongly coupled CDW systems and provideinsights into the significance of phase incoherence in `pseudogap' states.

Emergence of coherence in the charge-density wave state of 2H-NbSe$_2$