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

TL;DR

This study reveals that in 2H-NbSe$_2$, charge-density wave order initially develops with a well-defined amplitude but without long-range phase coherence, which only emerges at the transition temperature, highlighting the role of phase fluctuations.

Contribution

It demonstrates that phase coherence in CDW states can be decoupled from amplitude development, challenging the conventional view of simultaneous onset at T$_{cdw}$ in strongly coupled systems.

Findings

Short-range CDW order with a well-defined amplitude exists above T$_{cdw}$.

Long-range phase coherence appears only at T$_{cdw}$, leading to sharp electronic excitations.

Phase fluctuations are crucial in understanding pseudogap states in CDW materials.

Abstract

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T$_{cdw}$. Here we investigate, using photoemission, X-ray scattering and scanning tunneling microscopy, the canonical CDW compound 2H-NbSe$_2$ intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude that impacts the electronic dispersion, giving rise to an energy gap. The phase transition at T$_{cdw}$ marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in `pseudogap' states.