Quenching of phase coherence in quasi-one-dimensional ring crystals

A comparison of the single-particle (SP) dynamics of whisker and ring $\mathrm{Nb}{\mathrm{Se}}_3$ crystals provides new insight into the phase transition properties of quasi-one-dimensional charge density wave (CDW) systems. In the incommensurate CDW phase, SP relaxation triggered by an ultrafast laser pulse reflects the formation of collective states, and reveals the divergence of the relaxation time when approaching a transition temperature. The degree of divergence is less pronounced in rings than in whiskers, suggesting a loss of phase coherence in ring crystals characterized by a closed-loop topology.

Figure 1

(Color online). Electron micrographs of the topological samples: (a) Whisker and (b) ring. The corresponding transient reflectivity changes, $\Delta R$, at various temperatures below and above $T_{c2}$ in (c) and (d). The solid lines indicate the results of least-squares fitting.

Figure 2

(Color online) Temperature dependences of ${\tau }_s$ in the whisker (a) and ring (b) around $T_{c2}$. The solid line in (a) shows a theoretical fit (Ref. 8) to the data, and this is also shown in (b) for comparison, where a large reduction in ${\tau }_s$ and disagreement with the theoretical curve are clearly seen. Insets: Sketches of CDWs modulated on neighboring chains. Below the mean-field temperature, Coulomb repulsion tends to align the CDWs out of phase with each other.

Figure 3

(Color online) Semilogarithmic plots of the reflectivity changes for the whisker $(T=56\mathrm{K})$ and the ring $(T=52\mathrm{K})$, where the longest ${\tau }_s$ was obtained in each crystal. The plots are shifted vertically for clarity. The inset shows another plot for the ring. The solid line indicates the slope of $\exp {(-t∕\tau )}^{0.3}$, where $\tau$ is 1.61.

Figure 4

Fourier transform of the oscillation signal obtained by subtracting the exponential contributions from the data: (a) Spectrum for the whisker at $28\mathrm{K}$ and (b) spectrum for the ring at $27\mathrm{K}$. The peak at the lower frequency is that of an amplitude mode (AM).