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

Abstract

A comparison of the single-particle ͑SP͒ dynamics of whisker and ring NbSe 3 crystals provides new insight into the phase transition properties of quasi-one-dimensional charge density wave ͑CDW͒ 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. DOI: 10.1103/PhysRevB.73.153403 PACS number͑s͒: 78.47.ϩp, 71.45.Lr Over the last few decades, there has been intense interest in understanding the properties of charge density waves ͑CDW͒ in quasi-one-dimensional ͑1D͒ metals, where one of the most widely discussed issues is the influence of phase fluctuations on CDW transitions.1 In an uncoupled-1D system, large fluctuations greatly reduce the CDW transition temperature ͑T c ͒ below the mean-field transition temperature. CDWs undergo a phase transition only when long-range three-dimensional ͑3D͒ order develops.1 Indeed, a pronounced finite size effect has been observed in NbSe 3 , in which a reduction in the number of parallel chains makes the transitions less pronounced and reduces T c .2 In this sense, it is also expected that crystal topology will make a substantial contribution to the phase transition since the topology imposes additional constraints on interchain correlations. However, the effects of crystal topology on CDW properties are still poorly understood.Recently, several 1D transition metal chalcogenides of the type MX 3 were found to have various types of topological crystals, where the whisker crystals naturally form ring, Möbius, and figure-of-eight geometries.3,5 The small sizes and damage-free formations of these structures make it possible for CDWs to maintain their coherence within individual chains with a closed loop, thus making them good candidates for studying the effects of topology on the long-range ordering. In this work, we have investigated topological crystals of NbSe 3 by measuring time-resolved optical reflectivity changes. A comparison of the single-particle ͑SP͒ decay of whisker and ring structures reveals a significant difference, suggesting that the crystal topology influences their phase transitions.Figures 1͑a͒ and 1͑b͒ show scanning electron micrographs of a NbSe 3 whisker and ring, respectively. Both crystals were prepared by the chemical vapor transport method under virtually the same conditions. The whisker has a standard bulk with a length of a few mm ͑along the conducting axis b͒ and a width of 50 m. The ring has a somewhat different structure with an outer diameter of 50 m and an internal diameter of several m ͑conducting axis b in the tangential direction͒. The circumference of the center hole is around 10 m and this is comparable to the correlation length of CDWs ͑ ʈb Ͼ 2.5 m͒ 4 in this compound. The details of the growth mechani...

Polyhedral Topological Crystals

“…Crystal topology broke through a new stage of understanding of physical phenomena. 12,14,15 The topological crystals are conceptually different from conventional crystals. A crystal is constructed by the infinite repetition of atoms, as shown in Figure 1 (LEFT).…”

Topology-change surgery for crystals

“…These features of the crystals are consistent with the results of the previous experiments in which we have observed clear charge density waves and superconductivity in the ring-shaped crystals as well as single crystals. [10][11][12][13][14][15]18 In summary, we demonstrated that the topology-change surgery gives us valuable information in crystals. By cutting off the ring-shaped crystals of TaSe 3 , we found a phenomenological relation between the radius of curvature after the topology change and thickness.…”

“…[3][4][5] By the discovery of rings, Möbius rings and Hopf links of crystals of transition metal-trichalcogenide compound systems (NbSe 3 , NbS 3 , TaSe 3 , and TaS 3 ), [6][7][8][9] we obtained experimental systems for the interplay between the closed-ring topology and local order parameters. Using the topological crystals, effects of the closed-ring topology on charge density waves [10][11][12][13][14][15][16][17] and superconductivity 18 have been investigated. As well as the ordered phases in electron systems, the crystal orders of the topological crystals have rich problems of the interplay between the global topology.…”

Theory of photoexcited carrier relaxation across the energy gap of phase-ordered materials

“…Usually the anomalous T dependence of τ exp is observed in many gapped systems, for example, phaseordered systems showing an energy gap opening in the electron band below the transition temperature T c . It has been found that a wide variety of superconductors [1][2][3][4][5][6][7][8][9][10][11][12][13] and density-wave compounds [14][15][16][17][18][19] show diverging behavior of τ exp near T c , as confirmed by femtosecond time-resolved optical spectroscopy. 1,4,5,[7][8][9][10][11][12][13][14][15][16][17]19 The divergence of τ exp in these gapped systems is believed to result from a recursive energy transfer between electrons and phonons.…”