We discovered the chirality of charge density waves (CDW) in 1T-TiSe 2 by using scanning tunnelling microscopy (STM) and optical ellipsometry. We found that the CDW intensity becomes Ia 1 : Ia 2 : Ia 3 = 1 : 0.7 ± 0.1 : 0.5 ± 0.1, where Ia i (i =1, 2, 3) is the amplitude of the tunnelling current contributed by the CDWs. There were two states, in which the three intensity peaks of the CDW decrease clockwise and anticlockwise when we index each nesting vector in order of intensity in the Fourier transformation of the STM images. The chirality in CDW results in the three-fold symmetry breaking. Macroscopically, two-fold symmetry was indeed observed in optical measurement. We propose the new generalized CDW chirality H CDW ≡ q 1 · (q 2 × q 3 ), where q i are the nesting vectors, which is independent of the symmetry of components. The nonzero H CDW -the triple-q vectors do not exist in an identical plane in the reciprocal space -should induce a real-space chirality in CDW system.

We report the ultrafast optical response of quasiparticles (QPs) in both the pseudogap (PG) and superconducting (SC) states of an underdoped Bi2Sr2CaCu2O8 + y (Bi2212) single crystal measured with the time-resolved pump-probe technique. At a probe energy variant planck's over omegapr = 1.55 eV, it is found that the reflectivity change DeltaR/R changes its sign at exactly Tc, which allows the direct separation of the charge dynamics of PG and SC QPs. Further systematic investigations indicate that the transient signals associated with PG and SC QPs depend on the probe beam energy and polarization. By tuning them below Tc, two distinct components can be detected simultaneously, providing evidence for the coexistence of PG and SC QPs.

We report a study of the ultrafast single particle dynamics in quasi-one-dimensional NbSe 3 whisker crystals using a two-color pump-probe measurement. A selective enhancement of the relaxation dynamics connected with one of the two charge-density-wave ͑CDW͒ phases was realized by tuning the probe energy to around 1.5 eV, in which the temperature dependence across the corresponding phase transition shows a pronounced anomaly. A similar selective excitation was possible in the coherent CDW oscillation.

We evaluate the quasi-one-dimensional (1D) electron dynamics in a NbSe3 ring crystal using polarization vortex pulses with various azimuthal distributions. The single particle relaxation component reveals a large anisotropy on the crystal, indicating that the electrons in the ring maintain their 1D character. The results also suggest that the polarization vortex evaluates the global polarization property of the closed-loop electron that plays an important role in the quantum correlation phenomena such as the Aharonov-Bohm effect.

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...