Soliton analysis of the electro-optical response of blue bronze

In recent measurements on the charge-density-wave (CDW) conductor blue bronze (K_0.3MoO₃), the electro-transmittance and electro-reflectance spectra were searched for intragap states that could be associated with solitons created by injection of electrons into the CDW at the current contacts [Eur. Phys. J. B16 (2000), 295; Eur. Phys. J. B35 (2003) 233]. In this work, we adapt the model of soliton absorption in dimerized polyacetylene to the blue bronze results, to obtain the (order of magnitude) estimate that current induced solitons occur on less than ∼10% of the conducting chains. We discuss the implications of these results on models of soliton lifetimes and motion of CDW phase dislocations.     

Competing periodicities in fractionally filled one-dimensional bands

We present a variable temperature scanning tunneling microscopy and spectroscopy study of the Si(553)-Au atomic chain reconstruction. This quasi-one-dimensional system undergoes at least two charge density wave (CDW) transitions, which can be attributed to electronic instabilities in the fractionally filled 1D bands of the high-symmetry phase. Upon cooling, Si(553)-Au first undergoes a single-band Peierls distortion, resulting in period doubling along the chains. This Peierls state is ultimately overcome by a competing x3 CDW, which is accompanied by a x2 periodicity in between the chains. These locked-in periodicities indicate small charge transfer between the nearly 1/2-filled and 1/4-filled bands. The presence and the mobility of atomic-scale dislocations in the x3 CDW state indicates the possibility of manipulating phase solitons carrying a (spin, charge) of (1/2, +/- e/3) or (0, +/-2e/3).     

CDW CONDUCTION IN THE TRANSITION METAL TRICHALCOGENIDES

It is shown that solitons exist in a system of the pinning CDW. They are responsible for the periodic current noise. The dependence of the nonlinear conductivity on an applying field ε is calculated as ε exceeds a threshold value ε_T.     

Quantum melting of the charge-density-wave state in 1T-TiSe2

We report a Raman scattering study of low-temperature, pressure-induced melting of the charge-density-wave (CDW) phase of 1T-TiSe2. Our measurements reveal that the collapse of the CDW state occurs in three stages: (i) For P<5 kbar, the pressure dependence of the CDW amplitude mode energies and intensities are indicative of a "crystalline" CDW regime; (ii) for 525 kbar, the absence of amplitude modes reveals a metallic regime in which the CDW has melted.     

Non-ohmic conductivity of TaS3 in the low-temperature semiconducting regime

Electrical conductivity of the quasi one-dimensional conductor TaS₃ was measured in the low-temperature semiconducting regime. Below 100K, the conductivity along c-axis (l-d axis) in the low field limit is characterized by the activated process with the activation energy of 250K, and the current-field (I-E) characteristic is nonlinear, $\text{dI}\text{dE}$ increasing with the field strength. These results can be explained by the excitation of phase solitons associated with pinned CDW condensates.     

Quantum and classical mode softening near the charge-density-wave-superconductor transition of CuxTiSe2

Temperature- and x-dependent Raman scattering studies of the charge-density-wave (CDW) amplitude modes in Cu(x)TiSe(2) show that the amplitude mode frequency omega(0) exhibits identical power-law scaling with the reduced temperature T/T(CDW) and the reduced Cu content x/x(c), i.e., omega(0) approximately (1-p)(0.15) for p=T/T(CDW) or x/x(c), suggesting that mode softening is independent of the control parameter used to approach the CDW transition. We provide evidence that x-dependent mode softening in Cu(x)TiSe(2) is associated with the reduction of the electron-phonon coupling constant, and that x-dependent "quantum" (T approximately 0) mode softening suggests the presence of a quantum critical point within the superconductor phase of Cu(x)TiSe(2).     

Coexistence of gapless excitations and commensurate charge-density wave in the 2H transition metal dichalcogenides

An unexpected feature common to 2H transition metal dichalcogenides ( 2H TMDs) is revealed with a first-principles Wannier function analysis of the electronic structure of the prototype 2H TaSe2: The low-energy Ta "5d(z2)" bands governing the physics of a charge-density wave (CDW) is dominated by hopping between next-nearest neighbors. With this motivation we develop a minimal effective model for the CDW formation, in which the unusual form of the hopping leads to an approximate decoupling of the three sublattices. In the CDW phase one sublattice remains undistorted, leaving the bands associated with it ungapped everywhere in the Fermi surface, resolving the long-standing puzzle of the coexistence of gapless excitations and commensurate CDW in the 2H TMDs.     

Charge-density-wave-induced modifications to the quasiparticle self-energy in 2H- TaSe2

The self-energy of the photohole in 2H-TaSe2 is measured by angle-resolved photoemission spectroscopy as a function of binding energy and temperature. In the charge-density wave (CDW) state, a structure in the self-energy is detected at approximately 65 meV that cannot be explained by electron-phonon scattering. A reduction in the scattering rates below this energy indicates the collapse of a major scattering channel with the formation of the CDW state accompanying the appearance of a bosonic "mode" in the excitation spectrum of the system.     

The influence of impurities on the quasiparticle tunneling current between weakly coupled quasi-one-dimensional charge density waves

The dc and ac conductivity of a tunneling junction between two impure quasi-one-dimensional charge density wave (CDW) systems is calculated. The non-magnetic impurities are considered in the self-consistent Born approximation (SCBA). Impurities modify the density of states (DOS) of the pure CDW system for quasiparticles inside the energy region of the gap 2(T). As in the pure case, the theory predicts in addition to a tunneling current which is proportional to the product of the DOS a term proportional to the cosine of the order parameter phase difference. In the case of a normal state/CDW junction, analytical expressions are obtained forT=0 showing deviations from the pure case. The linear ac conductivity is obtained by the scaling relation between the dc and the ac response.     

电荷密度波经典模型的分析

从Grüner的非线性方程出发,克服了原作者略去二阶微分项所带来的理论缺陷.依据稳定周期解的结果,推出了单段CDW的启动电场的阈值和各分段的滑行速度与外场成正比的关系,揭示出单段CDW遵循欧姆定律是Grüner非线性方程的固有性质.并将此结果用于多分段模型,最终导出CDW非线性电导的指数律和阈场,它们与实验公式一致,同时也说明了窄带噪声的来源.还就多分段的串联问题,提出了“弹性连接”机理的内力处理方法,得到了更为理想的结果. 关键词： CDW 非线性电导 指数律 强作用杂质 弱作用杂质 弹性连接     

Negative resistance and local charge-density-wave dynamics

Charge-density-wave (CDW) dynamics is studied on a submicron length scale in NbSe(3) and o-TaS(3). Regions of negative absolute resistance are observed in the CDW sliding regime at sufficiently low temperatures. The origin of the negative resistance is attributed to the different forces that the deformed CDW and quasiparticles feel: the force on the CDW is merely caused by a difference of the electric potentials, while the quasiparticle current is governed by a difference of the electrochemical potentials.     

Composite multihump vector solitons carrying topological charge

We propose composite solitons carrying topological charge: multicomponent two dimensional [ (2+1)D] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The "spin" carried by these multimode composite solitons suggests 3D soliton interactions in which the particlelike behavior includes spin, in addition to effective mass, linear, and angular momenta.     

Chiral charge-density waves

We discovered the chirality of charge-density waves (CDW) in 1T-TiSe? by using STM and time-domain optical polarimetry. We found that the CDW intensity becomes Ia?∶Ia?∶Ia? = 1∶0.7 ± 0.1∶0.5 ± 0.1, where Ia(i) (i=1,2,3) is the amplitude of the tunneling current contributed by the CDWs. There were two states, in which the three intensity peaks of the CDW decrease clockwise and anticlockwise. The chirality in CDW results in the threefold symmetry breaking. Macroscopically, twofold symmetry was indeed observed in optical measurement. We propose the new generalized CDW chirality H(CDW) ≡ q?·(q?×q?), where q(i) are the CDW q 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.     

Bright and dark solitons for a variable-coefficient $$$$ dimensional Heisenberg ferromagnetic spin chain equation

Under investigation in this paper is a variable-coefficient \((2+1)\) dimensional Heisenberg ferromagnetic spin chain equation. Bilinear forms for the bright and dark soliton solutions are respectively obtained. Bright and dark solitons are obtained via the Hirota bilinear method. Features of the bright and dark solitons are discussed. Interaction properties of the bright and dark solitons are discussed via the asymptotic analysis, and stability of the bright and dark solitons is studied via the numerical calculation: (1) Amplitudes of the bright and dark solitons are not related to the coefficient \(\delta _{4}(t)\), while the soliton velocities are related to \(\delta _{4}(t)\). (2) Interactions between the bright two solitons are shown to be elastic, while interactions between the dark two solitons could be elastic or inelastic, which is determined by the values of \(\rho \). (3) Numerical calculation indicates that the bright solitons could not resist the disturbance of small perturbations, while the dark solitons could resist the disturbance of small perturbations.     

Dephasing of Andreev pairs entering a charge density wave

A Cooper pair from a s-wave superconductor (S) entering a conventional charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length ξ_CDW. It is thus practically impossible to observe a Josephson current through a CDW. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: (i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and (ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length ξ_SDW, not by the Fermi wave-length. A Josephson current through a SDW might be observed in a structure with contacts on a SDW separated by a distance ξ_SDW.     

Observation of multiple charge density wave phases in epitaxial monolayer 1T-VSe2 film

As a special order of electronic correlation induced by spatial modulation, the charge density wave (CDW) phenomena in condensed matters attract enormous research interests. Here, using scanning—tunneling microscopy in various temperatures, we discover a hidden incommensurate stripe-like CDW order besides the ($sqrt{7}$ × $sqrt{3}$) CDW phase at low-temperature of 4 K in the epitaxial monolayer 1T-VSe₂} film. Combining the variable-temperature angle-resolved photoemission spectroscopic (ARPES) measurements, we discover a two-step transition of an anisotropic CDW gap structure that consists of two parts Δ₁ and Δ₂. The gap part Δ₁ that closes around ～ 150 K is accompanied with the vanish of the ($sqrt{7}$ × $sqrt{3}$) CDW phase. While another momentum-dependent gap part Δ₂ can survive up to ～ 340 K, and is suggested to the result of the incommensurate CDW phase. This two-step transition with anisotropic gap opening and the resulted evolution in ARPES spectra are corroborated by our theoretical calculation based on a phenomenological form for the self-energy containing a two-gap structure Δ₁ + Δ₂, which suggests different forming mechanisms between the ($sqrt{7}$ × $sqrt{3}$) and the incommensurate CDW phases. Our findings provide significant information and deep understandings on the CDW phases in monolayer 1T-VSe₂} film as a two-dimensional (2D) material.     

Multidimensional solitons: Well-established results and novel findings

A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered. Physical realizations of multidimensional solitons in atomic Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are vulnerable to instabilities induced by the occurrence of the critical and supercritical collapse, respectively, in the same 2D and 3D models that give rise to the solitons. Vortex solitons are subject to a still stronger splitting instability. For this reason, a central problem is looking for physical settings in which 2D and 3D solitons may be stabilized. The review specifically addresses one well-established topic, viz., the stabilization of the 3D and 2D states, with S = 0 and 1, trapped in harmonic-oscillator (HO) potentials, and another topic which was developed very recently: the stabilization of 2D and 3D free-space solitons, which mix components with S = 0 and ± 1 (semi-vortices and mixed modes), in a binary system with the (pseudo-) spin-orbit coupling (SOC) between its components. The former model is based on the single cubic nonlinear Schrödinger/Gross-Pitaevskii equation (NLSE/GPE), while the latter one is represented by a system of two coupled GPEs. In both cases, the generic situations are drastically different in the 2D and 3D geometries. In the 2D settings, the stabilization mechanism creates a stable ground state (GS, which was absent without it), whose norm falls below the threshold value at which the critical collapse sets in. In the 3D geometry, the supercritical collapse does not allow to create a GS, but metastable solitons can be constructed.     

Deformation of a charge density wave in the vicinity of a point contact with a normal metal

The current-voltage characteristics of Cu-K_0.3MoO₃ point contacts between a metal and a semiconductor with a charge density wave (CDW) are studied for various diameters of the contacts in a wide range of temperatures T and voltages V. In the interval 80 K ? T ? 150 K, the current-voltage characteristics are correctly described in the framework of a semiconductor model: screening of an external electric field causes CDW deformation, shifts the chemical potential of quasiparticles, and changes the point contact resistance. It is shown that the chemical potential is above the middle of the Peierls gap in equilibrium and approaches the middle upon an increase in temperature. The current-voltage characteristics of point contacts with a diameter d ? 100 Å exhibit a sharp decrease in resistance for |V| > V _t , which is associated with the beginning of local CDW sliding within the contact region. The V _t (d, T) dependence can be explained by the size effect in the CDW phase slip.