Scanning tunnelling microscopy of charge-density waves in transition metal chalcogenides

We have used scanning tunnelling microscopes (STMs) operating at liquid helium and liquid nitrogen temperatures to image the charge-density waves (CDWs) in transition metal chalcogenides. The layer structure dichalcogenides TaSe₂, TaS₂, NbSe₂, VSe₂, TiSe₂ and TiS₂ have been studied including representative polytype phases such as 1T, 2H and 4Hb. Experimental results are presented for the complete range of CDW amplitudes and structures observed in these materials. In most cases both the CDW and the surface atomic structure have been simultaneously imaged. Results on the trichalcogenide NbSe₃ are also included.

The formation of the CDW along with the associated periodic lattice distortion gaps the Fermi surface (FS) and modifies the local density-of-states (LDOS) detected by the tunnelling process. The tunnelling microscopes have been operated mostly in the constant current mode which maps the LDOS at the position of the tunnelling tip. The relative amplitudes and profiles of the CDW superlattice and the atomic lattice have been measured and confirm on an atomic scale the CDW structures predicted by X-ray, electron and neutron diffraction. The absolute STM deflections are larger than expected for the CDW induced modifications of the LDOS above the surface and possible enhancement mechanisms are reviewed.

In the 2H trigonal prismatic coordination phases the CDWs involve a relatively small charge transfer and the atomic structure dominates the STM images. In the 1T octahedral coordination phases the charge transfer is large and the CDW structure dominates the STM image with an anomalously large enhancement of the STM profile. Systematic comparison of the STM profiles with band structure and FS information is included.

In the case of the 4Hb mixed coordination phases at the lowest temperatures two nearly independent CDWs form in alternate sandwiches. STM studies on 4Hb crystals with both octahedral and trigonal prismatic surface sandwiches have been carried out. The STM scans detect the relative strengths of the two CDWs as well as the interactions between the two types of CDW structure.

The STM scans are also able to detect defects and domain structure in the CDW image. Several examples will be given demonstrating the potential of the STM to detect these local variations in LDOS on an atomic scale. In contrast to the layer structure crystals the linear chain compound NbSe₃ shows a complex surface atomic structure as well as the formation of two CDWs. The surface atomic structure is resolved in the STM scans and profiles have detected the presence of the CDW modulation at 77K and 4.2K. These results demonstrate the feasibility of detecting CDW structure in the presence of complex atomic structure and using materials where dynamical CDW effects can also be studied by STM.

The range of STM results presented here show that the STM scans are extremely sensitive to the detail of the CDW structure and its effect on the LDOS. Although much of this structure has been deduced from diffraction studies, the ability to examine the CDW structure on an atomic scale with the STM is new. The sensitivity of the STM method suggests potential applications to a wide range of electronic structures in materials.     

Optical Bragg,atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frustrated optical lattices. The physically measurable quantities of the three experiments are the light scattering cross sections, the atom scattered clouds and the cavity leaking photons respectively. We show that the two photon Raman transition processes in the three detection methods not only couple to the density order parameter, but also the valence bond order parameter due to the hopping of the bosons on the lattice. This valence bond order coupling is very sensitive to any superfluid order or any valence bond (VB) order in the quantum phases to be probed. These quantum phases include not only the well-known superfluid and Mott insulating phases, but also other important phases such as various kinds of charge density waves (CDW), valence bond solids (VBS), and CDW-VBS phases with both CDW and VBS orders unique to frustrated lattices, and also various kinds of supersolids. We analyze respectively the experimental conditions of the three detection methods to probe these various quantum phases and their corresponding excitation spectra. We also address the effects of a finite temperature and a harmonic trap. We contrast the three scattering methods with recent in situ measurements inside a harmonic trap and argue that the two kinds of measurements are complementary to each other. The combination of both kinds of detection methods could be used to match the combination of Scanning tunneling microscopy (STM), the Angle Resolved Photo Emission spectroscopy (ARPES) and neutron scattering in condensed matter systems, therefore achieve the putative goals of quantum simulations     

Effect of charge density waves on the tunnel spectra of the Bi2Sr2CaCu2O8+δ superconductor

The differential tunnel conductance G _S of the junction between a normal metal and a superconductor with a charge density wave (CDW) is calculated as a function of the voltage V across the junction. The results are averaged over the spread of superconducting and CDW energy gaps in the nanoscale-inhomogeneous superconductor. It is shown that, if both order parameters are nonzero, a dip-hump structure is formed beyond the superconducting gap of G _S (V). If the phase of the CDW order parameter is not equal to π/2, a dip-hump structure will appear solely or mainly for one sign of the bias polarity. The results agree with the experimental data for Bi₂Sr₂CaCu₂O_8+δ and other high-temperature oxides     

Thermoelectric power of TTF[Ni(dmit)2]2

The 1D organic salt TTF[Ni(dmit)₂]₂ becomes superconductor with T_c=1.6 K under an applied hydrostatic pressure of 7 kbar. Structural determinations in this system lead us to suspect that superconductivity (SC) coexists with a charge density wave (CDW) instability at low pressure. In order to better understand how SC emerge from a CDW and to revisit the pressure–temperature phase diagram of the TTF[Ni(dmit)₂]₂ we performed transport and thermoelectric power measurements under pressure.     

Microscopic theory of longitudinal sound velocity in CDW and SDW ordered cuprate systems

We address here the self-consistent calculation of the spin density wave and the charge density wave gap parameters for high-T_c cuprates on the basis of the Hubbard model. In order to describe the experimental observations for the velocity of sound, we consider the phonon coupling to the conduction band in the harmonic approximation and then the expression for the temperature dependent velocity of sound is calculated from the real part of the phonon Green’s function. The effects of the electron–phonon coupling, the frequency of the sound wave, the hole doping concentration, the CDW coupling and the SDW coupling parameters on the sound velocity are investigated in the pure CDW phase as well as in the co-existence phase of the CDW and SDW states. The results are discussed to explain the experimental observations.     

Non-local conduction by charge-density waves in niobium triselenide

The threshold field E_T for the onset of nonlinear conduction in NbSe₃ has been measured using both the normal 4-terminal arrangement, and a transposed version with current flow between the inner pair and voltage measured between the outer. When the distance between the inner terminals is small, and the temperature between 60 and 110 K, E_T is significantly greater for the transposed than for the normal arrangement. The phenomenon is thought to demonstrate that the nonlinear conduction, which arises from motion of the charge-density wave (CDW) forming at 144 K, is non-local over distances of the order of 100μm.Further experiments indicate that E_T is greater with the transposed arrangement because the CDW then has to be broken near the inner terminals, in order that its central section might move independently. Evidence is presented that the breaking process at an inner terminal depends on whether current flows from or towards it, and that above 110 K breaking occurs even when the normal configuration is used, apparently because the CDW is then too weak to overcome the pinning introduced by the contact material.No corresponding effects have been observed in nonlinear conduction by the CDW which forms at 59 K.     

MX络合物中的晶格零点振动

利用自洽重整化方法,研究了不同电-声藕合作用下MX络合物中晶格零点振动对电荷密度波(CDW)的影响。对聚乙炔,无论电-声耦合作用强弱,键序波(BOW)总存在。而对MX络合物,计算表明,量子起伏对CDW的削弱作用依赖于电-声耦合作用的强弱。当电-声耦合作用强时,CDW的削弱小;相反,当电-声耦合作用弱时,CDW削弱大,甚至几乎被破坏。这一差异来源于以下事实,即在弱电-声耦合λ情况下,聚乙炔中光学模声子频率随λ^1/2减小,而在MX络合物中光学模声子频率与其裸值ω₀差 关键词：     

Stationary Josephson current in junctions involving d-wave superconductors with charge density waves: the temperature dependence and deviations from the law of corresponding states

Stationary Josephson current I _c in symmetric and non-symmetric junctions involving d-wave superconductors with charge density waves (CDWs) was calculated. It was found that, if CDWs are weak or absent, there exists an approximate proportionality between I _c and the product of superconducting order parameters in the electrodes (the law of corresponding states) for several factors affecting those quantities, such as the temperature, T, or one of the parameters characterizing the combined CDW superconducting phase (the degree of the Fermi surface dielectric gapping and the ratio between the parent superconducting and CDW order parameters). Otherwise, the dependences I _c (T) were shown to deviate from those in the absence of CDWs, and the relevant corresponding-state dependences from linearity, the deviations being especially strong at certain rotation angles of crystalline electodes with respect to the junction plane. Hence, making use of specially designed experimental setups and analyzing the I _c (T) and corresponding-state dependences, the existence of CDWs in cuprates and other non-conventional superconductors can be detected.     

Growth,crystal structure and transport properties of quasi one-dimensional conductors NbS3

We report synthesis of quasi-one-dimensional conductor NbS₃, TEM studies and transport properties of the prepared samples. The grown NbS₃ whiskers are Peierls conductors known as phase II with the transitions at T_P1=365 K and T_P2=150 K. CDW1 is stable and not so sensitive to growth conditions. It can slide and be synchronized by the external microwave irradiation up to 16 GHz. CDW2 strongly depends on growth conditions. Nevertheless, it also shows sliding and synchronization.     

Phase diagrams of bosonic AB<Subscript>n</Subscript> chains

The AB_{N ?1} chain is a system that consists of repeating a unit cell withN siteswhere between the A and B sites there is an energy difference ofλ. Weconsidered bosons in these special lattices and took into account the kinetic energy, thelocal two-body interaction, and the inhomogenous local energy in the Hamiltonian. We foundthe charge density wave (CDW) and superfluid and Mott insulator phases, and constructedthe phase diagram for N =2 and 3 atthe thermodynamic limit. The system exhibited insulator phases for densitiesρ =α/N, with α being an integer. Weobtained that superfluid regions separate the insulator phases for densities larger thanone. For any N value, we found that for integer densitiesρ, thesystem exhibits ρ +1 insulator phases, a Mott insulator phase, and ρ CDW phases. Fornon-integer densities larger than one, several CDW phases appear.     

Non-archimedean strings

A full set of factorized, dual, crossing-symmetric tree-level N-point amplitudes is constructed for non-archimedean closed strings. Momentum components and space-time coordinates are still valued in the field of real numbers, quantum amplitudes in that of complex numbers. It is the world-sheet parameters, which one integrates over, that become p-adic. For the closed string the parameters are valued in quadratic extensions of the fields Q_p of p-adic numbers (p = prime).     

Harmonic and subharmonic shapiro steps in orthorhombic Tas3

Observation of harmonic and subharmonic Shapiro steps in orthorhombic TaS₃ in the presence of combined rf and dc drive is reported, demonstrating that both the harmonic and subharmonic steps are a general characteristic of charge-density-wave response. Compared to NbSe₃, the noise spectrum is typically much broader in TaS₃, leading to poorly defined steps at small rf voltages. The steps sharpen with larger amplitudes of rf. Increased rf amplitude is also accompanied by an increase in the CDW current density at a given step, but this increase approaches a limiting value for large rf levels. The results are interpreted as evidence for increased coherence of the CDW response in the presence of large rf driving fields.     

The structure of t-channel exchanges in KN scattering

Recent phase-shift solutions are used to evaluate KN FESR integrals in order to examine zeros and phases of the t-channel exchange amplitudes in the most model-independent way. The results suggest that the line reversal breaking in KN CEX observed for pL ? 5.5 GeV/c is due to a large EXD breaking component in the A₂ exchange flip amplitude. The ? exchange flip amplitude is well described by a Regge pole amplitude with NWSZ at ?t ≈ 0.5 (GeV/c)². The imaginary parts of ? and ω exchange non-flip amplitudes are both peripheral.     

Density waves and supersolidity in rapidly rotating atomic Fermi gases

We study theoretically the low-temperature phases of a two-component atomic Fermi gas with attractive s-wave interactions under conditions of rapid rotation. We find that, in the extreme quantum limit, when all particles occupy the lowest Landau level, the normal state is unstable to the formation of charge density wave (CDW) order. At lower rotation rates, when many Landau levels are occupied, we show that the low-temperature phases can be supersolids, involving both CDW and superconducting order.     

Investigation of continuous-time quantum walk via spectral distribution associated with adjacency matrix

Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph C_n, complete graph K_n, graph G_n, finite path and some other finite and infinite graphs, where all are connected with orthogonal polynomials such as Hermite, Laguerre, Tchebichef, and other orthogonal polynomials. It is shown that using the spectral distribution, one can obtain the infinite time asymptotic behavior of amplitudes simply by using the method of stationary phase approximation (WKB approximation), where as an example, the method is applied to star, two-dimensional comb lattices, infinite Hermite and Laguerre graphs. Also by using the Gauss quadrature formula one can approximate the infinite graphs with finite ones and vice versa, in order to derive large time asymptotic behavior by WKB method. Likewise, using this method, some new graphs are introduced, where their amplitudes are proportional to the product of amplitudes of some elementary graphs, even though the graphs themselves are not the same as the Cartesian product of their elementary graphs. Finally, by calculating the mean end to end distance of some infinite graphs at large enough times, it is shown that continuous-time quantum walk at different infinite graphs belong to different universality classes which are also different from those of the corresponding classical ones.     

Low temperature asymptotic behaviours of the correlation functions in the one-dimensional fermi gas

The g-model of the one-dimensional (1-D) Fermi gas including the same site interaction g₄ is investigated in the self-consistent harmonic approximation (SCHA) for the Bosonized Hamiltonian. The asymptotic form of the gap of the spin-density excitation is determined at low temperatures. It is found that the phase transition is of first order and the transition exists if g₁₆ < 0 but does not if g₁₆ > 0. The correlation functions for the order parameters of the charge-density wave (CDW) and singlet-superconductor (SS) are evaluated at low temperatures.     

Rescattering effects in the decay of the A1

Rescattering effects in the 3π system in the A₁ region are studied with a method, which fulfils unitarity and has the proper analytic structure. Fairly small effects are obtained which confirm the result found in amplitude analyses, neglecting rescattering corrections, that the phases of the J^P = 1⁺ amplitudes vary only very little over the A₁ region. Similar results hold for the Q enhancement.