Anisotropy of 2H-NbSe_(2)in the superconducting and charge density wave states

Anisotropy is an important feature of layered materials,and a large anisotropy is usually related to the two-dimensional charac teristics.We investigated the anisotropy of the layered transition metal dicalcogenide 2H-NbSe_(2)in the superconducting and charge density wave(CDW)states using magnetotransport measurements.In the superconducting state,the normalized H_(c2)^(‖c)/H_(p)is independent of the thickness of 2H-NbSe_(2),while H_(c2)^(‖ab)/H_p increases significantly with decreasing thickness,where H_p is the Pauli limiting magnetic field and H_(c2)^(‖c)anu H_(c2)^(‖ab)are the upper critical fields in the c and ab directions,respectively.It is found that the superconducting anisotropy parameterγH_(c2)=H_(c2)^(‖ab)/H_(c2)^(‖c)increases with reduction in the thickness of 2H-NbSe_(2).In the CDW state,the angular(θ)dependence of magnetoresistance,R(H,θ)scales with H(cos^(2)θ+γ_(CDW)^(-2)sin^(2)θ)^(1/2),which decreases with increasing temperature and disappears at about 40 K.It is found that the CDW anisotropy parameterγ_(CDW)is much larger than the effective mass anisotropy but does not change a lot for ultrathin and bulk samples.Our results suggest the existence of three-dimensional superconductivity and quasi-two dimensional CDWs in bulk 2H-NbSe_(2).

Electronic states of domain walls in commensurate charge density wave ground state and mosaic phase in 1T-TaS_(2)

Domain walls(DWs)in the charge-density-wave(CDW)Mott insulator 1T-TaS_(2)have unique localized states,which play an important role in exploring the electronic properties of the material.However,the electronic states in DWs in 1TTaS_(2)have not been clearly understood,mostly due to the complex structures,phases,and interlayer stacking orders in the DW areas.Here,we explored the electronic states of DWs in the large-area CDW phase and mosaic phase of 1T-TaS_(2)by scanning tunneling spectroscopy.Due to the different densities of DWs,the electronic states of DWs show distinct features in these phases.In the large area CDW phase,both the domain and the DWs(DW1,DW2,DW4)have zero conductance at the Fermi level;while in the mosaic phase,they can be metallic or insulating depending on their environments.In areas with a high density of DWs,some electronic states were observed both on the DWs and within the domains,indicating delocalized states over the whole region.Our work contributes to further understanding of the interplay between CDW and electron correlations in 1T-TaS_(2).

Manipulating charge density wave state in kagome compound RbV_(3)Sb_(5)

Owing to the unique electronic structure,kagome materials AV_(3)Sb_(5)(A=K,Rb,Cs)provide a fertile platform of quantum phenomena such as the strongly correlated state and topological Dirac band.It is well known that RbV_(3)Sb_(5)exhibits a 2×2 unconventional charge density wave(CDW)state at low temperature,and the mechanism is controversial.Here,by using scanning tunneling microscopy/spectroscopy(STM/STS),we successfully manipulated the CDW state in the Sb plane of RbV_(3)Sb_(5),and realized a new3(1/2)×3(1/2)modulation together with the ubiquitous 2×2 period in the CDW state of RbV_(3)Sb_(5).This work provides a new understanding of the collective quantum ground states in the kagome materials.

Superconductivity and unconventional density waves in vanadium-based kagome materials AV_(3)Sb_(5)

Recently,the discovery of vanadium-based kagome metal AV_(3)Sb_(5)(A=K,Rb,Cs)has attracted great interest in the field of superconductivity due to the coexistence of superconductivity,non-trivial surface state and multiple density waves.In this topical review,we present recent works of superconductivity and unconventional density waves in vanadium-based kagome materials AV_(3)Sb_(5).We start with the unconventional charge density waves,which are thought to correlate to the time-reversal symmetry-breaking orders and the unconventional anomalous Hall effects in AV_(3)Sb_(5).Then we discuss the superconductivity and the topological band structure.Next,we review the competition between the superconductivity and charge density waves under different conditions of pressure,chemical doping,thickness,and strains.Finally,the experimental evidence of pseudogap pair density wave is discussed.

Density waves in a lattice hydrodynamic traffic flow model with the anticipation effect

By introducing the traffic anticipation effect in the real world into the original lattice hydrodynamic model, we present a new anticipation effect lattice hydrodynamic （AELH） model, and obtain the linear stability condition of the model by applying the linear stability theory. Through nonlinear analysis, we derive the Burgers equation and Korteweg-de Vries （KdV） equation, to describe the propagating behaviour of traffic density waves in the stable and the metastable regions, respectively. The good agreement between simulation results and analytical results shows that the stability of traffic flow can be enhanced when the anticipation effect is considered.

Charge Density Wave States and Structural Transition in Layered Chalcogenide TaSe_(2-x)Te_x

The structural features and three-dimensional nature of the charge density wave （CDW） state of the layered chalcogenide 1T-TaSe2-xTex （0≤x≤2.0） are characterized by Cs-corrected transmission electron microscopy measurements. Notable changes of both average structure and the CDW state arising from Te substitution for Se are clearly demonstrated in samples with x〉0.3. The commensurate CDW state characterized by the known star-of-David clustering in the 1T-TaSe2 crystal becomes visibly unstable with Te substitution and vanishes when x=0.3. The 1T-TaSe2-xTex （0.3≤x≤1.3） samples generally adopt a remarkable incommensurate CDW state with monoclinic distortion, which could be fundamentally in correlation with the strong qq-dependent electron-phonon coupling-induced period-lattice-distortion as identified in TaTe22. Systematic analysis demonstrates that the occurrence of superconductivity is related to the suppression of the commensurate CDW phase and the presence of discommensuration is an evident structural feature observed in the superconducting samples.

Charge density wave states in phase-engineered monolayer VTe_(2)

Charge density wave(CDW)strongly affects the electronic properties of two-dimensional(2D)materials and can be tuned by phase engineering.Among 2D transitional metal dichalcogenides(TMDs),VTe_(2)was predicted to require small energy for its phase transition and shows unexpected CDW states in its T-phase.However,the CDW state of H-VTe_(2)has been barely reported.Here,we investigate the CDW states in monolayer(ML)H-VTe_(2),induced by phase-engineering from T-phase VTe_(2).The phase transition between T-and H-VTe_(2)is revealed with x-ray photoelectron spectroscopy(XPS)and scanning transmission electron microscopy(STEM)measurements.For H-VTe_(2),scanning tunneling microscope(STM)and low-energy electron diffraction(LEED)results show a robust 2√3×2√3CDW superlattice with a transition temperature above 450 K.Our findings provide a promising way for manipulating the CDWs in 2D materials and show great potential in its application of nanoelectronics.

Observation of multiple charge density wave phases in epitaxial monolayer 1T-VSe_(2) 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(■) CDW phase at low-temperature of 4 K in the epitaxial monolayer 1T-VSe_(2) 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 △_(1) and△_(2). The gap part ?1 that closes around ~ 150 K is accompanied with the vanish of the(√7×√3) CDW phase. While another momentum-dependent gap part △_(2) 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 △_(1) +△_(2), which suggests different forming mechanisms between the(√7×√3) and the incommensurate CDW phases. Our findings provide significant information and deep understandings on the CDW phases in monolayer 1T-VSe_(2) film as a two-dimensional(2D) material.

Tunable charge density wave in TiS3 nanoribbons

Recently, modifications of charge density wave（CDW） in two-dimensional（2D） show intriguing properties in quasi-2D materials such as layered transition metal dichalcogenides（TMDCs）. Optical, electrical transport measurements and scanning tunneling microscopy uncover the enormous difference on the many-body states when the thickness is reduced down to monolayer. However, the CDW in quasi-one-dimensional（1D） materials like transition metal trichalcogenides（TMTCs） is yet to be explored in low dimension whose mechanism is likely distinct from their quasi-2D counterparts.Here, we report a systematic study on the CDW properties of titanium trisulfide（TiS3）. Two phase transition temperatures were observed to decrease from 53 K（103 K） to 46 K（85 K） for the bulk and 〈 15-nm thick nanoribbon, respectively,which arises from the increased fluctuation effect across the chain in the nanoribbon structure, thereby destroying the CDW coherence. It also suggests a strong anisotropy of CDW states in quasi-1D TMTCs which is different from that in TMDCs.Remarkably, by using back gate of-30 V ～ 70 V in 15-nm device, we can tune the second transition temperature from110 K（at-30 V） to 93 K（at 70 V） owing to the altered electron concentration. Finally, the optical approach through the impinging of laser beams on the sample surface is exploited to manipulate the CDW transition, where the melting of the CDW states shows a strong dependence on the excitation energy. Our results demonstrate TiS3 as a promising quasi-1D CDW material and open up a new window for the study of collective phases in TMTCs.

Effect of strain on charge density wave order inα-U

The effect of strain on charge density wave(CDW)order inα-U is investigated within the framework of relativistic density-functional theory.The energetical stability ofα-U with CDW distortion is enhanced by the tensile strain along a and b axes,which is similar to the case of negative pressure and normal.However,the tensile strain along c axis suppresses the energetical stability of CDW phase.This abnormal effect could be understood from the emergence of a new onedimensional atomic chain along c axis inα-U.Furthermore,this effect is supported by the calculations of Fermi surface and phonon mode,in which the topological objects and the dynamical instability show opposite behaviors between strains along a/b and c axes.

Structural and electrical transport properties of charge density wave material LaAgSb_(2)under high pressure

Layered lanthanum silver antimonide LaAgSb_(2)exhibits both charge density wave(CDW)order and Dirac-cone-like band structure at ambient pressure.Here,we systematically investigate the pressure evolution of structural and electronic properties of LaAgSb_(2)single crystal.We show that the CDW order is destabilized under compression,as evidenced by the gradual suppression of magnetoresistance.At P_(C)~22 GPa,synchrotron x-ray diffraction and Raman scattering measurements reveal a structural modification at room-temperature.Meanwhile,the sign change of the Hall coefficient is observed at 5 K.Our results demonstrate the tunability of CDW order in the pressurized LaAgSb_(2)single crystal,which can be helpful for its potential applications in the next-generation devices.

Evidence of spin density wave of CeOs_4Sb_(12)

Elastic neutron diffraction measurements were performed on single crystals to study the ground state below the mysterious exotic transition temperature 0.86 K. An antiferromagnetic order with a tiny moment of 0.027 μB per formula is formed as the ground state for CeOs4Sb12 below the transition point. Our neutron data gives the evidence of spin density wave state for CeOs4Sb12 in this work.

Glucose detection in a highly scattering medium with diffuse photon-pair density wave

We propose a novel optical method for glucose measurement based on difuse photon-pair density wave(DPPDW)in a multiple scattering medium(MSM)where the light scattering of photon-pair is induced by refractive index mismatch between scatters and phantom solution.Experi-mentally,the DPPDW propagates in MSM via a two frequency laser(TFL)beam wherein highly correlated pairs of linear polarized photons are generated.The reduced scattering coefficientμ2s and absorption coefficientμ2a of DPPDW are measured simultaneously in terms of the amplitude and phase measurements of the detected heterodyne signal under arrangement at different dis-tances between the source and detection fibers in MSM.The results show that the sensitivity of glucose detection via glucose-induced change of reduced scattering coefficient(δμ′2)is 0.049%mM^(-1)in a 1%intralipid solution.In addition,the linear range ofδμ′2s vs glucose concentration implies that this DPPDW method can be used to monitor glucose concentration continuously and noninvasively subcutaneously.

The density wave in a new anisotropic continuum model

In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries （KdV） equation, and the soliton solution is derived.

Density wave and topological superconductivity in the magic-angle-twisted bilayer-graphene

The model dependence in the study of the magic-angle twisted bilayer-graphene(MA-TBG)is an important issue in the research area.It has been argued previously that the two-band tight-binding(TB)model(per spin and valley)cannot serve as a start point for succeeding studies as it cannot correctly describe the topological aspect of the continuumtheory model near the Dirac nodes in the mini Brillouin zone(MBZ).For this purpose,we adopt the faithful TB model[Phys.Rev.B 99195455(2019)]with five bands(per spin and valley)as our start point,which is further equipped with extended Hubbard interactions.Then after systematic random-phase-approximation(RPA)based calculations,we study the electron instabilities of this model,including the density wave(DW)and superconductivity(SC),near the van Hove singularity(VHS).Our results are as follows.In the case neglecting the tiny inter-valley exchange interaction,the exact SU(2)K×SU(2)K symmetry leads to the degeneracy between the inter-valley charge DW(CDW)and the spin DW(SDW)(which would be mixed then),and that between the singlet d+id-wave and triplet p+ip-wave topological SCs.When a realistic tiny inter-valley exchange interaction is turned on with nonzero coefficient(J_H=0),the SDW or CDW is favored respectively at the critical point,determined by JH→0-or JH→0+.In the mean time,the degeneracy between the singlet d+id-wave and triplet p+ip-wave topological SCs is also lifted up by the tiny JH.These results are highly similar to the results of our previous study[arXiv:2003.09513]adopting the two-band TB model,with the reason lying in that both models share the same symmetry and Fermi-surface(FS)nesting character near the VHS.Such a similarity suggests that the low-energy physics of the doped MA-TBG is mainly determined by the symmetry and the shape of the FS of the doped system,and is insensitive to other details of the band structure,including the topological aspects near the Dirac nodes in the MBZ.

Thermodynamic Properties of the Charge density wave Transition in Potasium Blue Brone

Thermodynamic properties of the charge density wave(CDW) transition in potassium blue bronze K 0.3 MoO 3 are investigated by the measurement of specific heat. A second order phase transition is observed at 177.5 K. The specific heat jump, and enthalpy and entropy changes associated with the transition are estimated. The results suggest that the lattice plays an important role in thermodynamics for this compound. Analysis of the data near CDW transition shows that width of critical region is about 6 K and the critical behavior belongs to the universality class of the three dimensional XY model.

Competition of Quantum Anomalous Hall States and Charge Density Wave in a Correlated Topological Model

We investigate the topological phase transition driven by non-local electronic correlations in a realistic quantum anomalous Hall model consisting of d_(xy)–d_(x^(2)-y^(2)) orbitals. Three topologically distinct phases defined in the noninteracting limit evolve to different charge density wave phases under correlations. Two conspicuous conclusions were obtained: The topological phase transition does not involve gap-closing and the dynamical fluctuations significantly suppress the charge order favored by the next nearest neighbor interaction. Our study sheds light on the stability of topological phase under electronic correlations, and we demonstrate a positive role played by dynamical fluctuations that is distinct to all previous studies on correlated topological states.

Annealing-induced long-range charge density wave order in magnetic kagome FeGe:Fluctuations and disordered structure

Charge density wave(CDW) in kagome materials with the geometric frustration is able to carry unconventional characteristics.Recently, a CDW has been observed below the antiferromagnetic order in kagome FeGe, in which magnetism and CDW are intertwined to form an emergent quantum ground state. However, the CDW is only short-ranged and the structural modulation originating from it has yet to be determined experimentally. Here we realize a long-range CDW order by post-annealing process,and resolve the structure model through single crystal X-ray diffraction. Occupational disorder of Ge resulting from short-range CDW correlations above T_(CDW) is identified from structure refinements. The partial dimerization of Ge along the c axis is unveiled to be the dominant distortion for the CDW. Occupational disorder of Ge is also proved to exist in the CDW phase due to the random selection of partially dimerized Ge sites. Our work provides useful insights for understanding the unconventional nature of the CDW in FeGe.

Encoding innumerable charge density waves of FeGe into polymorphs of LiFe_(6)Ge_(6)

Kagome metals exhibit rich quantum states by the intertwining of lattice,charge,orbital and spin degrees of freedom.Recently,a novel charge density wave(CDW)ground state was discovered in kagome magnet FeGe and was revealed to be driven by lowering magnetic energy via large Ge1-dimerization.Here,based on DFTcalculations,we show that such mechanism will yield infinitely many metastable CDWs in FeGe due to different ways to arrange the Ge1-dimerization in enlarged superstructures.Intriguingly,utilizing these metastable CDWs,innumerable polymorphs of kagome magnet LiFe_(6)Ge_(6) can be stabilized by filling Li atoms in the voids right above/below the dimerized Ge1-sites in the CDW superstructures.Such polymorphs are very stable due to the presence of magnetic-energy-saving mechanism,in sharp contrast to the non-magnetic“166”kagome compounds.In this way,a one-to-one mapping of the metastable CDWs of FeGe to stable polymorphs of LiFe_(6)Ge_(6) is established.On one hand,the fingerprints of these metastable CDWs,i.e.,the induced in-plane atomic distortions and band gaps,are encoded into the corresponding stable polymorphs of LiFe_(6)Ge_(6),such that further study of their properties becomes possible.On the other hand,such innumerable polymorphs of LiFe_(6)Ge_(6) offer great degrees of freedom to explore the rich physics of magnetic kagome metals.We thus reveal a novel connection between the unusually abundant CDWs and structural polymorphism in magnetic kagome materials,and establish a new route to obtain structural polymorphism on top of CDW states.

Imaging momentum-space Cooper pair formation and its competition with the charge density wave gap in a kagome superconductor

The superconducting ground state of kagome metals AV_(3)Sb_(5)(where A stands for K,Rb,or Cs)emerges from an exotic charge density wave(CDW)state that potentially breaks both rotational and time reversal symmetries.However,the specifics of the Cooper pairing mechanism,and the nature of the interplay between these two states remain elusive,largely due to the lack of momentum-space(k-space)superconducting energy gap structure.By implementing Bogoliubov quasiparticle interference(B QPI)imaging,we obtain k-space information on the multiband superconducting gap structureΔ_(SC)^(i)(k)in pristine CsV_(3)Sb_(5).We show that the estimated energy gap on the vanadium d_(xy/x^(2)-y^(2))orbital is anisotropic but nodeless,with a minimal value located near the M point.Interestingly,a comparison ofΔ_(SC)^(i)(k)with the CDW gapΔ_(CDW)^(i)(k)obtained by angle-re solved photoemission spectro scopy(ARPES)reveals direct k-space competition between the se two order parameters,i.e.,the opening of a large(small)CDW gap at a given momentum corresponds to a small(large)superconducting gap.When the long-range CDW order is suppressed by replacing vanadium with titanium,we find a nearly isotropic energy gap on both the V and Sb bands.This information will be critical for identifying the microscopic pairing mechanism and its interplay with intertwined electro nic orders in this kagome superconductor family.