Superconductivity and unconventional density waves in vanadium-based kagome materials AV3Sb5

Recently, the discovery of vanadium-based kagome metal AV₃Sb₅ (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 AV₃Sb₅. 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 AV₃Sb₅. 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.     

Pressure tuning of the anomalous Hall effect in the kagome superconductor CsV3Sb5

Controlling the anomalous Hall effect(AHE)inspires potential applications of quantum materials in the next generation of electronics.The recently discovered quasi-2D kagome superconductor CsV₃Sb₅ exhibits large AHE accompanying with the charge-density-wave(CDW)order which provides us an ideal platform to study the interplay among nontrivial band topology,CDW,and unconventional superconductivity.Here,we systematically investigated the pressure effect of the AHE in CsV₃Sb₅.Our high-pressure transport measurements confirm the concurrence of AHE and CDW in the compressed CsV₃Sb₅.Remarkably,distinct from the negative AHE at ambient pressure,a positive anomalous Hall resistivity sets in below 35 K with pressure around 0.75 GPa,which can be attributed to the Fermi surface reconstruction and/or Fermi energy shift in the new CDW phase under pressure.Our work indicates that the anomalous Hall effect in CsV₃Sb₅ is tunable and highly related to the band structure.     

Tri-hexagonal charge order in kagome metal CsV3Sb5 revealed by 121Sb nuclear quadrupole resonance

We report ¹²¹Sb nuclear quadrupole resonance(NQR)measurements on kagome superconductor CsV₃Sb₅ with Tc=2.5 K.¹²¹Sb NQR spectra split after a charge density wave(CDW)transition at 94 K,which demonstrates a commensurate CDW state.The coexistence of the high temperature phase and the CDW phase between 91 K and 94 K manifests that it is a first order phase transition.The CDW order exhibits tri-hexagonal deformation with a lateral shift between the adjacent kagome layers,which is consistent with 2×2×2 superlattice modulation.The superconducting state coexists with CDW order and shows a conventional s-wave behavior in the bulk state.     

Evolution of superconductivity and charge order in pressurized RbV3Sb5

The kagome metals AV₃Sb₅(A=K,Rb,Cs)under ambient pressure exhibit an unusual charge order,from which superconductivity emerges.In this work,by applying hydrostatic pressure using a liquid pressure medium and carrying out electrical resistance measurements for RbV₃Sb₅,we find that the charge order becomes suppressed under a modest pressure pc(1.4 GPa3Sb₅.Our findings point to qualitatively similar temperature-pressure phase diagrams in KV₃Sb₅ and RbV₃Sb₅,{and suggest a close link}between the second superconducting dome and the high-pressure resistance anomalies.     

Surface-induced orbital-selective band reconstruction in kagome superconductor CsV3Sb5

The two-dimensional (2D) kagome superconductor CsV₃Sb₅ has attracted much recent attention due to the coexistence of superconductivity, charge orders, topology and kagome physics, which manifest themselves as distinct electronic structures in both bulk and surface states of the material. An interesting next step is to manipulate the electronic states in this system. Here, we report angle-resolved photoemission spectroscopy (ARPES) evidence for a surface-induced orbital-selective band reconstruction in CsV₃Sb₅. A significant energy shift of the electron-like band around Γ and a moderate energy shift of the hole-like band around M are observed as a function of time. This evolution is reproduced in a much shorter time scale by in-situ annealing of the CsV₃Sb₅ sample. Orbital-resolved density functional theory (DFT) calculations reveal that the momentum-dependent band reconstruction is associated with different orbitals for the bands around Γ and M, and the time-dependent evolution points to the change of sample surface that is likely caused by the formation of Cs vacancies on the surface. Our results indicate the possibility of orbital-selective control of the band structure via surface modification, which may open a new avenue for manipulating exotic phenomena in this material system, including superconductivity.     

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.     

(2+1)维Korteweg-de Vries方程的复合波解及局域激发

借助Maple符号计算软件,利用Pdccati方程(ζ′=a_0+a_1ζ+a_2ζ~2)展开法和变量分离法,得到了(2+1)维Korteweg-de Vries方程(KdV)包含q=C_1x+C_2y+C_3t+R(x,y,t)的复合波解,根据得到的孤立波解,构造出KdV方程新颖的复合波裂变和复合波湮灭等局域激发结构。     

Phase slippage at the interface: normal metal/sliding charge-density wave

Phase slippage is required at the current electrodes of quasi-one-dimensional conductors with a charge density wave (CDW) ground state for the conversion from free to condensed carriers. We have performed at the ESRF high-resolution X-ray measurements of the spatially varying shift q(x) of the CDW satellite wave vector between current contacts on a thin NbSe₃ whisker in the sliding state. Applying direct currents, we observe at 90 K a steep exponential decrease of the shift within a few hundred microns from the contact. The CDW strain profile q(x) reflects the carrier conversion process, via nucleation and growth of phase-dislocation loops. Pulsed current measurements of the shift q show important differences between pulsed and dc current data, revealing a spatially dependent relaxational behaviour of the CDW strain. Using time-resolved high spatial resolution X-ray we observe at 300 μm from the electrode a stretched exponential-type decay of the shift q(t) upon switching off the current (T=75 K): q(t)=q₀[exp(−t/τ)^μ] with τ=23 ms and μ=0.36.     

Measurement of the slope parameter for the neutral pion spectrum in KL → πππ decay

The π⁰ spectrum in the K_L⁰ → 3π decay was measured using a wire chambers magnetic spectrometer. In the usual approximation, the matrix element can be expressed as: M² ≈ 1 + 2a₀(M_K/M_π²)(2T_π⁰−T_π⁰max) + a₁(M_K²/M_π⁴)(2T_π⁰−T_π⁰max)². We obtained a₀ = −0.282 ± 0.011 and a₁ consistent with zero.     

高次柱面反射型太阳能聚光镜的光学设计

提出了一种新型高效太阳能聚光镜, 这种聚光镜用一组特定系数, a₂, a₄, a₆, a₈, a₁₀, a₁₂, a₁₄, a₁₆ 与 C的高次柱面内壁的一部分作为反射镜. 利用高次柱面方程和光反射定律, 推导出了在高次柱面内壁上太阳反射光束的方向矢量与高次柱面系数C, a₂,a₄, a₆, a₈, a₁₀, a₁₂, a₁₄, a₁₆的关系, 通过优化设计这些系数, 可以使入射到高次柱面内壁上的太阳光束反射后全部聚焦在一条与柱面母线平行的宽度很窄的线段上, 形成线聚光. 这组特定系数用粒子群优化算法求得, 并经计算机模拟证明其聚焦效果. 用这组特定系数的高次柱面作为聚光镜, 其对光的压缩比可达148倍, 其线性光斑可作为一种强光源或高温光源. 高次柱面反射镜可由金属或玻璃直接磨制而成, 也可由高次柱面骨架和铺设在骨架上的镀铝聚酯薄膜构成. 关键词： 太阳能聚光镜 高次柱面 多项式系数优化 线性聚焦     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

非晶锂离子导体B2O3-Li2O-LiCl一Al2O3中VO2+的电子自旋共振

两种非晶锂离子导体B₂O₃-0.7Li₂O-0.7LiCl-xAl₂O₃-0.1V₂O₅(x=0.05和0.15)的电子自旋共振谱研究表明:(i)ESR线型是高斯型,证实V₂O₅添加量适当;(ii)超精细结构来源于VO²⁺络离子,具有四角对称性,属C_4v群。越精细耦合张量的平行分量平均值A_//=0.0175cm^-1,垂直分量A_⊥=0.0063cm^-1。由g_//(g_⊥)求出其基态²B_2g与第一激发态²E_g的能级间距△₁=2.46×10⁴ cm^-1,基态与第二激发态²B_1g的能级间距△₂=3.03×10⁴ cm^-1;(iii)变温实验证实:Al₂O₃组分较少(x=0.05)的非晶ESR强度比x=0.15的非晶高3倍至2倍,而Al₂O₃组分越多则ESR强度随温升下降越小。     

Stability,electronic structure,and optical properties of lead-free perovskite monolayer Cs3B2X9(B=Sb,Bi;X=Cl,Br,I)and bilayer vertical heterostructure Cs3B2X9/Cs3B’2X9(B,B’=Sb,Bi;X=Cl,Br,I)

The lead-free perovskites Cs₃B₂X₉(B=Sb,Bi;X=Cl,Br,I)as the popular photoelectric materials have excellent optical properties with lower toxicity.In this study,we systematically investigate the stable monolayer Cs₃B₂X₉and bilayer vertical heterostructure Cs₃B₂X₉/Cs3B02X9(B,B0=Sb,Bi;X=Cl,Br,I)via first-principles simulations.By exploring the electrical structures and band edge positions,we find the band gap reduction and the band type transition in the heterostructure Cs₃B₂X₉/Cs3B02X9 due to the charge transfer between layers.Furthermore,the results of optical properties reveal light absorption from the visible light to UV region,especially monolayer Cs3Sb2I9 and heterostructure Cs3Sb2I9/Cs3Bi2I9,which have absorption peaks in the visible light region,leading to the possibility of photocatalytic water splitting.These results provide insights for more two-dimensional semiconductors applied in the optoelectronic and photocatalytic fields.     

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.     

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f₀ and a₀ resonances. The ππ → ππ, phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π⁰η and mass distributions in the T = 1 channel. Furthermore, the total and partial strong decay widths of the f₀ and a₀ resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below GeV.     

非金属二元氢化物分子振动固有频率与pKa常数的定量关系

提出了非金属二元氢化物分子振动固有频率的计算原理与方法.将基频和总频作为结构信息指数用于非金属二元氢化物的分子结构与pK_a常数的定量关系研究,结果表明,其相关系数大于0.995,得到的回归方程用于pK_a的计算,计算值与实验值比较,平均绝对误差小于1.82.     

Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

H3正三角形和H4正四面体结构的变分计算

采用改进排列通道量子力学(Modified Arrangement Channel Quantum Mechanics,简称MACQM)方法和变分法,计算了H₃体系正三角形和H₄体系的正四面体结构的能量曲线.当H₃体系原子核的间距R=1.74a₀,波函数变分参数α=1.03时,体系能量有最低值-1.58161 a.u.;当H₄体系原子核的间距R=1.60a₀,波函数变分参数α=1.07时,体系能量有最低值-2.28097 a.u.,这表明H₃体系的正三角形构型和H₄的正四面体结构是可以稳定存在的.     

非自治物质畸形波的传播操控

研究了(1+1)维的变系数Gross-Pitaevskii方程, 获得了该方程的精确畸形波解. 基于该精确畸形波解, 深入研究了非自治物质畸形波在随时间指数变化的相互作用下的传播动力学行为, 发现非自治畸形波除具有“来无影、去无踪”的不可预测特性外, 也可实现完全激发、抑制激发以及维持激发等操控. 研究表明, 畸形波操控的关键是对累积时间的最大值T_max 与峰值位置T₀ (或T_I,T_II)值大小关系的调节. 当T_max > T₀ (或T_I,T_II)时畸形波被快速地完全激发, 热原子团中的原子增加到凝聚体中. 当T_max = T₀ (或T_I,T_II) 时畸形波激发到最大振幅, 可以维持相当长的时间而不消失, 热原子团中的原子增加到凝聚体中. 当T_max < T₀ (或T_I,T_II)时畸形波没有充足的时间来激发而被抑制甚至消失, 凝聚体中的原子减少. 这些结果在理论和实际应用上具有启迪意义.