Review article to be published in a special issues of Physica C on stripes. 35 pages, 30 figures, new version including corrections and additions throughout the text
Stripe order where electrons self-organize into alternating periodic charge-rich and magnetically-ordered charge-poor parallel lines was proposed as a way of optimizing the kinetic energy of holes in a doped Mott insulator. Static stripes detected as extra peaks in diffraction patterns, appear in a number of oxide perovskites as well as some other systems. The more controversial dynamic stripes, which are not detectable by diffraction, may be universally present in copper oxide superconductors. Thus it is important to learn how to detect dynamic stripes as well as to understand their influence on electronic properties. This review article focuses on lattice vibrations (phonons) that might show signatures of the charge component of dynamic stripes. The first part of the article describes recent progress in learning about how the phonon signatures of different types of electronic charge fluctuations including stripes can be distinguished from purely structural instabilities and from each other. Then I will focus on the evidence for dynamic stripes in the phonon spectra of copper oxide superconductors.
Comment on ``Magnetoresistance Anomalies in Antiferromagnetic YBa$_2$Cu$_3$O$_{6+x}$: Fingerprints of Charged Stripes''
在最近的一封信中，Ando等人（cond-mat/9905071）在空穴掺杂的反铁磁YBa $_2$ Cu $_3$ O $_{6+x}$中发现了异常磁阻（MR），他们将其归因于带电条纹，即，将孔分离成线。在这篇评论中，我们表明，这些实验虽然有趣，但并不能证明条纹的存在。在我们看来，异常行为是由于（a，b）平面的电阻率的各向异性在散装和磁场相关的反铁磁（AF）域结构。畴壁不太可能是带电的条纹。
Doped antiferromagnets host a vast array of physical properties and learning how to control them is one of the biggest challenges of condensed matter physics. La$_{1.7}$Sr$_{0.3}$NiO$_4$ (LSNO) is a classic example of such a material. At low temperatures holes introduced via substitution of La by Sr segregate into lines to form boundaries between magnetically ordered domains in the form of stripes. The stripes become dynamic at high temperatures, but LSNO remains insulating presumably because an interplay between magnetic correlations and electron-phonon coupling localizes charge carriers. Mag…
We report an ultrahigh resolution resonant inelastic x-ray scattering (RIXS) study of the in-plane bond-stretching phonon mode in stripe-ordered cuprate La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$. Phonon softening and lifetime shortening are found around the charge ordering wave vector. In addition to these self-energy effects, the electron-phonon coupling is probed by its proportionality to the RIXS cross section. We find an enhancement of the electron-phonon coupling around the charge-stripe ordering wave vector upon cooling into the low-temperature tetragonal structure phase. These results s…
Josephson plasma resonance and phonon anomalies in trilayer Bi_2Sr_2Ca_2Cu_3O_10 superconductor
用椭圆偏振法测量了Bi_（2223）晶体的远红外（FIR）c轴电导率。低于T $_c$，在500 cm $^{-1}$附近产生强吸收带，对应于横向约瑟夫森等离子体。FIR频谱权重的相关增加导致了对Ferrell-Glover-Tinkham求和规则的巨大违反。c轴动能的增加占凝结能的相当大的一部分。我们还观察到声子异常，这表明约瑟夫森电流导致了激烈的变化的局部电场内块的紧密间隔的CuO $_2$平面。
We measure the dispersion of the Cu-O bond-stretching phonon mode in the high-temperature superconducting parent compound Ca$_2$CuO$_2$Cl$_2$. Our density functional theory calculations predict a cosine-shaped bending of the dispersion along both the ($ξ$00) and ($ξξ$0) directions, while comparison with previous results on Ca$_{1.84}$CuO$_2$Cl$_2$ show it only along ($ξ$00), suggesting an anisotropic effect which is not reproduced in calculation at optimal doping. Comparison with isostructural La$_{2-x}$Sr$_x$CuO$_4$ suggests that these calculations reproduce well the overdoped regime, however…
Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relati…
Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon ($e$-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped singleband Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte…
Lattice-decoupled rotatable stripe-like charge order within the strange metal phase of 2M-WS2
State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；School of Materials Science and Engineering, Shanghai Jiao Tong University（上海交通大学材料科学与工程学院）；National Laboratory of Solid State Microstructures and School of Physics, Nanjing University（南京大学固体微结构物理国家级重点实验室和物理学院）；School of Materials Science and Engineering, Beihang University（北京航空航天大学材料科学与工程学院）；Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science（马普物质结构与动力学研究所自由电子激光科学中心）；State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Science（中国科学院上海硅酸盐研究所高性能陶瓷与超微结构国家重点实验室）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Southern University of Science and Technology（南方科技大学）；Hefei National Laboratory（合肥国家实验室）
We study the lattice dynamics of iron superconductor FeSe, and address the fundamental question of how important is proper description of fluctuating magnetic moments in metallic systems for phonon dispersion and phonon density of states. We show that Density Functional Theory (DFT)+ embedded Dynamical Mean-Field Theory (eDMFT) functional approach, which truly captures the fluctuating local moments, largely eliminates the deficiency of DFT for description of lattice dynamics in correlated metallic systems, and predicts phonon dispersion and phonon density of states in very good agreement with …
Following previous works reporting an anomalous behavior of several zone-center optical phonons across the magnetic transition of square lattice iridates Sr2IrO4 and Sr3Ir2O7, we have investigated the lattice dynamics as a function of momentum in these materials by means of high-resolution inelastic x-ray scattering (IXS). The observed phonon energies and scattering intensities across the Brillouin zone are in excellent agreement with ab-initio lattice dynamical calculations based on non-magnetic density-functional-perturbation theory (DFPT). Our results do not evidence any renormalization of …
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $α$-RuCl3 using inelastic X-ray scattering with meV resolut…
We present an ab initio approach for the calculation of phonon self-energies and their fluctuation diagnostics, which allows us to identify the electronic processes behind phonon anomalies. Application to the transition-metal-dichalcogenide monolayer 1H-TaS$_2$ reveals that coupling between the longitudinal-acoustic phonons and the electrons from an isolated low-energy metallic band is entirely responsible for phonon anomalies such as the mode softening and associated charge-density waves observed in this material. Our analysis allows us to distinguish between different mode-softening mechanis…
Charge density waves (CDWs) are ubiquitous in under-doped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate under-doped Bi$_2$Sr$_{1.4}$La$_{0.6}$CuO$_{6+δ}$ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and …
The detailed temperature dependence of the infrared-active mode in Fe$_{1.03}$Te ($T_N\simeq 68$ K) and Fe$_{1.13}$Te ($T_N\simeq 56$ K) has been examined, and the position, width, strength, and asymmetry parameter determined using an asymmetric Fano profile superimposed on an electronic background. In both materials the frequency of the mode increases as the temperature is reduced; however, there is also a slight asymmetry in the line shape, indicating that the mode is coupled to either spin or charge excitations. Below $T_N$ there is an anomalous decrease in frequency and the mode shows litt…
We performed optical studies on CaFeAsF single crystals, a parent compound of the 1111-type iron-based superconductors that undergoes a structural phase transition from tetragonal to orthorhombic at $T_s$ = 121 K and a magnetic one to a spin density wave (SDW) state at $T_N$ = 110 K. In the low temperature optical conductivity spectrum, after the subtraction of a narrow Drude peak, we observe a pronounced singularity around 300 cm$^{-1}$ that separates two regions of quasilinear conductivity. We outline that these characteristic absorption features are signatures of Dirac fermions, similar to …
Giant phonon anomalies in the pseudo-gap phase of TiOCl
本文报道了自旋为1/2的量子磁体TiOCl的红外和拉曼光谱结果。在声子谱的温度依赖性中发现了巨大的异常，这暗示了电子自由度与晶格的不寻常耦合。这些异常发展在一个广泛的温度间隔，这表明存在一个扩展的波动制度。这定义了一个伪能隙相，其特征在于局部自旋能隙。在100 K以下，维度交叉导致二聚基态，自旋能隙约为2 $Δ_{spin}\approx$ ~430 K.
Scalable Simulation of Strongly Correlated Electron-Phonon Systems via Non-Gaussian Matrix Product States
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Polarization- and temperature-dependent Raman data along with theoretical simulations are presented for the Kagome ferromagnet Fe_3Sn_2. Eight out of nine expected phonon modes were identified. The experimental energies compare well with those from the simulations. The analysis of the line widths indicates relatively strong phonon-phonon coupling in the range 0.1 to 1. The temperature-dependent frequencies of three A_{1g} modes show weak anomalies at approximately 100 K. In contrast, the linewidths of all phonon modes follow the conventional exponential broadening up to room temperature except…
The origin of the low-temperature ferromagnetic instability in YTiO3 driven by the interplay between lattice, orbital, spin, and charge degrees of freedom is on the background of lattice dynamics. We present a comprehensive study of temperature-dependent polarized Raman scattering in a nearly stoichiometric orthorhombic YTiO3 single crystal. The lattice-dynamics calculations authenticate the assignment for the observed Ag- and B2g-symmetry modes in terms of the atoms vibrational patterns. The obtained results suggest that trigonal GdFeO3-type distortions become unstable against tetragonal Jahn…
Temperature-dependent reflectivity studies on the non-magnetic kagome metal RbV$_3$Sb$_5$ in a broad energy range (50 cm$^{-1}$ $-$ 20000 cm$^{-1}$, equivalent to 6 meV $-$ 2.5 eV) down to 10 K are reported. Below $T_{\rm CDW}=102$ K, the optical spectra demonstrate a prominent spectral-weight transfer from low to higher energies as the fingerprint of the charge-density wave (CDW) formation with the opening of a partial gap. A detailed analysis reveals two energy scales of, respectively, $\sim$ 800 cm$^{-1}$ (100 meV) and 360 cm$^{-1}$ (45 meV), the latter visible below 50 K only. Additionally…
Bulk charge density waves are now reported in nearly all high-temperature superconducting cuprates, with the noticeable exception of one particular family: the copper oxychlorides. Here, we used resonant inelastic X-ray scattering to reveal a bulk charge density waves in these materials. Combining resonant inelastic X-ray scattering with non-resonant inelastic X-ray scattering, we investigate the interplay between the lattice excitations and the charge density wave, and evidence the phonon anomalies of the Cu-O bond-stretching mode at the charge density wave wave-vector. We propose that such e…
We investigate the crystal structure and lattice vibrations of Sr$_2$IrO$_4$ by a combined phonon Raman scattering and x-ray powder diffraction experiment under pressures up to $66$ GPa and room temperature. Density functional theory (DFT) and $ab$-initio lattice dynamics calculations were also carried out. A first-order structural phase transition associated with an $8$ % collapse of the $c$-axis is observed at high pressures, with phase coexistence being observed between $\sim 40$ and $55$ GPa. At lower pressures, lattice and phonon anomalies were observed, reflecting crossovers between isos…
MnV$_2$O$_4$ in the spinel structure is known to exhibit coupled orbital and spin ordering, and its Raman spectra show interesting anomalies in its low-temperature phase. With a goal to explain this behavior involving coupled spins and phonons, we determine here the spin-phonon couplings in MnV$_2$O$_4$ from a theoretical analysis of its phonon spectra and their dependence on spin-ordering and electron correlations, obtained from first-principles density functional theoretical calculations. Using these in an analysis based on a Landau-like theory, we uncover the mechanism governing the Raman a…
The ability to probe symmetry breaking transitions on their natural time scales is one of the key challenges in nonequilibrium physics. Stripe ordering represents an intriguing type of broken symmetry, where complex interactions result in atomic-scale lines of charge and spin density. Although phonon anomalies and periodic distortions attest the importance of electron-phonon coupling in the formation of stripe phases, a direct time-domain view of vibrational symmetry breaking is lacking. We report experiments that track the transient multi-THz response of the model stripe compound La$_{1.75}$S…
Fe$^{3+}$ $S = 5/2$ ions form saw-tooth like chains along the $a$ axis of the oxo-selenite Fe$_2$O(SeO$_3$)$_2$ and an onset of long-range magnetic order is observed for temperatures below $T_C = 105$ K. This order leads to distinct fingerprints in phonon mode linewidths and energies as resolved by Raman scattering. In addition, new excitations with small linewidths emerge below $T = 150$ K, and are assigned to two-magnon scattering processes with the participation of flat-band and high energy magnon branches. From this a set of exchange coupling constants is estimated. The specific ratio of t…
Magnetic spinels (with chemical formula $AX_{2}$O$_{4}$, with $X$ a 3$d$ transition metal ion) that also have an orbital degeneracy are Jahn-Teller active and hence possess a coupling between spin and lattice degrees of freedom. At high temperatures, MgV$_{2}$O$_{4}$ is a cubic spinel based on V$^{3+}$ ions with a spin $S$=1 and a triply degenerate orbital ground state. A structural transition occurs at T$_{OO}$=63 K to an orbitally ordered phase with a tetragonal unit cell followed by an antiferromagnetic transition of T$_{N}$=42 K on cooling. We apply neutron spectroscopy in single crystals …
Interplay of Spin and Lattice Degrees of Freedom in the Frustrated Antiferromagnet CdCr_2O_4: High-field and Temperature Induced Anomalies of the Elastic Constants
