The $t$-$J$-$U$ model of high-$T_c$ copper-oxide superconductors incorporates both the on-site Coulomb repulsion and kinetic exchange interaction and yields a semi-quantitative description of the static properties of those materials. We extend this analysis to dynamic quantities and address collective spin- and charge excitations in the correlated metallic state of the $t$-$J$-$U$ model. We employ VWF+$1/\mathcal{N}_f$ approach that combines the variational wave function (VWF) approach with the expansion in the inverse number of fermionic flavors ($1/\mathcal{N}_f$). It is shown that the resonant (paramagnon) contribution to the dynamic magnetic susceptibility remains robust as one interpolates between the Hubbard- and $t$-$J$-model limits, whereas the incoherent continuum undergoes substantial renormalization. Energy of the collective charge mode diminishes as the strong-coupling limit is approached. We also introduce the concept of effective kinetic exchange interaction that allows for a unified interpretation of magnetic dynamics in the Hubbard, $t$-$J$, and $t$-$J$-$U$ models. The results are discussed in the context of recent resonant inelastic $x$-ray scattering experiments for the high-$T_c$ cuprates.
The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-…
We used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor YBa2Cu3O6+x over a wide range of doping levels (0.1 < x < 1). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all x. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rath…
The nature of the spin excitations in superconducting cuprates is a key question toward a unified understanding of the cuprate physics from long-range antiferromagnetism to superconductivity. The intense spin excitations up to the over-doped regime revealed by resonant inelastic X-ray scattering bring new insights as well as questions like how to understand their persistence or their relation to the collective excitations in ordered magnets (magnons). Here, we study the evolution of the spin excitations upon hole-doping the superconducting cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ by disentangling…
Recently resonant inelastic x-ray scattering experiments reported fine details of the charge excitations around the in-plane momentum ${\bf q}_{\parallel}=(0,0)$ for various doping rates in electron-doped cuprates ${\rm La_{2-x}Ce_xCuO_4}$. We find that those new experimental data are well captured by acoustic-like plasmon excitations in a microscopic study of the layered $t$-$J$ model with the long-range Coulomb interaction. The acoustic-like plasmon is not a usual plasmon typical to the two-dimensional system, but has a small gap proportional to the interlayer hopping $t_z$.
Resonant inelastic x-ray scattering (RIXS) tuned for the Cu L edge is a possible tool to detect charge excitations in cuprate superconductors. We theoretically investigate the possibility for observing a collective charge excitation by the RIXS. The RIXS process via the intermediate state inevitably makes the spectral weight of charge excitation stronger in electron doping than in hole doping. Electron-hole asymmetry also appears in the dynamical charge structure factor, showing a new enhanced small-momentum low-energy mode in electron doping. These facts indicate a possibility of detecting th…
A Unified Theory for the Cuprates, Iron-Based and Similar Superconducting Systems: Application for Spin and Charge Excitations in the Hole-Doped Cuprates
Superconductivity originates from the coupling between charge carriers and bosonic excitations of either phononic or electronic origin. Identifying the most relevant pairing glue is a key step towards a clear understanding of the unconventional superconductivity. Here, by applying the ultrafast optical spectroscopy on the electron-doped cuprates La$_{1.9}$Ce$_{0.1}$CuO$_{4\pmδ}$, we discern a bosonic mode of electronic origin that has the strongest coupling with the charge carriers near $T_c$. We argue that this mode is associated with the two-dimensional antiferromagnetic spin fluctuations, a…
Phenomenological theory of spin excitations in La- and Y-based cuprates
受最近镧基铜氧化物非弹性中子散射（INS）实验的启发，基于费米学理论，我们研究了镧基（例如，La $_{2-x}$ Sr $_x$ CuO $_4$）和Y基（例如，YBa $_2$ Cu $_3$ O $_y$）铜酸盐。在超导态下，YBa $_2$ Cu $_3$ O $_y$的自旋激发由频率为40 meV的尖锐共振峰控制。在共振频率以下和以上，不相称（IC）峰发展并且峰的强度急剧降低。在正常状态下，不发生共振激发，IC峰合并成相称的峰。La $_{2-x}$ Sr $_x$ CuO $_4$的自旋激发与Y基的有很大的不同，即由于超导能隙的减小和可能的自旋条纹有序的存在，不存在共振峰。光谱仅在预期的共振频率（约18毫电子伏）增强，而它仍然是不相称的。另一方面，在频率55 meV的另一个频率尺度也被揭示，即频谱是相称的，在这个频率的局部最大值。我们详细阐述了所有的结果的基础上的费米面拓扑结构和d波超导性，并建议自旋条纹顺序也是重要的，在决定的La基铜氧化物的自旋激发。给出了Y基和La基铜氧化物的自旋激发相干图。
Dispersive spin excitations in highly overdoped cuprates revealed by resonant inelastic x-ray scattering
利用共振非弹性X射线散射（RIXS）在铜$L$吸收边，我们已经观察到强烈的，分散的自旋激发在高度过掺杂的Tl $_2$ Ba $_2$ CuO $_{6+δ}$（超导$T_c =6$ K），一种化合物，其正常状态的电荷传输和热力学性质已被广泛研究，并显示出典型的费米液体行为。补充RIXS实验上稍过掺杂的Tl $_2$ Ba $_2$ CuO $_{6+δ}$（$T_c =89$ K）和Y $_{1-x}$ Ca $_{x}$ Ba $_2$ Cu $_3$ O $_{6+δ}$化合物跨越广泛的掺杂水平表明，这些激发表现出的能量和能量积分光谱权重密切类似的反铁磁振子在未掺杂的铜酸盐。令人惊讶的共存费米液体的电荷激发和高能量的自旋激发，让人想起反铁磁绝缘体在高度过掺杂的化合物提出了挑战，目前的理论模型的铜酸盐。
Recently it was reported experimentally that the monolayer graphene can be doped to beyond the Van Hove singularity. We study theoretically the possible superconductivity and the corresponding spin excitations of the monolayer graphene in this doping region. A static spin-density-wave state is favorable due to the nested Fermi surface as the Fermi level is doped to the Van Hove singularity point. Superconductivity may be realized upon further doping. The spin excitations in the superconducting state are studied theoretically based on the random phase approximation. The overall features are qua…
High temperature cuprate superconductors consist of stacked CuO2 planes, with primarily two dimensional electronic band structures and magnetic excitations, while superconducting coherence is three dimensional. This dichotomy highlights the importance of out-of-plane charge dynamics, believed to be incoherent in the normal state, yet lacking a comprehensive characterization in energy-momentum space. Here, we use resonant inelastic x-ray scattering (RIXS) with polarization analysis to uncover the pure charge character of a recently discovered collective mode in electron-doped cuprates. This mod…
We use neutron scattering to study magnetic excitations near the antiferromagnetic wave vector in the underdoped single-layer cuprate HgBa2CuO4+δ (superconducting transition temperature Tc ~ 88 K, pseudogap temperature T* ~ 220 K). The response is distinctly enhanced below T* and exhibits a Y-shaped dispersion in the pseudogap state, whereas the superconducting state features an X-shaped (hourglass) dispersion and a further resonance-like enhancement. A large spin gap of about 40 meV is observed in both states. This phenomenology is reminiscent of that exhibited by bilayer cuprates. The resona…
We propose that cuprate superconductors are in the vicinity of a spontaneous d-wave type Fermi surface symmetry breaking, often called a d-wave Pomeranchuk instability. This idea is explored by means of a comprehensive study of magnetic excitations within the slave-boson mean-field theory of the t-J model. We can naturally understand the pronounced xy anisotropy of magnetic excitations in untwinned YBa_{2}Cu_{3}O_{y} and the sizable change of incommensurability of magnetic excitations at the transition temperature to the low-temperature tetragonal lattice structure in La_{2-x}Ba_{x}CuO_{4}. In…
Unveiling the nature of collective charge excitations in a cuprate superconductor
The Chinese University of Hong Kong（香港中文大学）；Universität Zürich（苏黎世大学）；Diamond Light Source（钻石光源）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；KTH Royal Institute of Technology（瑞典皇家理工学院）；The University of Tokyo（东京大学）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；Institut Néel, CNRS and Université Grenoble Alpes（内尔研究所，法国国家科学研究中心与格勒诺布尔阿尔卑斯大学）
Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of compounds, there exists no information for structurally simple HgBa$_2$CuO$_{4+δ}$. Here we report neutron scattering results for HgBa$_2$CuO$_{4+δ}$ (superconducting transition temperature T$_c$ $\sim$ 71 K, pseudogap temperature T* $\sim$ 305 K) that demonstrate the absence of the two most prominent features of the magnetic excitation spectrum of t…
We use resonant inelastic x-ray scattering (RIXS) to probe the propagation of plasmons in the electron-doped cuprate superconductor Sr$_{0.9}$La$_{0.1}$CuO$_2$ (SLCO). We detect a plasmon gap of $\sim$~120 meV at the two-dimensional Brillouin zone center, indicating that low-energy plasmons in SLCO are not strictly acoustic. The plasmon dispersion, including the gap, is accurately captured by layered $t$-$J$-$V$ model calculations. A similar analysis performed on recent RIXS data from other cuprates suggests that the plasmon gap is generic and its size is related to the magnitude of the interl…
