X-ray techniques have been used for more than a century to study the atomic and electronic structure in virtually any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional x-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom -- charge, orbital, spin, and lattice -- paved the way for the emergence and success of resonant x-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. Here we review the recent resonant x-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order -- a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the milestones in the development of resonant x-ray scattering, as well as the basic theoretical formalism underlying its unique capabilities. The rest of the review will focus on the recent contributions of resonant scattering to the tremendous advancements in our description and understanding of charge order. To conclude, we propose a series of present and upcoming challenges, and discuss the future outlook for this technique.
We investigate resonant inelastic X-ray scattering (RIXS) at the O $K$-edge in insulating cuprates by means of three methods: cluster perturbation theory (CPT), Hartree--Fock approximation (HFA) and exact diagonalization (ED) method. We consider the three-band Hubbard model and show the overall momentum-dependence of the Zhang--Rice singlet (ZRS) excitation and charge-transfer excitation by the CPT combining with the perturbation scheme. A comparison of the RIXS spectra calculated using CPT and HFA reveals different momentum-dependencies through the changes in the properties of the upper Hubba…
High Tc superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic X-ray scattering (RIXS) to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors [La2-xSrxCuO4 (LSCO) and Bi2Sr1.6La0.4CuO6+d (Bi2201)], crucially completing t…
Collective nature of spin excitations in superconducting cuprates probed by resonant inelastic x-ray scattering
利用共振非弹性X射线散射（RIXS）技术，研究了高温超导体YBa_2Cu_3 O_（6 +x）在宽掺杂范围（0.1 < x < 1）内的色散自旋激发。当入射光子能量从共振条件失谐时，仔细监测激发分布，发现自旋激发能对所有x都与失谐无关。这些发现表明，掺杂铜氧化物中自旋翻转RIXS分布的最大部分来自磁集体模式，而不是最近理论上提出的非相干粒子-空穴激发[Benjamin等人，Phys. Rev. Lett. 112，247002（2014）]。在铜酸盐的电子系统的理论描述的影响进行了讨论。
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-…
Resonant Inelastic X-ray Scattering (RIXS) Spectra for Ladder Cuprates
梯状化合物Sr $_{14}$ Cu $_{24}$ O $_{41}$作为超导铜氧化物的准一维类似物和当Sr被Ca取代时作为其自身的超导体都是令人感兴趣的。为了模拟该化合物的共振非弹性X射线散射（RIXS）谱，我们研究了较简单的SrCu $_{2}$ O $_{3}$体系，该体系的晶体结构包含非常相似的梯形平面。我们用只含Cu的两带紧束缚模型近似计算了SrCu $_{2}$ O $_{3}$的LDA色散.强关联效应被纳入反铁磁基态的假设。角分辨光电子能谱（ARPES）和RIXS的梯形化合物的数据被发现是在合理的符合我们的理论预测。
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。
Explaining the mechanism of superconductivity in the high-$T_c$ cuprates requires an understanding of what causes electrons to form Cooper pairs. Pairing can be mediated by phonons, the screened Coulomb force, spin or charge fluctuations, excitons, or by a combination of these. An excitonic pairing mechanism has been postulated, but experimental evidence for coupling between conduction electrons and excitons in the cuprates is sporadic. Here we use resonant inelastic x-ray scattering (RIXS) to monitor the temperature dependence of the $\underline{d}d$ exciton spectrum of Bi$_2$Sr$_2$CaCu$_2$O$…
Bimagnon studies in cuprates with Resonant Inelastic X-ray Scattering at the O K edge. I - An assessment on La2CuO4 and a comparison with the excitation at Cu L3 and Cu K edges
We theoretically analyze the intensity of the resonant inelastic X-ray scattering (RIXS) based on Ansatz that the electron is fractionalized into two components. By fitting the angle resolved photoemission spectroscopy (ARPES) data of a cuprate high-$T_{\rm c}$ superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ and the accompanied machine learning results obtained before by Yamaji {\it et al.} (arXiv:1903.08060), we determine the paprameters of the two-component fermion model which describes the electron fractionalization. The RIXS spectra are predicted by using this description. We find that the in…
Charge order has now been observed in several cuprate high-temperature superconductors. We report a resonant inelastic x-ray scattering experiment on the electron-doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_4$ that demonstrates the existence of dynamic correlations at the charge order wave vector. Upon cooling we observe a softening in the electronic response, which has been predicted to occur for a d-wave charge order in electron-doped cuprates. At low temperatures, the energy range of these excitations coincides with that of the dispersive magnetic modes known as paramagnons. Furthermore, measureme…
One of the key issues in unraveling the mystery of high Tc superconductivity in the cuprates is to understand the normal state outside the superconducting dome. Here we perform scanning tunneling microscopy and spectroscopy measurements on a heavily overdoped, non-superconducting (Bi,Pb)2Sr2CuO6+x cuprate. Spectroscopic imaging reveals dispersive quasiparticle interferences and the Fourier transforms uncover the evolution of momentum space topology. More interestingly, we observe nanoscale patches of static charge order with sqrt(2)*sqrt(2) periodicity. Both the dispersive quasiparticle interf…
