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Abstract FeSe_1−xS_xremains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe_1−xS_xwithx > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe_0.81S_0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates. 

Charge order has been a central focus in the study of cuprate high-temperature superconductors due to its intriguing yet not fully understood connection to superconductivity. Recent advances in resonant inelastic x-ray scattering (RIXS) in the soft x-ray regime have enabled the first momentum-resolved studies ofdynamiccharge order correlations in the cuprates. This progress has opened a window for a more nuanced investigation into the mechanisms behind the formation of charge order (CO) correlations. This review provides an overview of RIXS-based measurements of dynamic CO correlations in various cuprate materials. It specifically focuses on electron-doped cuprates and Bi-based hole-doped cuprates, where the CO-related RIXS signals may reveal signatures of the effective Coulomb interactions. This aims to explore a connection between two central phenomena in the cuprates: strong Coulomb correlations and CO-forming tendencies. Finally, we discuss current open questions and potential directions for future RIXS studies as the technique continues to improve and mature, along with other probes of dynamic correlations that would provide a more comprehensive picture. 

Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over theq_x-q_yscattering plane in underdoped Bi₂Sr₂CaCu₂O_8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in theq_x-q_yscattering plane with radius equal to the magnitude of the charge order wave vector,q_CO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [q_x= ±q_CO,q_y= 0] and [q_x= 0,q_y= ±q_CO]) as the origin of the observed correlations. 

Ultrafast resonant soft x-ray scattering is used to monitor the dynamics of the charge density wave order in YBa 2 Cu 3 O 6+x .