The momentum dependence of the superconducting gap in the cuprates has been debated, with most experiments reporting a deviation from a simple $d_{x^2-y^2}$ form in the underdoped regime and a few experiments claiming that a simple $d_{x^2-y^2}$ form
persists down to the lowest dopings. We affirm that the superconducting gap function in sufficiently underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ (Bi-2212) deviates from a simple textit{d}-wave form near the antinode. This is observed in samples where doping is controlled only by oxygen annealing, in contrast to claims that this effect is only seen in cation-substituted samples. Moreover, a quasiparticle peak is present at the antinode down to p$=$0.08, refuting claims that a deviation from a simple textit{d}-wave form is a data analysis artifact stemming from difficulty in assessing a gap in the absence of a quasiparticle.
High-temperature superconductivity (HTSC) mysteriously emerges upon doping holes or electrons into insulating copper oxides with antiferromagnetic (AFM) order. It has been thought that the large energy scale of magnetic excitations, compared to phono
n energies for example, lies at the heart of an electronically-driven superconducting phase at high temperatures. However, despite extensive studies, little information is available for comparison of high-energy magnetic excitations of hole- and electron-doped superconductors to assess a possible correlation with the respective superconducting transition temperatures. Here, we use resonant inelastic x-ray scattering (RIXS) at the Cu L3-edge to reveal high-energy collective excitations in the archetype electron-doped cuprate Nd2-xCexCuO4 (NCCO). Surprisingly, despite the fact that the spin stiffness is zero and the AFM correlations are short-ranged, magnetic excitations harden significantly across the AFM-HTSC phase boundary, in stark contrast with the hole-doped cuprates. Furthermore, we find an unexpected and highly dispersive mode in superconducting NCCO that is undetected in the hole-doped compounds, which emanates from the zone center with a characteristic energy comparable to the pseudogap, and may signal a quantum phase distinct from superconductivity. The uncovered asymmetry in the high-energy collective excitations with respect to hole and electron doping provides additional constraints for modeling the HTSC cuprates.
Using time-dependent Ginzburg-Landau theory, we study the role of amplitude and phase fluctuations in the recovery of charge and spin stripe phases in response to a pump pulse that melts the orders. For parameters relevant to the case where charge or
der precedes spin order thermodynamically, amplitude recovery governs the initial time scales, while phase recovery controls behavior at longer times. In addition to these intrinsic effects, there is a longer spin re-orientation time scale related to the scattering geometry that dominates the recovery of the spin phase. Coupling between the charge and spin orders locks the amplitude and similarly the phase recovery, reducing the number of distinct time scales. Our results well reproduce the major experimental features of pump-probe x-ray diffraction measurements on the striped nickelate La$_{1.75}$Sr$_{0.25}$NiO$_4$. They highlight the main idea of this work, which is the use of time-dependent Ginzburg-Landau theory to study systems with multiple coexisting order parameters.
We investigate the order parameter dynamics of the stripe-ordered nickelate, La$_{1.75}$Sr$_{0.25}$NiO$_4$, using time-resolved resonant X-ray diffraction. In spite of distinct spin and charge energy scales, the two order parameters amplitude dynamic
s are found to be linked together due to strong coupling. Additionally, the vector nature of the spin sector introduces a longer re-orientation time scale which is absent in the charge sector. These findings demonstrate that the correlation linking the symmetry-broken states does not unbind during the non-equilibrium process, and the time scales are not necessarily associated with the characteristic energy scales of individual degrees of freedom.
High resolution resonant inelastic x-ray scattering has been performed to reveal the role of lattice-coupling in a family of quasi-1D insulating cuprates, Ca$_{2+5x}$Y$_{2-5x}$Cu$_5$O$_{10}$. Site-dependent low energy excitations arising from progres
sive emissions of a 70 meV lattice vibrational mode are resolved for the first time, providing a direct measurement of electron-lattice coupling strength. We show that such electron-lattice coupling causes doping-dependent distortions of the Cu-O-Cu bond angle, which sets the intra-chain spin exchange interactions. Our results indicate that the lattice degrees of freedom are fully integrated into the electronic behavior in low dimensional systems.
The dynamics of an order parameters amplitude and phase determines the collective behaviour of novel states emerged in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of its ability to measure material properties at
atomic and electronic time scales and create excited states not accessible by the conventional means can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here, combining time-resolved femotosecond optical and resonant x-ray diffraction measurements on striped La1.75Sr0.25NiO4, we reveal unforeseen photo-induced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, unlike thermal phase fluctuations near the critical temperature in equilibrium10. Importantly, relaxation of the phase fluctuations are found to be an order of magnitude slower than that of the order parameters amplitude fluctuations, and thus limit charge order recovery. This discovery of new aspect to phase fluctuation provides more holistic view for the importance of phase in ordering phenomena of quantum matter.
We performed resonant soft X-ray diffraction on known charge density wave (CDW) compounds, rare earth tri-tellurides. Near the $M_5$ (3d - 4f) absorption edge of rare earth ions, an intense diffraction peak is detected at a wavevector identical to th
at of CDW state hosted on Te$_2$ planes, indicating a CDW-induced modulation on the rare earth ions. Surprisingly, the temperature dependence of the diffraction peak intensity demonstrates an exponential increase at low temperatures, vastly different than that of the CDW order parameter. Assuming 4f multiplet splitting due to the CDW states,we present a model to calculate X-ray absorption spectrum and resonant profile of the diffraction peak, agreeing well with experimental observations. Our results demonstrate a situation where the temperature dependence of resonant X-ray diffraction peak intensity is not directly related to the intrinsic behavior of the order parameter associated with the electronic order, but is dominated by the thermal occupancy of the valence states.
Recent laser angle-resolved photoemission spectroscopy studies have established the presence of a new kink in the low-energy nodal dispersion of Bi$_2$Sr$_2$CaCu$_2$O$+{8+delta}$ (Bi-2212). The energy scale (~8-15 meV) of this kink appears below the
maximum of the superconducting gap $delta_0$. Therefore it is difficult to interpret this feature in terms of the usual coupling to a sharp dispersionless mode. In this paper we examine electron-phonon coupling to the in-plane acoustic phonon branch arising from the modulation of the screened Coulomb potential. We demonstrate that such a coupling has a strong forward scattering peak, and as a consequence, a kink occurs in the dispersion at an energy scale shifted by the local gap $delta(k)$. In addition, considerations for the reduction of screening with underdoping naturally explains the observed doping dependence of the low-energy kink. These results point to a strong coupling to the acoustic branch which is peaked in the forward scattering direction and has important implications for transport and pairing in the high-T$_c$ cuprates.
We present angle-resolved photoemission spectroscopy (ARPES) studies of the cuprate high-temperature superconductors which elucidate the relation between superconductivity and the pseudogap and highlight low-energy quasiparticle dynamics in the super
conducting state. Our experiments suggest that the pseudogap and superconducting gap represent distinct states, which coexist below T$_c$. Studies on Bi-2212 demonstrate that the near-nodal and near-antinodal regions behave differently as a function of temperature and doping, implying that different orders dominate in different momentum-space regions. However, the ubiquity of sharp quasiparticles all around the Fermi surface in Bi-2212 indicates that superconductivity extends into the momentum-space region dominated by the pseudogap, revealing subtlety in this dichotomy. In Bi-2201, the temperature dependence of antinodal spectra reveals particle-hole asymmetry and anomalous spectral broadening, which may constrain the explanation for the pseudogap. Recognizing that electron-boson coupling is an important aspect of cuprate physics, we close with a discussion of the multiple kinks in the nodal dispersion. Understanding these may be important to establishing which excitations are important to superconductivity.
The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal
dispersion of Bi2Sr2CaCu2O8+d (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is non-universal, in contrast to assumed phenomenology. This is used together with laser-ARPES measurements of the gap velocity, v2, to resolve discrepancies with thermal conductivity measurements.
