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We identify a new kind of elementary excitations, spin-rotons, in the doped Mott insulator. They play a central role in deciding the superconducting transition temperature Tc, resulting in a simple Tc formula,Tc=Eg/6, with Eg as the characteristic energy scale of the spin rotons. We show that the degenerate S=1 and S=0 rotons can be probed by neutron scattering and Raman scattering measurements, respectively, in good agreement with the magnetic resonancelike mode and the Raman A1g mode observed in the high-Tc cuprates.
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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 mode disperses along both the in- and, importantly, out-of-plane directions, revealing its three dimensional nature. The periodicity of the out-of-plane dispersion corresponds to the CuO2 plane distance rather than the crystallographic c-axis lattice constant, suggesting that the interplane Coulomb interaction drives the coherent out-of-plane charge dynamics. The observed properties are hallmarks of the long-sought acoustic plasmon, predicted for layered systems and argued to play a substantial role in mediating high temperature superconductivity.
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 phonon 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.
A resonant inelastic x-ray scattering (RIXS) study of overdamped spin-excitations in slightly underdoped La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) with $x=0.12$ and $0.145$ is presented. Three high-symmetry directions have been investigated: (1) the antinodal $(0,0)rightarrow (1/2,0)$, (2) the nodal $(0,0)rightarrow (1/4,1/4)$ and (3) the zone boundary direction $(1/2,0)rightarrow (1/4,1/4)$ connecting these two. The overdamped excitations exhibit strong dispersions along (1) and (3), whereas a much more modest dispersion is found along (2). This is in strong contrast to the undoped compound La$_{2}$CuO$_4$ (LCO) for which the strongest dispersions are found along (1) and (2). The $t-t^{prime}-t^{primeprime}-U$ Hubbard model used to explain the excitation spectrum of LCO predicts $-$ for constant $U/t$ $-$ that the dispersion along (3) scales with $(t^{prime}/t)^2$. However, the diagonal hopping $t^{prime}$ extracted on LSCO using single-band models is low ($t^{prime}/tsim-0.16$) and decreasing with doping. We therefore invoked a two-orbital ($d_{x^2-y^2}$ and $d_{z^2}$) model which implies that $t^{prime}$ is enhanced. This effect acts to enhance the zone-boundary dispersion within the Hubbard model. We thus conclude that hybridization of $d_{x^2-y^2}$ and $d_{z^2}$ states has a significant impact on the zone-boundary dispersion in LSCO.
Heavily electron-doped iron-selenide (HEDIS) high-transition-temperature (high-$T_{rm{c}}$) superconductors, which have no hole Fermi pockets, but have a notably high $T_{rm{c}}$, have challenged the prevailing $s$$_pm$ pairing scenario originally proposed for iron pnictides containing both electron and hole pockets. The microscopic mechanism underlying the enhanced superconductivity in HEDIS remains unclear. Here, we used neutron scattering to study the spin excitations of the HEDIS material Li$_{0.8}$Fe$_{0.2}$ODFeSe ($T_{rm{c}}$ = 41 K). Our data revealed nearly ring-shaped magnetic resonant excitations surrounding ($pi$, $pi$) at $sim$ 21 meV. As the energy increased, the spin excitations assumed a diamond shape, and they dispersed outward until the energy reached $sim$ 60 meV and then inward at higher energies. The observed energy-dependent momentum structure and twisted dispersion of spin excitations near ($pi$, $pi$) are analogous to those of hole-doped cuprates in several aspects, thus implying that such spin excitations are essential for the remarkably high $T_{rm{c}}$ in these materials.
The origin of the exceptionally strong superconductivity of cuprates remains a subject of debate after more than two decades of investigation. Here we follow a new lead: The onset temperature for superconductivity scales with the strength of the anomalous normal-state scattering that makes the resistivity linear in temperature. The same correlation between linear resistivity and Tc is found in organic superconductors, for which pairing is known to come from fluctuations of a nearby antiferromagnetic phase, and in pnictide superconductors, for which an antiferromagnetic scenario is also likely. In the cuprates, the question is whether the pseudogap phase plays the corresponding role, with its fluctuations responsible for pairing and scattering. We review recent studies that shed light on this phase - its boundary, its quantum critical point, and its broken symmetries. The emerging picture is that of a phase with spin-density-wave order and fluctuations, in broad analogy with organic, pnictide, and heavy-fermion superconductors.
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