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Joerg Fink
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In a recent paper by Husain et al. [PRX 9, 041062 (2019)], the two-particle electronic excitations in Bi2Sr2CaCu2O8+x have been studied by Electron Energy-Loss Spectroscopy in reflection (R-EELS) in the strange metal range between underdoped and overdoped materials. The authors conclude that there are no well defined plasmons. Rather they obtain a momentum-independent continuum which they discuss in terms of holographic theories. In this Comment it is pointed out that the experimental results are in stark contrast to previous EELS in transmission (T-EELS), Resonant Inelastic X-ray Scattering (RIXS), and optical studies. The differences can be probably explained by an inaccurate momentum scale in the R-EELS experiments. Furthermore, it is shown, that many material specific experimental results from T-EELS, R-EELS, RIXS, and optical spectroscopy can be explained by a more traditional extended Lindhard model. This model describes the energy, the width, and the dispersion of normal and acoustic plasmons in cuprates, as well as the continuum. The latter is explained by electron-hole excitations inside a lifetime broadened conduction band. This continuum is directly related to the scattering rates of the charge carriers, which in turn, by a feed back process, lead to the continuum.
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A normal metal exhibits a valence plasmon, which is a sound wave in its conduction electron density. The mysterious strange metal is characterized by non-Boltzmann transport and violates most fundamental Fermi liquid scaling laws. A fundamental question is: Do strange metals have plasmons? Using momentum-resolved inelastic electron scattering (M-EELS) we recently showed that, rather than a plasmon, optimally-doped Bi$_{2.1}$Sr$_{1.9}$Ca$_{1.0}$Cu$_{2.0}$O$_{8+x}$ (Bi-2212) exhibits a featureless, temperature-independent continuum with a power-law form over most energy and momentum scales [M. Mitrano, PNAS 115, 5392-5396 (2018)]. Here, we show that this continuum is present throughout the fan-shaped, strange metal region of the phase diagram. Outside this region, dramatic changes in spectral weight are observed: In underdoped samples, spectral weight up to 0.5 eV is enhanced at low temperature, biasing the system towards a charge order instability. The situation is reversed in the overdoped case, where spectral weight is strongly suppressed at low temperature, increasing quasiparticle coherence in this regime. Optimal doping corresponds to the boundary between these two opposite behaviors at which the response is temperature-independent. Our study suggests that plasmons do not exist as well-defined excitations in Bi-2212, and that a featureless continuum is a defining property of the strange metal, which is connected to a peculiar crossover where the spectral weight change undergoes a sign reversal.
We recently reported [1,2] measurements of the charge density fluctuations in the strange metal cuprate Bi$_{2.1}$Sr$_{1.9}$Ca$_{1.0}$Cu$_{2.0}$O$_{8+x}$ using both reflection M-EELS and transmission EELS with $leq$10 meV energy resolution. We observed the well-known 1 eV plasmon in this material for momentum $qlesssim$ 0.12 r.l.u., but found that it does not persist to large $q$. For $qgtrsim0.12$ r.l.u., we observe a frequency-independent continuum, similar to that observed in early Raman scattering experiments [3,4], that correlates highly with the strange metal phase [2]. In his Comment (arXiv:2103.10268), Joerg Fink claims we do not see the plasmon, and that our results are inconsistent with optics, RIXS, and the authors own transmission EELS measurements with $sim$100 meV resolution from the early 1990s [5,6]. The author claims we have made a trigonometry error and are measuring a larger momentum than we think. The author asserts that the two-particle excitations of cuprate strange metals are accurately described by weakly interacting band theory in RPA with corrections for conduction band carrier lifetimes and Umklapp effects. Here, we show that the authors Comment is in contradiction with known information from the literature. At $qlesssim0.12$ r.l.u. we see the same 1 eV plasmon as other techniques. Moreover we compute our momentum correctly, adjusting the sample and detector angles during an energy scan to keep $q$ fixed. The only discrepancy is between our data and the results of Ref. [5] for $qgtrsim0.12$ r.l.u. where, because of the coarse resolution used, the data had to be corrected for interference from the elastic line. A reexamination of these corrections in early transmission EELS measurements would likely shed light on this discrepancy.
Besides the mechanism responsible for high critical temperature superconductivity, the grand unresolved issue of the cuprates is the occurrence of a strange metallic state above the so-called pseudogap temperature $T^*$. Even though such state has been successfully described within a phenomenological scheme, the so-called Marginal Fermi-Liquid theory, a microscopic explanation is still missing. However, recent resonant X-ray scattering experiments identified a new class of charge density fluctuations characterized by low characteristic energies and short correlation lengths, which are related to the well-known charge density waves. These fluctuations are present over a wide region of the temperature-vs-doping phase diagram and extend well above $T^*$. Here we investigate the consequences of charge density fluctuations on the electron and transport properties and find that they can explain the strange metal phenomenology. Therefore, charge density fluctuations are likely the long-sought microscopic mechanism underlying the peculiarities of the metallic state of cuprates.
In hole-doped cuprates there is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstruction of the Fermi surface. In $YBa_2Cu_3O_y$ charge order emerges in two steps: a 2D order found at zero field and at high temperature inside the pseudogap phase, and a 3D order that is superimposed below the superconducting transition $T_c$ when superconductivity is weakened by a magnetic field. Several issues still need to be addressed such as the effect of disorder, the relationship between those charge orders and their respective impact on the Fermi surface. Here, we report high magnetic field sound velocity measurements of the 3D charge order in underdoped $YBa_2Cu_3O_y$ in a large doping range. We found that the 3D charge order exists over the same doping range as its 2D counterpart, indicating an intimate connection between the two distinct orders. Moreover, we argue that the Fermi surface is reconstructed above the onset temperature of 3D charge order.
We have studied the influence of disorder induced by electron irradiation on the normal state resistivities $rho(T)$ of optimally and underdoped YBa2CuOx single crystals, using pulsed magnetic fields up to 60T to completely restore the normal state. We evidence that point defect disorder induces low T upturns of rho(T) which saturate in some cases at low T in large applied fields as would be expected for a Kondo-like magnetic response. Moreover the magnitude of the upturns is related to the residual resistivity, that is to the concentration of defects and/or their nanoscale morphology. These upturns are found quantitatively identical to those reported in lower Tc cuprates, which establishes the importance of disorder in these supposedly pure compounds. We therefore propose a realistic phase diagram of the cuprates, including disorder, in which the superconducting state might reach the antiferromagnetic phase in the clean limit.
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