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Register a new userReply to arXiv:2103.10268 `Comment on Crossover of Charge Fluctuations across the Strange Metal Phase Diagram
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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.
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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.
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.
In a comment on arXiv:1006.5070v1, Drechsler et al. present new band-structure calculations suggesting that the frustrated ferromagnetic spin-1/2 chain LiCuVO4 should be described by a strong rather than weak ferromagnetic nearest-neighbor interaction, in contradiction with their previous calculations. In our reply, we show that their new results are at odds with the observed magnetic structure, that their analysis of the static susceptibility neglects important contributions, and that their criticism of the spin-wave analysis of the bound-state dispersion is unfounded. We further show that their new exact diagonalization results reinforce our conclusion on the existence of a four-spinon continuum in LiCuVO4, see Enderle et al., Phys. Rev. Lett. 104 (2010) 237207.
In a comment on arXiv:1006.5070v2, Drechsler et al. claim that the frustrated ferromagnetic spin-1/2 chain LiCuVO4 should be described by a strong rather than weak ferromagnetic nearest-neighbor interaction, in contradiction with their previous work. Their comment is based on DMRG and ED calculations of the magnetization curve and the magnetic excitations. We show that their parameters are at odds with the magnetic susceptibility and the magnetic excitation spectrum, once intensities are taken into account, and that the magnetization curve cannot discriminate between largely different parameter sets within experimental uncertainties. We further show that their new exact diagonalization results support the validity of the RPA-approach, and strongly reinforce our conclusion on the existence of a four-spinon continuum in LiCuVO4, see Enderle et al., Phys. Rev. Lett. 104 (2010) 237207.
We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined by L. Isaev, G. Ortiz, and J. Dukelsky, arXiv:1003.5205, are misplaced.
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