Consistency between reflection M-EELS and optical spectroscopy measurements of the long-wavelength density response of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$

Jin Chen; Xuefei Guo; Christian Boyd; Simon Bettler; Caitlin Kengle; Dipanjan Chaudhuri; Farzaneh Hoveyda; Ali Husain; John Schneeloch; Genda Gu; Philip Phillips; Bruno Uchoa; Tai-Chang Chiang; Peter Abbamonte

arXiv · 2306.03681

Consistency between reflection M-EELS and optical spectroscopy measurements of the long-wavelength density response of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$

Jin Chen·Xuefei Guo·Christian Boyd·Simon Bettler·Caitlin Kengle·Dipanjan Chaudhuri·Farzaneh Hoveyda·Ali Husain·John Schneeloch·Genda Gu·Philip Phillips·Bruno Uchoa·Tai-Chang Chiang·Peter Abbamonte

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Abstract

The density fluctuation spectrum captures many fundamental properties of strange metals. Using momentum-resolved electron energy-loss spectroscopy (M-EELS), we recently showed that the density response of the strange metal Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212) at large momentum, $q$, exhibits a constant-in-frequency continuum [Mitrano, PNAS $\textbf{115}$, 5392 (2018); Husain, PRX $\textbf{9}$, 041062 (2019)] reminiscent of the marginal Fermi liquid (MFL) hypothesis of the late 1980s [Varma, PRL $\textbf{63}$, 1996 (1989)]. However, reconciling this observation with infrared (IR) optics experiments, which show a well-defined plasmon excitation at $q \sim 0$, has been challenging. Here we report M-EELS measurements of Bi-2212 using 4$\times$ improved momentum resolution, allowing us to reach the optical limit. For momenta $q<0.04$ r.l.u., the M-EELS data show a plasmon feature that is quantitatively consistent with IR optics. For $q>0.04$ r.l.u., the spectra become incoherent with an MFL-like, constant-in-frequency form. We speculate that, at finite frequency, $\omega$, and nonzero $q$, some attribute of this Planckian metal randomizes the probe electron, causing it to lose information about its own momentum.

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Jin Chen, Xuefei Guo, Christian Boyd, Simon Bettler, Caitlin Kengle, Dipanjan Chaudhuri, Farzaneh Hoveyda, Ali Husain, John Schneeloch, Genda Gu, Philip Phillips, Bruno Uchoa, Tai-Chang Chiang, Peter Abbamonte. 2023-06-06. Consistency between reflection M-EELS and optical spectroscopy measurements of the long-wavelength density response of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$. https://arxiv.org/abs/2306.03681

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