Crossover of Charge Fluctuations across the Strange Metal Phase Diagram

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Crossover of Charge Fluctuations across the Strange Metal Phase Diagram

Ali A. Husain, Matteo Mitrano, Melinda S. Rak, Samantha Rubeck, Bruno Uchoa, Katia March, Christian Dwyer, John Schneeloch, Ruidan Zhong, G. D. Gu, and Peter Abbamonte

Phys. Rev. X 9, 041062 – Published 26 December 2019

Abstract

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, 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 et al., Proc. Natl. Acad. Sci. U.S.A. 115, 5392 (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 toward 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.

Received 11 March 2019
Revised 20 October 2019

DOI:https://doi.org/10.1103/PhysRevX.9.041062

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quasiparticles & collective excitations

Cuprates Strongly correlated systems

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ali A. Husain ^1,*, Matteo Mitrano ¹, Melinda S. Rak ¹, Samantha Rubeck¹, Bruno Uchoa², Katia March³, Christian Dwyer³, John Schneeloch⁴, Ruidan Zhong ⁴, G. D. Gu⁴, and Peter Abbamonte^1,†

¹Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73069, USA
³Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
⁴Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA

^*ahusain6@illinois.edu
^†abbamonte@mrl.illinois.edu

Popular Summary

A crowning achievement of condensed-matter physics is the Fermi-liquid theory of metals. It reduces the incredibly complicated problem of $10^{23}$ interacting electrons to a simple model of weakly interacting electron quasiparticles plus some collective oscillations, called plasmons, which are sound waves in the electron fluid. While this paradigm is widely successful for simple metals, it fails to describe the enigmatic “strange metal” phase found in many strongly correlated quantum materials. Because of its ubiquity in correlated systems ranging from hard metallic oxides to soft organics, understanding the strange metal has become one of the great unsolved problems in condensed-matter physics. To help address this problem, we investigate how plasmons behave in strange metals by directly measuring charge fluctuations in a prototypical sample.

We rely on the newly developed technique of momentum-resolved inelastic electron scattering to measure charge fluctuations in a strange metal at a variety of temperatures and doping strengths. We find that in the strange metal phase, this material lacks a well-defined plasmon excitation but instead exhibits a highly damped continuum of excitations that is featureless in both energy and momentum. This observation strikingly contrasts with conventional metals, in which plasmon excitations are well defined. Outside of the strange metal regime, the continuum is highly structured and temperature dependent because of many-body effects that remain to be understood.

Our study suggests that a momentum-independent continuum of charge fluctuations is the defining fingerprint of the strange metal state, providing a crucial observable to test microscopic theories aiming to describe this enigmatic phase of matter.

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Vol. 9, Iss. 4 — October - December 2019

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Figure 1
$χ^{''} (q, ω)$ at room temperature (RT, or 300 K) (a)–(d) and low temperature (LT, either 100 K or 115 K) (e)–(h) for all four dopings studied. All momenta are measured in reciprocal lattice units and are oriented along the $(1, - 1)$ direction. No significant $q$ dependence is seen for any doping or temperature. At 300 K, the spectra vary only slightly with doping, compared to the dramatic doping dependence below approximately 0.5 eV at low temperature.
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Figure 2
Collapse of $Π^{''} (q, ω)$ for all momenta for each of the four doping values studied, achieved simply by dividing by $q^{2}$ . All momenta are measured in reciprocal lattice units. The spectra are taken at $T = 100 K$ except for the OD50K sample, which is measured at 115 K. Apart from the $q^{2}$ scaling of the magnitude, which is required by the $f$ -sum rule, the spectra are essentially momentum independent.
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Figure 3
(a)–(d) Temperature dependence of $χ^{''} (q^{*} = 0.24 r . l . u ., ω)$ for each doping level studied. Note that the energy axis is plotted on a log scale to emphasize the spectral weight change below 0.5 eV. (e) Doping and temperature dependence of the spectral weight change $ξ$ , as defined in the main text to be the spectral weight between 0.1 and 0.5 eV referenced to optimal doping at 150 K. The crossover from spectral weight accumulation to depletion with doping is evident, as is the sign reversal at optimal doping.
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Figure 4
Evolution of the MEELS continuum spectral weight across the Bi-2212 phase diagram, which is constructed from the data in Refs. [18, 19, 44, 45]. Here, $AFM = antiferromagnet$ , $SC = superconductor$ , $PG = pseudogap$ , $FL = Fermi liquid$ , and $SM = strange metal$ . The colored points represent the spectral weight change $ξ$ in Fig. 3. $ξ$ is small throughout the SM region in which the continuum remains featureless. Outside the SM, the continuum spectral weight changes rapidly with a different sign in the underdoped and overdoped regimes.
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Figure 5
$V_{fit} (q)$ determined by minimizing Eq. (a1) for OD50K and the subsequent fit using Eq. (3), obtaining a proportionality constant of $(7.9 \pm 0.3) \times 10^{3} eV \cdot Å^{2}$ . Vertical error bars reflect statistical fitting uncertainties, while horizontal error bars reflect the momentum resolution of the MEELS instrument of $0.03 Å^{- 1}$ . For reference, curves evaluated with $d = 13 Å$ and $d = 19 Å$ are also shown.
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Figure 6
Comparison of MEELS and transmission STEM EELS of OP91K Bi-2212 at 300 K. The raw STEM EELS spectrum is shown in gray, and the antisymmetrized spectrum is shown in orange. The MEELS spectrum in red is taken at a momentum transfer of 0.5 r.l.u. (inset). Phase-contrast TEM image of the sample region investigated, showing the Bi-2212 supermodulation with wavelength $λ \approx 26 Å$ , verifying the structural integrity of the sample used in STEM EELS measurements.
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