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Reply to arXiv:2103.10268 `Comment on "Crossover of Charge Fluctuations across the Strange Metal Phase Diagram'''
Authors:
Ali Husain,
Matteo Mitrano,
Melinda S. Rak,
Samantha Rubeck,
Bruno Uchoa,
Katia March,
Christian Dwyer,
John Schneeloch,
Ruidan Zhong,
Genda D. Gu,
Peter Abbamonte
Abstract:
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 $q\lesssim$ 0.12 r.l.u., but found that it does not persist to large $q$. For…
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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 $q\lesssim$ 0.12 r.l.u., but found that it does not persist to large $q$. For $q\gtrsim0.12$ 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 author's own transmission EELS measurements with $\sim$100 meV resolution from the early 1990's [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 author's Comment is in contradiction with known information from the literature. At $q\lesssim0.12$ 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 $q\gtrsim0.12$ 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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Submitted 10 June, 2021; v1 submitted 6 June, 2021;
originally announced June 2021.
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Observation of Pines' Demon in Sr$_2$RuO$_4$
Authors:
A. A. Husain,
E. W. Huang,
M. Mitrano,
M. S. Rak,
S. I. Rubeck,
X. Guo,
H. Yang,
C. Sow,
Y. Maeno,
B. Uchoa,
T. C. Chiang,
P. E. Batson,
P. W. Phillips,
P. Abbamonte
Abstract:
The characteristic excitation of a metal is its plasmon, which is a quantized collective oscillation of its electron density. In 1956, David Pines predicted that a distinct type of plasmon, dubbed a "demon," could exist in three-dimensional metals containing more than one species of charge carrier. Consisting of out-of-phase movement of electrons in different bands, demons are acoustic, electrical…
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The characteristic excitation of a metal is its plasmon, which is a quantized collective oscillation of its electron density. In 1956, David Pines predicted that a distinct type of plasmon, dubbed a "demon," could exist in three-dimensional metals containing more than one species of charge carrier. Consisting of out-of-phase movement of electrons in different bands, demons are acoustic, electrically neutral, and do not couple to light, so have never been detected in an equilibrium, three-dimensional metal. Nevertheless, demons are believed to be critical for diverse phenomena including phase transitions in mixed-valence semimetals, optical properties of metal nanoparticles, "soundarons" in Weyl semimetals, and high temperature superconductivity in, for example, metal hydrides. Here, we present evidence for a demon in Sr$_2$RuO$_4$ from momentum-resolved electron energy-loss spectroscopy (M-EELS). Formed of electrons in the $β$ and $γ$ bands, the demon is gapless with a room temperature velocity $v=1.065 \pm 0.12 \times 10^5$ m/s and critical momentum $q_c=0.08$ reciprocal lattice units. Its spectral weight violates low-energy partial sum rules, affirming its neutral character. Our study confirms a 66-year old prediction and suggests that demons may be a pervasive feature of multiband metals.
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Submitted 27 May, 2022; v1 submitted 13 July, 2020;
originally announced July 2020.
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Crossover of Charge Fluctuations across the Strange Metal Phase Diagram
Authors:
A. A. Husain,
M. Mitrano,
M. S. Rak,
S. I. Rubeck,
B. Uchoa,
J. Schneeloch,
R. Zhong,
G. D. Gu,
P. Abbamonte
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 (M-EELS) we recently showed that, rather than a plasmon…
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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.
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Submitted 11 November, 2019; v1 submitted 10 March, 2019;
originally announced March 2019.
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Anomalous density fluctuations in a strange metal
Authors:
M. Mitrano,
A. A. Husain,
S. Vig,
A. Kogar,
M. S. Rak,
S. I. Rubeck,
J. Schmalian,
B. Uchoa,
J. Schneeloch,
R. Zhong,
G. D. Gu,
P. Abbamonte
Abstract:
A central mystery in high temperature superconductivity is the origin of the so-called "strange metal," i.e., the anomalous conductor from which superconductivity emerges at low temperature. Measuring the dynamic charge response of the copper-oxides, $χ''(q,ω)$, would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with meV re…
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A central mystery in high temperature superconductivity is the origin of the so-called "strange metal," i.e., the anomalous conductor from which superconductivity emerges at low temperature. Measuring the dynamic charge response of the copper-oxides, $χ''(q,ω)$, would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with meV resolution. Here, we present the first measurement of $χ''(q,ω)$ for a cuprate, optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ ($T_c=91$ K), using momentum-resolved inelastic electron scattering. In the medium energy range 0.1-2 eV relevant to the strange metal, the spectra are dominated by a featureless, temperature- and momentum-independent continuum persisting to the eV energy scale. This continuum displays a simple power law form, exhibiting $q^2$ behavior at low energy and $q^2/ω^2$ behavior at high energy. Measurements of an overdoped crystal ($T_c=50$ K) showed the emergence of a gap-like feature at low temperature, indicating deviation from power law form outside the strange metal regime. Our study suggests the strange metal exhibits a new type of charge dynamics in which excitations are local to such a degree that space and time axes are decoupled.
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Submitted 14 May, 2018; v1 submitted 6 August, 2017;
originally announced August 2017.
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Signatures of exciton condensation in a transition metal dichalcogenide
Authors:
Anshul Kogar,
Melinda S. Rak,
Sean Vig,
Ali A. Husain,
Felix Flicker,
Young Il Joe,
Luc Venema,
Greg J. MacDougall,
Tai C. Chiang,
Eduardo Fradkin,
Jasper van Wezel,
Peter Abbamonte
Abstract:
Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed momentum-resolved electron energy-loss spectroscopy (M-EELS), we study electronic collective mode…
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Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed momentum-resolved electron energy-loss spectroscopy (M-EELS), we study electronic collective modes in the transition metal dichalcogenide semimetal, 1T-TiSe$_2$. Near the phase transition temperature, T$_c$ = 190 K, the energy of the electronic mode falls to zero at nonzero momentum, indicating dynamical slowing down of plasma fluctuations and crystallization of the valence electrons into an exciton condensate. Our study provides compelling evidence for exciton condensation in a three-dimensional solid and establishes M-EELS as a versatile technique sensitive to valence band excitations in quantum materials.
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Submitted 15 January, 2018; v1 submitted 13 November, 2016;
originally announced November 2016.
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Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)
Authors:
Sean Vig,
Anshul Kogar,
Matteo Mitrano,
Ali A. Husain,
Vivek Mishra,
Melinda S. Rak,
Luc Venema,
Peter D. Johnson,
Genda D. Gu,
Eduardo Fradkin,
Michael R. Norman,
Peter Abbamonte
Abstract:
One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, $χ({\bf q},ω)$. The imaginary part, $χ''({\bf q},ω)$, defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. $χ$ quantifies the electronic compressibility of a material, its response to ext…
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One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, $χ({\bf q},ω)$. The imaginary part, $χ''({\bf q},ω)$, defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. $χ$ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a fully momentum-resolved means to measure $χ({\bf q},ω)$ at the meV energy scale relevant to modern elecronic materials. Here, we demonstrate a way to measure $χ$ with quantitative momentum resolution by applying alignment techniques from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, which we refer to here as "M-EELS," allows direct measurement of $χ''({\bf q},ω)$ with meV resolution while controlling the momentum with an accuracy better than a percent of a typical Brillouin zone. We apply this technique to finite-q excitations in the optimally-doped high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale and with full momentum control.
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Submitted 12 September, 2017; v1 submitted 14 September, 2015;
originally announced September 2015.