Unusual Dynamic Charge Correlations in Simple-Tetragonal ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$

Open Access

Unusual Dynamic Charge Correlations in Simple-Tetragonal ${HgBa}_{2} {CuO}_{4 + δ}$

B. Yu, W. Tabis, I. Bialo, F. Yakhou, N. B. Brookes, Z. Anderson, Y. Tang, G. Yu, and M. Greven

Phys. Rev. X 10, 021059 – Published 16 June 2020

Abstract

The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved charge correlations are still in their infancy. Such information is crucial in order to help discern the connection between CDW and pseudogap phenomena, and to understand the extent to which charge correlations in general shape the phase diagram. We report a resonant inelastic x-ray scattering study of the underdoped cuprate superconductor ${HgBa}_{2} {CuO}_{4 + δ}$ ( $T_{c} = 70 K$ ). At 250 K, above the previously established temperature $T_{CDW} \approx 200 K$ that signifies the onset of quasistatic short-range CDW order, we observe significant dynamic correlations that are broadly peaked at about 40 meV and centered at the two-dimensional wave vector $q_{CDW}$ . This energy scale is comparable to both the superconducting gap and the low-energy pseudogap. At 70 K, we observe a quasistatic CDW peak at $q_{CDW}$ , but the dynamic correlations around 40 meV remain virtually unchanged, and we identify a new feature: dynamic correlations well above the optic phonon range that are broadly peaked in the 150–200 meV range. A similar energy scale was previously identified in other experiments as a high-energy pseudogap. The observation of three distinct features in the charge response is highly unusual for a CDW system and suggests that charge order in the cuprates is complex. We demonstrate that other single-layer cuprates exhibit approximately the same relative strength of high- to low-temperature energy-integrated charge signal, which points to the universal existence of significant dynamic correlations. Intriguingly, the two energy scales identified here are also comparable to those of the superconducting glue function extracted from other spectroscopic techniques, consistent with a dual charge and magnetic nature of the pairing glue. We further determine the paramagnon dispersion along [1, 0], across $q_{CDW}$ , and find it to be consistent with magnetic excitations measured by inelastic neutron scattering. Unlike for some other cuprates, our result points to the absence of a discernible coupling between charge and magnetic excitations.

Received 4 July 2019
Revised 13 April 2020
Accepted 29 April 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021059

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)

Charge order Pseudogap Superconductivity

Cuprates

Resonant inelastic x-ray scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

B. Yu¹, W. Tabis ^1,2,3, I. Bialo ^2,3, F. Yakhou⁴, N. B. Brookes⁴, Z. Anderson ¹, Y. Tang¹, G. Yu¹, and M. Greven¹

¹School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
²Institute of Solid State Physics, TU Wien, 1040 Vienna, Austria
³AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, 30-059 Krakow, Poland
⁴European Synchrotron Radiation Facility, 71 Avenue de Martyrs, CS40220, F-38043 Grenoble Cedex 9, France

Popular Summary

Unraveling the connection between superconductivity, patterns of charge organization, and partial energy gaps in the cuprates is a major thrust in quantum materials research. The elusive superconducting pairing glue might be associated with dynamic charge correlations, which are fluctuations of the electronic density, but momentum- and energy-resolved measurements with the required energy resolution have not been possible until recently. Here, we report one of the first resonant inelastic x-ray scattering studies of cuprate charge dynamics with meaningful energy resolution to resolve such correlations.

We study Hg-Ba-Cu-O, arguably the best model system among the hundreds of cuprate compounds because of its high structural symmetry and high optimal superconducting transition temperature of nearly 100 K. In addition to the well-known static charge modulation, we find an unexpected large charge-fluctuation scale, which provides comprehensive insight into the electronic properties of the cuprates by connecting these new findings to a range of prior observations regarding the pseudogap phenomenon and superconducting pairing. Our results are broadly consistent with a recent phenomenological model for the cuprates.

Key Image

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 10, Iss. 2 — April - June 2020

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Hg1201 phase diagram ( $p > 0.04$ ), extrapolated to $p = 0$ based on results for other cuprates [1]. Solid blue line, doping dependence of the superconducting (SC) transition temperature $T_{c} (p)$ [39]. Dark gray region, deviation (not to scale) of $T_{c} (p)$ from estimated parabolic dependence (dashed blue line). $T_{N}$ , Néel temperature, marking the transition to antiferromagnetic (AF) order. $T^{*}$ , pseudogap (PG) temperature, estimated from deviation from strange-metal (SM) $T$ -linear resistivity [40, 41]. $T^{* *}$ , temperature below which Fermi-liquid (FL) behavior is clearly observed in the PG state [40, 41, 42, 43]. $T_{RXD}$ , onset of short-range CDW correlations estimated from RXS [9, 19]. $T_{OPT}$ , characteristic temperature observed in time-resolved optical reflectivity [44]. $T_{RIXS}$ , temperatures at which the Hg1201 sample ( $T_{c} = 70 K$ , $p \sim 0.086$ ) was measured in the present work. (b),(c) Momentum-energy contours of RIXS spectra at 70 and 250 K, obtained with $σ$ polarization. Dashed lines, full width at half maximum (FWHM) energy resolution of 60 meV. (d) Spectra at select $H$ values, obtained with $σ$ polarization; data are vertically shifted for clarity.
Reuse & Permissions
Figure 2
(a)–(d) $σ$ -polarized RIXS intensity spectra at 70 and 250 K, integrated over the 60 meV FWHM instrument resolution, centered at 0, 60, 120, and 180 meV energy loss. (e) $σ$ - and (f) $π$ -polarized RIXS spectra at 70 and 250 K, integrated over larger energy windows, as indicated. In all cases, the 70 K curves are vertically shifted for clarity. The black lines in (a)–(e) are polynomial momentum dependences, and the same in each case at low and high temperature. Blue and red lines in (a)–(e) are fits to Gaussian profiles plus a smoothly varying contribution at 70 and 250 K, respectively. Blue and red lines in (f) are guides to the eye. Vertical dashed gray lines indicate $q_{CDW}$ . The errors are one standard deviation (square root of total photon count).
Reuse & Permissions
Figure 3
Energy dependence for (a) $σ$ and (b) $π$ polarization of fitted Gaussian amplitude from energy-integrated data such as those shown in Figs. 2. The error bars indicate fit errors. Insets: Enlargement of the range $(- 250, - 100) meV$ ; the dashed red line in the inset of (a) indicates the possibility of nonzero charge scattering in this energy range at 250 K. Blue and red shaded areas indicate the instrument resolution of 60 meV (FWHM). Gaussian fits to Stokes and anti-Stokes scattering at 250 K (dashed red lines; sum, solid red lines) yield 41(4) and 64(12) meV for the peak position and intrinsic (deconvoluted) FWHM peak width. Gaussian fits to three peaks at 70 K (blue lines) capture (1) quasistatic, (2) low-energy ( $\sim 40 meV$ ), and (3) high-energy [peak at 163(12) meV, intrinsic width of 77(16) meV (FWHM)] contributions to the CDW response; the latter is not discerned in $π$ polarization, for which the charge response is expected and seen to be weaker [68]. (c),(d) Difference in amplitude between 70 and 250 K from (a) and (b), respectively, after correcting the 250 K data for the Bose factor. Green and purple shaded areas indicate the instrument resolution; vertical dashed lines indicate peak centers obtained from fits to Gaussian profiles, which are consistent within error with zero energy transfer. The orange shaded area in (c) indicates the net response centered at 160(6) meV.
Reuse & Permissions
Figure 4
(a). RIXS spectra for Hg1201 at numerous wave vectors along [1, 0], obtained with $π$ polarization. Data are vertically shifted for clarity. Blue and red bars indicate the paramagnon energy obtained from fits to a damped harmonic oscillator (see text and Ref. [68]). (b) Dispersion of magnetic excitations in Hg1201 measured by RIXS (this work; $p = 0.086$ , $T_{c} = 70 K$ ) and neutron scattering for two Hg1201 samples: one with nearly the same doping level and $T_{c} = 71 K$ [53], and the other with a slightly lower doping level of $p \approx 0.064$ and $T_{c} = 55 K$ [66]. Blue dashed line, heuristic fit to nearest-neighbor spin-wave theory (see text). Error bars for RIXS data are set to 30 meV, i.e., half of the FWHM energy resolution. The contour indicates the relative charge intensity at 70 K [Fig. 3].
Reuse & Permissions
Figure 5
(a) Energy-integrated RIXS (EIRIXS) data for Hg1201, integrated over the entire experimental energy range $(- 10, 2) eV$ , both at $T_{c}$ and 250 K. (b) Prior RXS data for Hg1201 at the same doping level and temperatures as in (a), along with 70 K data taken off resonance with an incident photon energy of 929 eV, reproduced from Ref. [9]. (c) RXS measurement of ${Bi}_{2} {Sr}_{2 - x} {La}_{x} {CuO}_{6 + δ}$ (Bi2201, $x = 0.115$ ) at $\sim T_{c}$ and 300 K, reproduced from Ref. [8]. (d) RXS results for superconducting electron-doped ${Nd}_{2 - x} {Ce}_{x} {CuO}_{4}$ (NCCO, $x = 0.145$ ) at $\sim T_{c}$ and 300 K, reproduced from Ref. [18]. In all cases, the high-temperature data are vertically shifted for comparison with the low-temperature result. Black dashed lines, assumed linear background. Solid lines, fits to Gaussian peak plus assumed linear background. Estimates of relative peak amplitudes are indicated in all panels.
Reuse & Permissions
Figure 6
Comparison of RIXS results for dynamic charge and paramagnon response in Hg1201 with estimates for the superconducting pairing glue. The black solid and dashed lines are the amplitudes of the charge and magnetic excitations in Hg1201 at $T = T_{c} = 70 K$ from the present work. As discussed in the text, the charge signal is multiplied by a factor of 10. The red solid line indicates the local magnetic susceptibility of Hg1201 measured by neutron scattering at the nearly same doping level [53]. The blue shaded area is the bosonic glue function extracted from optical measurements of optimally doped Hg1201 ( $T_{c} = 97 K$ ) at 100 K [63]; in this work, the glue function was not extracted for underdoped Hg1201, but it was established from analysis of other cuprates that the two characteristic energy scales are rather robust in the relevant doping range. The solid blue line is a glue function estimate for Bi2212 from Raman spectroscopy [64], again at optimal doping; results in $B_{1 g}$ and $B_{2 g}$ symmetry are weighted $2 ∶ 1$ to best highlight the close correspondence of the energy scales with the RIXS result.
Reuse & Permissions

Physical Review X

Unusual Dynamic Charge Correlations in Simple-Tetragonal HgBa2CuO4+δ

B. Yu, W. Tabis, I. Bialo, F. Yakhou, N. B. Brookes, Z. Anderson, Y. Tang, G. Yu, and M. Greven

Phys. Rev. X 10, 021059 – Published 16 June 2020

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Popular Summary

Article Text

Supplemental Material

References

Issue

Subject Areas

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Reuse & Permissions

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Unusual Dynamic Charge Correlations in Simple-Tetragonal ${HgBa}_{2} {CuO}_{4 + δ}$