Superconducting Fluctuations in Overdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$

Open Access

Superconducting Fluctuations in Overdoped ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$

Yu He, Su-Di Chen, Zi-Xiang Li, Dan Zhao, Dongjoon Song, Yoshiyuki Yoshida, Hiroshi Eisaki, Tao Wu, Xian-Hui Chen, Dong-Hui Lu, Christoph Meingast, Thomas P. Devereaux, Robert J. Birgeneau, Makoto Hashimoto, Dung-Hai Lee, and Zhi-Xun Shen

Phys. Rev. X 11, 031068 – Published 28 September 2021

Abstract

Fluctuating superconductivity—vestigial Cooper pairing in the resistive state of a material—is usually associated with low dimensionality, strong disorder, or low carrier density. Here, we report single-particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in the heavily hole-doped cuprate superconductor ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ ( $T_{c} = 66 K$ ) despite the high carrier density. With a sign-problem-free quantum Monte Carlo calculation, we show how a partially flat band at $(π, 0)$ can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.

Received 16 April 2021
Revised 15 June 2021
Accepted 26 July 2021
Corrected 26 October 2021

DOI:https://doi.org/10.1103/PhysRevX.11.031068

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)

Impurities in superconductors Superconducting fluctuations Superconducting phase transition Superfluid density

Cuprates High-temperature superconductors

Angle-resolved photoemission spectroscopy Methods in superconductivity Nuclear magnetic resonance Quantum Monte Carlo

Condensed Matter, Materials & Applied Physics

Corrections

26 October 2021

Correction: The previously published Fig. 4(a) contained an inset labeling error that was introduced at proof stage and has been replaced.

Authors & Affiliations

Yu He ^1,2,3,4,*, Su-Di Chen ^1,3,*, Zi-Xiang Li^2,*, Dan Zhao^5,6, Dongjoon Song⁷, Yoshiyuki Yoshida⁷, Hiroshi Eisaki⁷, Tao Wu^5,6, Xian-Hui Chen^5,6, Dong-Hui Lu⁸, Christoph Meingast⁹, Thomas P. Devereaux^10,3, Robert J. Birgeneau^2,4, Makoto Hashimoto ⁸, Dung-Hai Lee^2,4, and Zhi-Xun Shen ^1,3

¹Department of Applied Physics, Stanford University, Stanford, California 94305, USA
²Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
³Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
⁴Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁵Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
⁶CAS Key Laboratory of Strongly-coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
⁷National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8565, Japan
⁸Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁹Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
¹⁰Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA

^*These authors contributed equally to this work.

Popular Summary

Superconductivity arises when electrons pair up to form Cooper pairs below some transition temperature. Some materials exhibit superconducting fluctuations—Cooper pairs that persist even above this temperature. Unless a superconductor is extremely disordered, is two dimensional, or has low kinetic energy, fluctuating superconductivity should thrive only at temperatures extremely near this transition. However, we report thermodynamic, magnetic, and spectral evidence of superconducting fluctuations persisting up to 30% above the superconducting transition temperature in a metallic, heavily hole-doped cuprate superconductor.

To detect the superconducting fluctuations, we use an intense beam of monochromatic x rays to break Cooper pairs and eject the lone electrons, whose kinematic properties are then analyzed in a photoelectron analyzer. Those ejected from fluctuating Cooper pairs have different energy and momentum distributions from the regular electrons in a metal or a superconductor, which are linked to thermodynamic and magnetic anomalies at temperatures substantially above the superconducting transition. State-of-the-art numerical simulations help reveal the hidden role of many uncharacteristically slow electrons behind the exceptional fluctuations. This revelation offers a new engineering target to help tranquilize the fluctuations and thus improve the superconducting temperature in many anisotropic superconductors.

The low-energy electronic structure anisotropy will be further explored as a new tuning knob to control superconducting fluctuations and the transition temperature. Superoxygenated cuprates, given their simplicity shown in this work, will also become the next major platform to investigate the high-temperature superconducting mechanism.

Key Image

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 11, Iss. 3 — July - September 2021

Subject Areas

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Thermal superconducting fluctuation effect in conventional and unconventional superconductors. Superconducting gap opening temperature $T_{pair}$ divided by zero resistance temperature $T_{c}$ tallied according to the resistivity right above $T_{c}$ for (top) thin film superconductors and (bottom) bulk superconductors. Arrows denote increasing disorder in thin film systems and increasing hole doping in the cuprates. Except for TBG and TTG systems, $T_{pair}$ is exclusively determined from heat capacity or single-particle spectra [16]. MATBG (MATTG), magic angle twisted bilayer (trilayer) graphene; $FeSe / STO$ , monolayer FeSe on $Nb ∶ {SrTi O}_{3}$ ; BKFA, ${Ba}_{1 - x} K_{x} {Fe}_{2} {As}_{2}$ ; BFCA, $Ba ({Fe}_{1 - x} {Co}_{x})_{2} {As}_{2}$ ; BKBO, ${Ba}_{1 - x} K_{x} {BiO}_{3}$ ; BPBO, ${BaPb}_{1 - x} {Bi}_{x} O_{3}$ ; SOFFA, ${SmO}_{1 - x} F_{x} FeAs$ ; YBCO, ${YBa}_{2} {Cu}_{3} O_{7 - δ}$ ; Tl2201, ${Tl}_{2} {Ba}_{2} {CuO}_{6 + δ}$ ; LSCO, $(La, Sr)_{2} {CuO}_{4}$ ; Bi2212, ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ [16].
Reuse & Permissions
Figure 2
Bulk magnetic and thermodynamic properties of a heavily overdoped Bi-2212 with $T_{c} = 66 K$ . (a) dc diamagnetic response at 5 Oe, for fields both perpendicular (solid circles) and parallel (open circles) to the ${CuO}_{2}$ plane. (b) In- and out-of-plane resistivity near $T_{c}$ . (c) In-plane linear lattice expansion coefficient $α$ . (d) Molar specific heat $c_{p}$ . In both (c) and (d), a linear background (gray dashed line) is removed to highlight the superconducting transition in the bottom curve plotted to the right axes on an enlarged scale.
Reuse & Permissions
Figure 3
Temperature-dependent high-resolution antinodal energy-momentum spectra in heavily overdoped Bi-2212 with $T_{c} = 66 K$ . (a) Fermi surface map integrated within 10 meV of the chemical potential of a Pb-free sample in the normal state. Red bar denotes the parallel momentum of the spectra shown in subsequent panels. (b)–(j) Fermi-function-divided antinodal spectra along the BZ boundary in a Pb-doped sample. (k) Fitted energy-momentum dispersions of both the electron and hole Bogoliubov quasiparticles at various temperatures. Red circles indicate the normal state dispersion at 145 K. Thin lines shaded in gray are the averaged energies of the electron and hole Bogoliubov quasiparticle branches. Vertical dashed lines denote the Fermi momenta and gap minima momenta. (l) Calculated particle-hole mixing ratio, expressed in its arc tangent value, from the fitted intensity ratio of the electron and hole Bogoliubov quasiparticle branches near $T_{c}$ . $π / 4$ represents equal particle-hole mixture. Black line shows the BCS expectation when $v_{F} \cdot k_{F} ≫ Δ$ .
Reuse & Permissions
Figure 4
Temperature dependence of the antinodal EDCs. Fermi-function-divided EDCs at (a) antinodal $k_{F}$ and (b) $(π, 0)$ . Insets depict the two momenta in the Brillouin zone. Spectra are normalized to 1 over [0, 100] meV binding energy. Green and red lines denote $T_{gap} \sim 90 K$ and $T_{c} \sim 66 K$ , respectively. Black circles mark the apparent spectral peak position, and the red dashed line marks the ungapped van Hove point position. Temperature-dependent (c) spectral peak binding energy, (d) spectral peak height, and (e) spectral intensity at $E_{F}$ from the antinodal $k_{F}$ (yellow) and $(π, 0)$ (blue). Right-hand axis in (e) corresponds to the frequency shift from the ${}^{63}{Cu}$ nuclear spin resonance (red). Gray lines are guides to exemplify normal state spectral weight evolution. Curves in (d) are offset for clarity.
Reuse & Permissions
Figure 5
Band structure contribution to the superconducting fluctuation examined by quantum Monte Carlo simulations. Tight-binding band structures with (a) a steep dispersion and (b) a shallow and flat dispersion near $(π, 0)$ . The along high symmetry cuts are shown by red lines on their respective Fermi surfaces in the insets. (c) Experimentally measured normal state spectra along the same high symmetry cuts for $p = 0.22$ samples. Gray bars are the superconducting gap sizes. Calculated temperature-dependent single-particle spectra at the antinode for (d) the steep dispersion and (e) the shallow flat dispersion, when anisotropic superconductivity is induced by a $B_{1 g}$ phonon. Spectral intensity is normalized so the total area is 1. The curves are offset proportional to temperature $T = 1 / β$ . The electron-phonon coupling strength $λ$ is set to 0.25. $t = 1 e V$ is the hopping energy used in the tight-binding model.
Reuse & Permissions

Physical Review X

Superconducting Fluctuations in Overdoped Bi2Sr2CaCu2O8+δ

Yu He, Su-Di Chen, Zi-Xiang Li, Dan Zhao, Dongjoon Song, Yoshiyuki Yoshida, Hiroshi Eisaki, Tao Wu, Xian-Hui Chen, Dong-Hui Lu, Christoph Meingast, Thomas P. Devereaux, Robert J. Birgeneau, Makoto Hashimoto, Dung-Hai Lee, and Zhi-Xun Shen

Phys. Rev. X 11, 031068 – Published 28 September 2021

Abstract

Physics Subject Headings (PhySH)

Corrections

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

Reuse & Permissions

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Superconducting Fluctuations in Overdoped ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$