Revealing the Coulomb interaction strength in a cuprate superconductor

S.-L. Yang, J. A. Sobota, Y. He, Y. Wang, D. Leuenberger, H. Soifer, M. Hashimoto, D. H. Lu, H. Eisaki, B. Moritz, T. P. Devereaux, P. S. Kirchmann, and Z.-X. Shen

Phys. Rev. B 96, 245112 – Published 8 December 2017

Abstract

We study optimally doped ${Bi}_{2} {Sr}_{2} {Ca}_{0.92} Y_{0.08} {Cu}_{2} O_{8 + δ}$ (Bi2212) using angle-resolved two-photon photoemission spectroscopy. Three spectral features are resolved near 1.5, 2.7, and 3.6 eV above the Fermi level. By tuning the photon energy, we determine that the 2.7-eV feature arises predominantly from unoccupied states. The 1.5- and 3.6-eV features reflect unoccupied states whose spectral intensities are strongly modulated by the corresponding occupied states. These unoccupied states are consistent with the prediction from a cluster perturbation theory based on the single-band Hubbard model. Through this comparison, a Coulomb interaction strength $U$ of 2.7 eV is extracted. Our study complements equilibrium photoemission spectroscopy and provides a direct spectroscopic measurement of the unoccupied states in cuprates. The determined Coulomb $U$ indicates that the charge-transfer gap of optimally doped Bi2212 is 1.1 eV.

Received 13 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.245112

Physics Subject Headings (PhySH)

Electronic structure

High-temperature superconductors Strongly correlated systems

Perturbation theory Photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S.-L. Yang^1,2,*, J. A. Sobota^1,3, Y. He^1,2, Y. Wang^1,2, D. Leuenberger^1,2, H. Soifer¹, M. Hashimoto⁴, D. H. Lu⁴, H. Eisaki⁵, B. Moritz¹, T. P. Devereaux¹, P. S. Kirchmann^1,†, and Z.-X. Shen^1,2,‡

¹Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
²Geballe Laboratory for Advanced Materials, Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA
³Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁴Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
⁵Electronics and Photonics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8558, Japan

^*Present address: Kavli Institute at Cornell for Nanoscale Science, Laboratory of Atomic and Solid State Physics, Department of Physics, and Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853, USA.
^†kirchman@slac.stanford.edu
^‡zxshen@stanford.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 24 — 15 December 2017

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Overview of the two-photon photoemission (2PPE) data on OP96 Bi2212 at 20 K. (a) Illustration of the ARPES and 2PPE processes. $E_{F}, E_{un}$ , and $E_{vac}$ are defined in the text. (b) 2PPE spectrum along the Brillouin zone diagonal. At the zone center, features $α, β$ , and $γ$ are identified near 1.5, 2.7, and 3.6 eV, respectively. The intensities in the energy range of $3.4 \sim 4.8$ eV are magnified by a factor of 15 to highlight the weak feature $γ$ .
Reuse & Permissions
Figure 2
Illustration of different two-photon excitation schemes. Notations are the same as in Fig. 1. (a) Unoccupied-state spectroscopy. The resolved binding energy is ( $E_{un} - E_{F}$ ) and does not depend on the photon energy. (b) Occupied-state spectroscopy. The resolved binding energy is ( $E_{oc} + h ν - E_{F}$ ) and depends on the photon energy. (c) Resonant excitation of unoccupied states. The spectral intensity is enhanced with respect to the nonresonant schemes in (a) and (b).
Reuse & Permissions
Figure 3
Photon energy dependence of the 2PPE features. (a, b) 2PPE spectra near the zone center using (a) 4.5-eV and (b) 4.8-eV photons. Both spectra are obtained with $9.5 \times 10^{12}$ photons/(pulse ${cm}^{2}$ ). [(c, d)] Comparison of the EDCs at (c) $k_{| |} = - 0.3$ and (d) $0 Å^{- 1}$ . Each EDC is obtained by integrating over a momentum window of $0.1 Å^{- 1}$ . The cuts are indicated by dashed lines in (a) and (b).
Reuse & Permissions
Figure 4
Resonant 2PPE process for feature $γ$ using 4.5-eV photons. (a) Illustration of the momentum-space trajectory (solid brown) for the spectra in (b). Overlaid on the graphs are the tight-binding Fermi surfaces (solid black) [32]. (b) 2PPE spectrum of feature $γ$ using 4.5-eV photons and ARPES spectrum of the occupied states near $E_{F}$ using 6-eV photons.
Reuse & Permissions
Figure 5
Influence of initial states on feature $α$ . (a) ARPES spectrum of OP96 Bi2212 along the zone diagonal using 22.7-eV photons. The energy axis is offset by 4.5 eV to be compared with the 2PPE spectrum. (b) 2PPE spectrum on the same sample using 4.5-eV photons.
Reuse & Permissions
Figure 6
Calculated spectrum using cluster perturbation theory. (a) Theoretical single-particle spectral function calculated by CPT for optimal doping and $U = 2.7$ eV. The charge-transfer gap $Δ_{CT} \sim 1.1 eV$ is marked on the spectrum. (b) Theoretical unoccupied spectrum in the experimentally measured momentum and energy range. The corresponding color scales are indicated on top of panels (a) and (b). (c) Comparison of an experimental EDC taken at the zone center and the theoretical counterparts for various $U$ values. EDCs are offset on a log scale for clear demonstration. The theoretical EDCs are multiplied by a Fermi-Dirac function with the Fermi edge at 4.5 eV above $E_{F}$ , which is the cutoff energy for 2PPE. The best match is obtained for $U = 2.7$ eV.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics