Formation of electron pairs is essential to superconductivity. For conventional superconductors, tunnelling spectroscopy has established that pairing is mediated by bosonic modes (phonons); a peak in the second derivative of tunnel current d²I/dV² corresponds to each phonon mode^{1, 2, 3}. For high-transition-temperature (high-T_c) superconductivity, however, no boson mediating electron pairing has been identified. One explanation could be that electron pair formation⁴ and related electron–boson interactions are heterogeneous at the atomic scale and therefore challenging to characterize. However, with the latest advances in d²I/dV² spectroscopy using scanning tunnelling microscopy, it has become possible to study bosonic modes directly at the atomic scale⁵. Here we report d²I/dV² imaging^{6, 7, 8} studies of the high-T_c superconductor Bi₂Sr₂CaCu₂O₈₊. We find intense disorder of electron–boson interaction energies at the nanometre scale, along with the expected modulations in d²I/dV² (refs 9, 10). Changing the density of holes has minimal effects on both the average mode energies and the modulations, indicating that the bosonic modes are unrelated to electronic or magnetic structure. Instead, the modes appear to be local lattice vibrations, as substitution of ¹⁸O for ¹⁶O throughout the material reduces the average mode energy by approximately 6 per cent—the expected effect of this isotope substitution on lattice vibration frequencies⁵. Significantly, the mode energies are always spatially anticorrelated with the superconducting pairing-gap energies, suggesting an interplay between these lattice vibration modes and the superconductivity.

1. LASSP, Department of Physics, Cornell University, Ithaca, New York 14853, USA
2. Department of Physics, University of Tokyo, Tokyo, 113-8656, Japan
3. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
4. AIST, 1-1-1 Central 2, Umezono, Tsukuba, Ibaraki, 305-8568, Japan
5. Department of Physics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan
6. Theoretical Division, MS B262, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Correspondence to: J. C. Davis¹ Correspondence and requests for materials should be addressed to J.C.D. (Email: jcdavis@ccmr.cornell.edu).

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