Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-Tc superconductors


An understanding of the missing antinodal electronic excitations in the pseudogap state is essential for uncovering the physics of the underdoped cuprate high-temperature superconductors1,2,3,4,5,6. The majority of high-temperature experiments performed thus far, however, have been unable to discern whether the antinodal states are rendered unobservable due to their damping or whether they vanish due to their gapping7,8,9,10,11,12,13,14,15,16,17,18. Here, we distinguish between these two scenarios by using quantum oscillations to examine whether the small Fermi surface pocket, found to occupy only 2% of the Brillouin zone in the underdoped cuprates19,20,21,22,23,24, exists in isolation against a majority of completely gapped density of states spanning the antinodes, or whether it is thermodynamically coupled to a background of ungapped antinodal states. We find that quantum oscillations associated with the small Fermi surface pocket exhibit a signature sawtooth waveform characteristic of an isolated two-dimensional Fermi surface pocket25,26,27,28,29,30,31,32. This finding reveals that the antinodal states are destroyed by a hard gap that extends over the majority of the Brillouin zone, placing strong constraints on a drastic underlying origin of quasiparticle disappearance over almost the entire Brillouin zone in the pseudogap regime7,8,9,10,11,12,13,14,15,16,17,18.

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Fig. 1: Two proposed scenarios of the pseudogap ground state in YBa2Cu3O6 + x.
Fig. 2: Enhanced quantum oscillations compared to measurements on previous samples.
Fig. 3: Signature quantum oscillations from an isolated 2D Fermi surface with no reservoir density of states at the Fermi level.
Fig. 4: Reservoir contribution \({\zeta }_{{\rm{res}}}\) to the electronic density of states at the Fermi level from harmonic analysis.

Data availability

The data represented in Figs. 24 are available from the University of Cambridge data repository (https://doi.org/10.17863/CAM.50169). All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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M.H., Y.-T.H. and S.E.S. acknowledge support from the Royal Society, the Winton Programme for the Physics of Sustainability, EPSRC (studentship, grant no. EP/P024947/1 and EPSRC Strategic Equipment grant no. EP/M000524/1) and the European Research Council (grant no. 772891). S.E.S. acknowledges support from the Leverhulme Trust by way of the award of a Philip Leverhulme Prize. H.Z., J.W. and Z.Z. acknowledge support from the National Key Research and Development Program of China (grant no. 2016YFA0401704). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement no. DMR-1644779, the state of Florida and the US Department of Energy. Work performed by M.K.C., R.D.M. and N.H. was supported by the US DOE BES ‘Science of 100 T’ programme.

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M.H., Y.-T.H., K.A.M., H.Z., J.W., Z.Z., M.K.C., R.D.M., S.E.S. and N.H. performed high-magnetic-field measurements. Y.-T.H., J.P., T.L., M.L.T. and B.K. prepared single crystals. M.H., Y.-T.H., R.D.M., G.G.L., S.E.S. and N.H. contributed to data analysis. S.E.S. and N.H. conceived the project. S.E.S. and N.H. wrote the manuscript with M.H. and Y.-T.H., with contributions from all authors.

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Correspondence to Neil Harrison.

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Supplementary Figs. 1–9 and discussion.

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Hartstein, M., Hsu, Y., Modic, K.A. et al. Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-Tc superconductors. Nat. Phys. 16, 841–847 (2020). https://doi.org/10.1038/s41567-020-0910-0

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