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# Mottness at finite doping and charge instabilities in cuprates

## Abstract

The influence of Mott physics on the doping–temperature phase diagram of copper oxides represents a major issue that is the subject of intense theoretical and experimental efforts. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p → Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping pcr ≈ 0.16 irrespective of the temperature, and it can be well described by dynamical mean-field theory calculations. We argue that the onset of low-temperature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p < pcr region of the phase diagram. This discovery sets a new framework for theories of charge order and low-temperature phases in underdoped copper oxides.

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## Acknowledgements

We thank M. Grilli, A. Bianconi, L. Benfatto, F. Cilento, D. Fausti, F. Parmigiani, L. De’ Medici, M. Minola, B. Keimer and J. Bonča for useful and fruitful discussions. The research activities of M.F. have received funding from the European Union, under the project ERC-692670 (FIRSTORM). F.B. acknowledges financial support from the MIUR-Futuro in ricerca 2013 Grant in the frame of the ULTRANANO Project (project number: RBFR13NEA4). M.C. and C.G. acknowledge financial support from MIUR through the PRIN 2015 Programme (Prot. 2015C5SEJJ001). M.C. acknowledges funding by SISSA/CNR project ‘Superconductivity, Ferroelectricity and Magnetism in Bad Metals’ (Prot. 232/2015). F.B., G.F. and C.G. acknowledge support from Università Cattolica del Sacro Cuore through D.1, D.2.2 and D.3.1 grants. F.B. and G.F. acknowledge financial support from Fondazione E.U.L.O. D.B. acknowledges the Emmy Noether Programme of the Deutsche Forschung Gemeinschaft. G.C. acknowledges funding from the European Union Horizon 2020 Programme under Grant Agreement 696656 Graphene Core 1. This research was undertaken thanks in part to funding from the Max Planck-UBC Centre for Quantum Materials and the Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program. The work at UBC was supported by the Killam, Alfred P. Sloan, and Natural Sciences and Engineering Research Council of Canada’s (NSERC’s) Steacie Memorial Fellowships (A.D.); the Alexander von Humboldt Fellowship (A.D.); the Canada Research Chairs Program (A.D.); and the NSERC, Canada Foundation for Innovation (CFI), and CIFAR Quantum Materials.

## Author information

Authors

### Contributions

C.G. coordinated the research activities with input from all the coauthors, in particular S.P., S.D.C., F.B., M.F., M.C., A.D. and G.C. The NOPA-based pump–probe set-up was designed and developed by D.B. and G.C. The time-resolved optical measurements were performed by S.P., S.D.C., N.M., A.R., P.A., F.B., G.F., D.B., G.C. and C.G. The analysis of the time-resolved data was performed by S.P., S.D.C., N.M. and C.G. The mean-field estimation of the charge-transfer shift was carried out by M.F. The DMFT calculations were carried out by M.C. The La-Bi2201 crystals were characterized by S.L., R.C. and A.D. The RXS measurements were performed by R.C. and A.D. The text was written by C.G. with major input from S.P., S.D.C., F.B., G.F., D.B., S.L., M.F., M.C., A.D. and G.C. All authors extensively discussed the results and the interpretation and revised the manuscript.

### Corresponding author

Correspondence to C. Giannetti.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 644 kb)

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Peli, S., Conte, S., Comin, R. et al. Mottness at finite doping and charge instabilities in cuprates. Nature Phys 13, 806–811 (2017). https://doi.org/10.1038/nphys4112

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