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Holographic maps of quasiparticle interference

Nature Physics volume 12, pages 1052–1056 (2016)Cite this article

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Abstract

The analysis of Fourier-transformed scanning tunnelling microscopy images with subatomic resolution is a common tool for studying the properties of quasiparticle excitations in strongly correlated materials. Although Fourier amplitudes are generally complex valued, earlier analysis primarily focused on their absolute values. Their complex phases were often deemed random, and thus irrelevant, due to the unknown positions of the impurities in the sample. Here we show how to factor out these random phases by analysing overlaps between Fourier amplitudes that differ by reciprocal lattice vectors. The resulting holographic maps provide important and previously unknown information about the electronic structures. When applied to superconducting cuprates, our method solves a long-standing puzzle of the dichotomy between equivalent wavevectors. We show that d-wave Wannier functions of the conduction band provide a natural explanation for experimental results that were interpreted as evidence for competing unconventional charge modulations. Our work opens a new pathway to identify the nature of electronic states in scanning tunnelling microscopy.

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Figure 1: Main steps and notations involved in the creation of holographic maps.
Figure 2: Experimentally measured holographic maps for an optimally doped sample of Bi2201 with critical temperature Tc = 35 K, at voltage V = 40 meV.
Figure 3: Schematic and theoretical g maps.
Figure 4: Theoretical holographic maps generated from the g map depicted in Fig. 3c.
Figure 5: Trial Wannier functions.

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Acknowledgements

We are grateful to M. Boyer, K. Chatterjee, E. Hudson and D. Wise for giving us access to their unpublished experimental data. We acknowledge useful discussions with E. Altman, S. Davis, J. Hoffman, E. Hudson, R. Markiewicz, S. Sachdev and A. Stern. This work is supported by the Israel Science Foundation (grant No. 1542/14). E.D. acknowledges support from Harvard-MIT CUA, NSF Grant No. DMR-1308435, MURI-AFOSR, the ARO-MURI on Atomtronics, ARO MURI Qusim Program, M. Rossler, the Walter Haefner Foundation, the Humboldt Foundation, the Simons Foundation, and the ETH Foundation.

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Authors and Affiliations

  1. Department of Physics, Bar Ilan University, Ramat Gan 5290002, Israel

    Emanuele G. Dalla Torre

  2. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    Yang He & Eugene Demler

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  1. Emanuele G. Dalla Torre
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Contributions

All three authors equally contributed to the present study. E.G.D.T., Y.H. and E.D. conceived the idea of holographic maps and demonstrated their relation to the Wannier functions, E.G.D.T. and Y.H. analysed the experimental data, E.G.D.T. performed the numerical calculations, E.G.D.T., Y.H. and E.D. wrote the manuscript.

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Correspondence to Emanuele G. Dalla Torre.

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Dalla Torre, E., He, Y. & Demler, E. Holographic maps of quasiparticle interference. Nature Phys 12, 1052–1056 (2016). https://doi.org/10.1038/nphys3829

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