- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Long-range hopping in the confined electronic states of atomically constructed Cs chains on InSb(110)

Niek. M. M. Aarts*, Anna M. H. Krieg*, Emil Sierda*, Anna Reinhold, Danis Badrtinov, Yann in ‘t Veld†, Brian Kiraly‡, Elze J. Knol, Malte Rösner§ et al.

Daniel Wegner∥ and Alexander A. Khajetoorians

  • Institute for Molecules and Materials, Radboud University, 6525 AJ Nijmegen, The Netherlands

  • *These authors contributed equally to this work.
  • †Present address: Institute of Theoretical Physics, Universität Hamburg, 22607 Hamburg, Germany.
  • ‡Present address: School of Physics and Astronomy, University of Nottingham, Nottingham, United Kingdom.
  • §Present address: Faculty of Physics, Bielefeld University, 33501 Bielefeld, Germany.
  • ∥Contact author: d.wegner@science.ru.nl
  • Contact author: a.khajetoorians@science.ru.nl
PDF

Phys. Rev. B 114, 185126 – Published 23 September, 2026

DOI: https://doi.org/10.1103/6bgc-gwzd

Abstract

Solid-state quantum simulation is a powerful approach in which the material properties of a tunable platform are used to emulate user-defined model Hamiltonians. One of the biggest challenges in materials-based quantum simulation is understanding how to exactly map material-specific changes onto model parameters in a given Hamiltonian. Here, we study the electronic structure resulting from tailored quasi-1D atomic Cs chains constructed atom by atom, using scanning tunneling microscopy and spectroscopy with the aim to uncover how Cs adatoms on InSb can be used for quantum simulation. We study the dependence of the Cs-induced confined electronic states as a function of various parameters of the chain structure. We find that the lowest-level states can be well described by a 1D confinement potential, determined by the chain length, and that the critical parameter determining the depth of the attractive potential is the Cs density. We relate the observations to a lattice model Hamiltonian with exponential long-range hopping, and compare the calculated local density of states with the experimental observations, which reproduce the lowest energy states well. We find deviations from the 1D-confinement potential description for the higher-energy states, which we detail and speculate on its origin. These studies are critical for developing this material platform toward quantum simulation of electronic structure.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (35)

  1. R. Blatt and C. F. Roos, Quantum simulations with trapped ions, Nat. Phys. 8, 277 (2012).
  2. I. Bloch, Ultracold quantum gases in optical lattices, Nat. Phys. 1, 23 (2005).
  3. I. Bloch, J. Dalibard, and S. Nascimbene, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
  4. Y. Cao et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
  5. Y. Cao et al., Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  6. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  7. A. A. Houck, H. E. Türeci, and J. Koch, On-chip quantum simulation with superconducting circuits, Nat. Phys. 8, 292 (2012).
  8. D.-S. Lühmann, C. Weitenberg, and K. Sengstock, Emulating molecular orbitals and electronic dynamics with ultracold atoms, Phys. Rev. X 5, 031016 (2015).
  9. A. Singha et al., Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice, Science 332, 1176 (2011).
  10. H. C. Jiang and T. P. Devereaux, Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t’, Science 365, 1424 (2019).
  11. H. C. Jiang and S. A. Kivelson, High temperature superconductivity in a lightly doped quantum spin liquid, Phys. Rev. Lett. 127, 097002 (2021).
  12. S. S. Gong, W. Zhu, and D. N. Sheng, Robust d-wave superconductivity in the square-lattice t-J model, Phys. Rev. Lett. 127, 097003 (2021).
  13. S. T. Jiang, D. J. Scalapino, and S. R. White, Ground-state phase diagram of the t-t'-J model, Proc. Natl. Acad. Sci. USA 118, e2109978118 (2021).
  14. S. N. Kempkes et al., Robust zero-energy modes in an electronic higher-order topological insulator, Nat. Mater. 18, 1292 (2019).
  15. M. Slot et al., p-band engineering in artificial electronic lattices, Phys. Rev. X 9, 011009 (2019).
  16. M. R. Slot et al., Experimental realization and characterization of an electronic Lieb lattice, Nat. Phys. 13, 672 (2017).
  17. R. Drost, T. Ojanen, A. Harju, and P. Liljeroth, Topological states in engineered atomic lattices, Nat. Phys. 13, 668 (2017).
  18. M. N. Huda, S. Kezilebieke, T. Ojanen, R. Drost, and P. Liljeroth, Tuneable topological domain wall states in engineered atomic chains, npj Quantum Mater. 5, 17 (2020).
  19. L. C. Collins, T. G. Witte, R. Silverman, D. B. Green, and K. K. Gomes, Imaging quasiperiodic electronic states in a synthetic Penrose tiling, Nat. Commun. 8, 15961 (2017).
  20. K. K. Gomes, W. Mar, W. Ko, F. Guinea, and H. C. Manoharan, Designer Dirac fermions and topological phases in molecular graphene, Nature (London) 483, 306 (2012).
  21. S. Fölsch, P. Hyldgaard, R. Koch, and K. H. Ploog, Quantum confinement in monatomic Cu chains on Cu(111), Phys. Rev. Lett. 92, 056803 (2004).
  22. N. Nilius, T. M. Wallis, and W. Ho, Development of one-dimensional band structure in artificial gold chains, Science 297, 1853 (2002).
  23. S. Fölsch, J. Yang, C. Nacci, and K. Kanisawa, Atom-by-atom quantum state control in adatom chains on a semiconductor, Phys. Rev. Lett. 103, 096104 (2009).
  24. S. Fölsch, J. Martínez-Blanco, J. Yang, K. Kanisawa, and S. C. Erwin, Quantum dots with single-atom precision, Nat. Nanotechnol. 9, 505 (2014).
  25. V. Pham, K. Kanisawa, and S. Fölsch, Quantum rings engineered by atom manipulation, Phys. Rev. Lett. 123, 066801 (2019).
  26. V. D. Pham, Y. Pan, S. C. Erwin, and S. Fölsch, Quantum dots on the InAs(110) cleavage surface created by atom manipulation, Phys. Rev. Res. 6, 013269 (2024).
  27. E. Sierda et al., Quantum simulator to emulate lower-dimensional molecular structure, Science 380, 1048 (2023).
  28. B. Kiraly et al., Anisotropic two-dimensional screening at the surface of black phosphorus, Phys. Rev. Lett. 123, 216403 (2019).
  29. K. Hashimoto et al., Quantum hall transition in real space: From localized to extended states, Phys. Rev. Lett. 101, 256802 (2008).
  30. S. Becker, M. Liebmann, T. Mashoff, M. Pratzer, and M. Morgenstern, Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting, Phys. Rev. B 81, 155308 (2010).
  31. S. Becker et al., Probing electron-electron interaction in quantum Hall systems with scanning tunneling spectroscopy, Phys. Rev. Lett. 106, 156805 (2011).
  32. M. Morgenstern et al., Scanning tunneling microscopy of two-dimensional semiconductors: Spin properties and disorder, Physica E 44, 1795 (2012).
  33. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, Band parameters for III–V compound semiconductors and their alloys, J. Appl. Phys. 89, 5815 (2001).
  34. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  35. https://doi.org/10.61686/YDRHT18202.

Outline

Information

Phys. Rev. B 114, 185126– Published 23 September, 2026
  • Received 12 February 2026
  • Revised 9 June 2026
  • Accepted 28 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation