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Inelastic Tunneling into Multipolaronic Bound States in Single-Layer MoS2

Camiel van Efferen1, Laura Pätzold2, Tfyeche Y. Tounsi1, Arne Schobert2, Michael Winter2, Yann in ’t Veld2, Mark Georger1, Affan Safeer1, Christian Krämer1 et al.

Jeison Fischer1, Jan Berges3, Thomas Michely1, Roberto Mozara2, Tim Wehling2,4, and Wouter Jolie1,*

  • *Contact author: wjolie@ph2.uni-koeln.de
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Phys. Rev. X 15, 031030 – Published 29 July, 2025

DOI: https://doi.org/10.1103/l8lg-ny6m

Abstract

Polarons are quasiparticles that arise from the interaction of electrons or holes with lattice vibrations. Though polarons are well studied across multiple disciplines, experimental observations of polarons in two-dimensional crystals are sparse. We use scanning tunneling microscopy and spectroscopy to measure inelastic excitations of polaronic bound states emerging from coupling of nonpolar zone-boundary phonons to Bloch electrons in n-doped metallic single-layer MoS2. The latter is kept chemically pristine via contactless chemical doping. Tunneling into the vibrationally coupled polaronic states leads to a series of evenly spaced peaks in the differential conductance on either side of the Fermi level. Combining density functional (perturbation) theory with a recently developed ab initio electron-lattice downfolding technique, we show that the energy spacing stems from the longitudinal-acoustic phonon mode that flattens at the Brillouin zone edge and is responsible for the formation of stable multipolarons in metallic MoS2.

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Popular Summary

One open question in condensed matter physics is whether polarons—quasiparticles formed when electrons interact with the lattice—can exist in clean, single-layer materials like MoS2. Although earlier studies speculated about this possibility, direct evidence had been lacking. In our work, we provide experimental observation of multipolaronic bound states in metallic monolayer MoS2.

To uncover this, we use scanning tunneling microscopy and spectroscopy along with theoretical simulations. We prepare clean, doped monolayer MoS2 by intercalating cesium or europium atoms under a graphene sheet, which turns the material metallic. Our spectroscopic measurements reveal evenly spaced peaks in the differential conductance, which signal strong coupling between electrons and phonons in the crystal—evidence that stable multipolarons can form. To explain these results, we model the system using a new multiscale method to describe electron-lattice interactions. The simulations show that strong coupling to specific phonons causes the lattice to distort locally, binding multiple electrons together into multipolaron states.

Our study shows that metallic 2D materials like MoS2 can naturally host multipolarons when electron-phonon coupling is strong and doping is tuned properly. This not only helps us understand how electrons behave in 2D semiconductors but also points to new ways of controlling quantum states through material design.

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Phys. Rev. X 15, 031030– Published 29 July, 2025
  • Received 21 August 2024
  • Revised 14 April 2025
  • Accepted 17 June 2025
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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.

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