• Open Access

Tomonaga-Luttinger Liquid in a Box: Electrons Confined within MoS2 Mirror-Twin Boundaries

Wouter Jolie, Clifford Murray, Philipp S. Weiß, Joshua Hall, Fabian Portner, Nicolae Atodiresei, Arkady V. Krasheninnikov, Carsten Busse, Hannu-Pekka Komsa, Achim Rosch, and Thomas Michely
Phys. Rev. X 9, 011055 – Published 28 March 2019

Abstract

Two- or three-dimensional metals are usually well described by weakly interacting, fermionic quasiparticles. This concept breaks down in one dimension due to strong Coulomb interactions. There, low-energy electronic excitations are expected to be bosonic collective modes, which fractionalize into independent spin- and charge-density waves. Experimental research on one-dimensional metals is still hampered by their difficult realization, their limited accessibility to measurements, and by competing or obscuring effects such as Peierls distortions or zero bias anomalies. Here we overcome these difficulties by constructing a well-isolated, one-dimensional metal of finite length present in MoS2 mirror-twin boundaries. Using scanning tunneling spectroscopy we measure the single-particle density of the interacting electron system as a function of energy and position in the 1D box. Comparison to theoretical modeling provides unambiguous evidence that we are observing spin-charge separation in real space.

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  • Received 1 November 2018

DOI:https://doi.org/10.1103/PhysRevX.9.011055

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

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wouter Jolie1,2,*, Clifford Murray1, Philipp S. Weiß3, Joshua Hall1, Fabian Portner3, Nicolae Atodiresei4, Arkady V. Krasheninnikov5,6, Carsten Busse1,2,7, Hannu-Pekka Komsa6, Achim Rosch3, and Thomas Michely1

  • 1II. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
  • 2Institut für Materialphysik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany
  • 3Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
  • 4Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum, 52428 Jülich, Germany
  • 5Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany
  • 6Department of Applied Physics, Aalto University School of Science, PO Box 11100, FI-00076 Aalto, Finland
  • 7Department Physik, Universität Siegen, 57068 Siegen, Germany

  • *wjolie@ph2.uni-koeln.de

Popular Summary

Every physicist has encountered the particle in a 1D box in lectures on quantum mechanics. This problem assumes independent, noninteracting particles. However, in real systems that approximate a 1D box, such as carbon nanotubes or metallic wires on semiconductors, electrons do interact strongly. The impact of these interactions—as described by the Tomonaga-Luttinger liquid theory—is dramatic: it results in spin-charge separation, an unusual behavior in which the spin and charge of an electron appear to split. Here, we report on the first direct observation of this behavior in a 1D box.

Our 1D box is created between two monolayer islands of molybdenum disulfide, one of which is the mirror image of the other. The finite, straight line at their interface hosts the confined 1D states. Using a scanning tunneling microscope, we measure the single-particle density of the interacting electron system in the 1D box as a function of energy and position. The data can be explained only by assuming the presence of a Tomonaga-Luttinger liquid. Because of the liquid’s confinement, the spin and charge excitations become visible individually, each with their own specific energy, probability density distribution, and spin or charge character, respectively.

This new approach provides a direct and quantitative comparison of experimental data with Tomonaga-Luttinger liquid theory and may enable exploration of its limitations. This will become increasingly relevant in the future as miniaturization of devices reaches atomic limits.

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Vol. 9, Iss. 1 — January - March 2019

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