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  • Open Access

Valley Zeeman effect and Landau levels in two-dimensional transition metal dichalcogenides

Fengyuan Xuan

Su Ying Quek*

  • Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Block S16, Level 6, 6 Science Drive 2, Singapore 117546

  • Department of Physics, Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore

  • *phyqsy@nus.edu.sg
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Phys. Rev. Research 2, 033256 – Published 17 August, 2020

DOI: https://doi.org/10.1103/PhysRevResearch.2.033256

Abstract

This paper presents a theoretical description of both the valley Zeeman effect (g-factors) and Landau levels in two-dimensional H-phase transition metal dichalcogenides (TMDs) using the Luttinger-Kohn approximation with spin-orbit coupling. At the valley extrema in TMDs, energy bands split into Landau levels with a Zeeman shift in the presence of a uniform out-of-plane external magnetic field. The Landau level indices are symmetric in the K and K′ valleys. We develop a numerical approach to compute the single-band g-factors from first principles without the need for a sum over unoccupied bands. Many-body effects are included perturbatively within the GW approximation. Nonlocal exchange and correlation self-energy effects in the GW calculations increase the magnitude of single-band g-factors compared to those obtained from density functional theory. Our first-principles results give spin- and valley-split Landau levels, in agreement with recent optical experiments. The exciton g-factors deduced in this work are also in good agreement with experiment for the bright and dark excitons in monolayer WSe2, as well as the lowest-energy bright excitons in MoSe2−WSe2 heterobilayers with different twist angles.

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Outline

Information

Phys. Rev. Research 2, 033256– Published 17 August, 2020
  • Received 14 February 2020
  • Revised 3 July 2020
  • Accepted 7 July 2020
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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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