Coulomb interactions are crucial in determining the ground state of an ideal two-dimensional electron gas (2DEG) in the limit of low electron densities1. In this regime, Coulomb interactions dominate over single-particle phase-space filling. In silicon and gallium arsenide, electrons are typically localized at these low densities. In contrast, in transition-metal dichalcogenides (TMDs), Coulomb correlations in a 2DEG can be anticipated at experimentally relevant electron densities. Here, we investigate a 2DEG in a gated monolayer of the TMD molybdenum disulfide2. We measure the optical susceptibility, a probe of the 2DEG which is local, minimally invasive and spin selective3. In a magnetic field of 9.0 T and at electron concentrations up to n ≃ 5 × 1012 cm−2, we present evidence that the ground state is spin-polarized. Out of the four available conduction bands4,5, only two are occupied. These two bands have the same spin but different valley quantum numbers. Our results suggest that only two bands are occupied even in the absence of a magnetic field. The spin polarization increases with decreasing 2DEG density, suggesting that Coulomb interactions are a key aspect of the symmetry breaking. We propose that exchange couplings align the spins6. The Bohr radius is so small7 that even electrons located far apart in phase-space interact with each other6.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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We thank J. Klinovaja, D. Loss and D. Miserev, and also G. Burkard, A. Pearce and A. Kormányos, for discussions. The work in Basel was financially supported by SNF (Project No. 200020_156637), NCCR QSIT and QCQT. P.M. acknowledges support from grants OTKA PD-121052, OTKA FK123894 and the Bolyai Fellowship. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, JSPS KAKENHI grant numbers JP18K19136 and the CREST (JPMJCR15F3), JST.
The authors declare no competing interests.
Journal peer review information: Nature Nanotechnology thanks Ahmet Avsar and Benedikt Scharf for their contribution to the peer review of this work.
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Roch, J.G., Froehlicher, G., Leisgang, N. et al. Spin-polarized electrons in monolayer MoS2. Nat. Nanotechnol. 14, 432–436 (2019). https://doi.org/10.1038/s41565-019-0397-y
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