Spin-orbit coupling in elemental two-dimensional materials

Kurpas, Marcin; Faria, Paulo E.; Gmitra, Martin; Fabian, Jaroslav

doi:10.1103/physrevb.100.125422

Cited by 62 publications

(43 citation statements)

References 53 publications

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“…However, the spin-orbit coupling can lead to a reduction of m z , while preserving m x = m y = 0, as shown in Ref. [30] for 2D hexagonal crystals. Nevertheless, in most cases, taking m z = 1/2 was demonstrated to be a reasonable approximation [31].…”

Section: Introductionmentioning

confidence: 77%

Exciton g factors of van der Waals heterostructures from first-principles calculations

et al. 2020

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External fields are a powerful tool to probe optical excitations in a material. The linear energy shift of an excitation in a magnetic field is quantified by its effective g factor. Here we show how exciton g factors and their sign can be determined by converged first-principles calculations. We apply the method to monolayer excitons in semiconducting transition metal dichalcogenides and to interlayer excitons in MoSe 2 /WSe 2 heterobilayers and obtain good agreement with recent experimental data. The precision of our method allows us to assign measured g factors of optical peaks to specific transitions in the band structure and also to specific regions of the samples. This revealed the nature of various, previously measured interlayer exciton peaks. We further show that, due to specific optical selection rules, g factors in van der Waals heterostructures are strongly spinand stacking-dependent. The calculation of orbital angular momenta requires the summation over hundreds of bands, indicating that for the considered two-dimensional materials the basis set size is a critical numerical issue. The presented approach can potentially be applied to a wide variety of semiconductors.

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Section: Introductionmentioning

confidence: 77%

Exciton g factors of van der Waals heterostructures from first-principles calculations

et al. 2020

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“…1a reveal that all the conduction and valence bands around the K -points are spin split because of spin–orbit coupling. The combination of mirror-plane and time-reversal symmetry suggests that spin in the out-of-plane direction, S z , is a good quantum number with opposite orientations in the + K and − K -valleys 28 , 29 . Figure 2e shows the CB+2 − band, color-coded by the calculated 〈 S z 〉 expectation value.…”

Section: Resultsmentioning

confidence: 99%

Narrow-band high-lying excitons with negative-mass electrons in monolayer WSe2

et al. 2021

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Monolayer transition-metal dichalcogenides (TMDCs) show a wealth of exciton physics. Here, we report the existence of a new excitonic species, the high-lying exciton (HX), in single-layer WSe2 with an energy of ~3.4 eV, almost twice the band-edge A-exciton energy, with a linewidth as narrow as 5.8 meV. The HX is populated through momentum-selective optical excitation in the K-valleys and is identified in upconverted photoluminescence (UPL) in the UV spectral region. Strong electron-phonon coupling results in a cascaded phonon progression with equidistant peaks in the luminescence spectrum, resolvable to ninth order. Ab initio GW-BSE calculations with full electron-hole correlations explain HX formation and unmask the admixture of upper conduction-band states to this complex many-body excitation. These calculations suggest that the HX is comprised of electrons of negative mass. The coincidence of such high-lying excitonic species at around twice the energy of band-edge excitons rationalizes the excitonic quantum-interference phenomenon recently discovered in optical second-harmonic generation (SHG) and explains the efficient Auger-like annihilation of band-edge excitons.

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“…1 . Similar to other buckled 2D materials made of group V elements, such as blue phosphorene, arsenene or antimonene 22 , the band gap of monolayer nitrogene is indirect. The size of the indirect gap for the PBE exchange correlation functional is , eV, and is in agreement with the values reported by others 13 .…”

Section: Resultsmentioning

confidence: 81%

“…Nitrogen is a light element with the atomic number Z=14. Therefore, spin–orbit coupling (SOC) in nitrogene is expected to be weak 22 , similar to graphene 23 and phosphorene 12 . Indeed, in a recent theoretical study, Lee et al 10 observed no significant effects of SOC on the band structure of buckled nitrognene.…”

Section: Introductionmentioning

confidence: 99%

Spin–orbit coupling in buckled monolayer nitrogene

Jureczko

Kurpas

2022

Sci Rep

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Buckled monolayer nitrogene has been recently predicted to be stable above the room temperature. The low atomic number of nitrogen atom suggests, that spin–orbit coupling in nitrogene is weak, similar to graphene or silicene. We employ first principles calculations and perform a systematic study of the intrinsic and extrinsic spin–orbit coupling in this material. We calculate the spin mixing parameter $$b^2$$ b 2 , reflecting the strength of the intrinsic spin–orbit coupling and find, that $$b^2$$ b 2 is relatively small, on the order of $$10^{-6}$$ 10 - 6 . It also displays a weak anisotropy, opposite for electrons and holes. To study extrinsic effects of spin–orbit coupling we apply a transverse electric field enabling spin–orbit fields $$\Omega$$ Ω . We find, that $$\Omega$$ Ω are on the order of a single $$\mu$$ μ eV in the valence band, and tens to a hundred of $$\mu$$ μ eV in the conduction band, depending on the applied electric field. Similar to $$b^2$$ b 2 , $$\Omega$$ Ω is also anisotropic, in particular for the conduction electrons.

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Spin-orbit coupling in elemental two-dimensional materials

Cited by 62 publications

References 53 publications

Exciton g factors of van der Waals heterostructures from first-principles calculations

Exciton g factors of van der Waals heterostructures from first-principles calculations

Narrow-band high-lying excitons with negative-mass electrons in monolayer WSe2

Spin–orbit coupling in buckled monolayer nitrogene

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