Effect of spin-orbit interaction on the excitonic effects in single-layer, double-layer, and bulk MoS2 (1306.4257v2)

Abstract: We present converged ab-initio calculations of the optical absorption spectra of single-layer, bi-layer, and bulk MoS$_2$. Both the quasiparticle-energy calculations (on the level of the GW approximation) and the calculation of the absorption spectra (on the level of the Bethe-Salpeter equation) explicitly include spin-orbit coupling, using the full spinorial Kohn-Sham wave-functions as input. Without excitonic effects, the absorption spectra would have the form of a step-function, corresponding to the joint-density of states of a parabolic band-dispersion in 2D. This profile is deformed by a pronounced bound excitonic peak below the continuum onset. The peak is split by spin-orbit interaction in the case of single-layer and (mostly) by inter-layer interaction in the case of double-layer and bulk MoS$_2$. The resulting absorption spectra are thus very similar in the three cases but the interpretation of the spectra is different. Differences in the spectra can be seen around 3 eV where the spectra of single and double-layer are dominated by a strongly bound exciton.

Analysis of Spin-Orbit Interaction on Excitonic Effects in MoS$_2$

The paper "Effect of spin-orbit interaction on the excitonic effects in single-layer, double-layer, and bulk MoS$_2$" presents a comprehensive investigation into the role of spin-orbit coupling in modifying the optical properties of molybdenum disulfide (MoS$_2$) across different thickness regimes. This research uses advanced ab initio calculations to extract the optical absorption spectra and elucidates the interaction dynamics in single-layer, double-layer, and bulk forms of MoS$_2$.

Computational Approach

The authors employed converged ab initio methods focusing on quasiparticle-energy calculations within the GW approximation and optical spectra through the Bethe-Salpeter equation, integrating spin-orbit coupling in both cases. The utilization of full spinorial Kohn-Sham wave functions as input is a critical aspect of the paper, ensuring accurate portrayal of spin-orbit effects on excitonic behavior. By choosing a dense k-point sampling, they effectively addressed the convergence challenges typically inherent in Bethe-Salpeter calculations, contributing to more reliable optical spectra.

Key Findings and Numerical Results

1. Bandgap Characteristics:
   • A significant variance in bandgap nature is noted between single-layer and multilayer structures. Single-layer MoS$_2$ exhibits a direct bandgap of approximately 2.41 eV (GW corrected), whereas double-layer and bulk forms possess indirect bandgaps due to interlayer interactions modifying band edge positions.
   • Spin-orbit coupling results in valence band splitting at the $K$ point. Quantified splits of 112.0 meV (single-layer), 160.0 meV (double-layer), and 230.6 meV (bulk) were established through detailed GW calculations.
2. Optical Absorption Spectra:
   • Despite the bandgap differences, the optical absorption spectra are characterized by pronounced excitonic peaks which remain remarkably stable across different layers. The shift in oscillator strength into excitonic peaks below the continuum onset is attributed to excitonic binding energies which largely offset bandgap corrections.
   • Distinctive A and B peaks are linked directly to transitions at the $K$ point—unique to the spin-orbit split valence band maximum.
3. Excitonic Features:
   • Notably, the paper identifies the presence of a strong excitonic peak at approximately 3.0 eV, especially in single-layer MoS$_2$, which is anticipated based on transitions from the joint density of states along the $\Gamma-K$ high-symmetry line.
   • Excitonic wave functions demonstrate extensive spread in-plane but are confined to individual layers in multi-layered structures, highlighting negligible inter-layer excitonic coupling due to the van der Waals gap.

Implications and Future Directions

The insights provided by this paper have both theoretical and practical implications. The detailed understanding of spin-orbit interaction effects and excitonic properties of MoS$_2$ reinforces its potential in optoelectronic applications, including spintronics and valleytronics. The ability to tailor excitonic interactions based on layer thickness could lead to improved designs in layered semiconductor devices.

Future research may explore modulating these excitonic effects through strain engineering or external perturbations such as electric fields. Such studies would advance MoS$_2$'s adaptability in various technological realms including flexible electronics and quantum computing applications.

In summary, this paper offers a critical examination of spin-orbit interaction effects on excitonic phenomena within MoS$_2$, contributing valuable insights to the ongoing development of advanced materials with tunable electronic and optical properties.