In-plane Propagation of Light in Transition Metal Dichalcogenide Monolayers: Optical Selection Rules

Abstract: The optical selection rules for inter-band transitions in WSe2, WS2 and MoSe2 transition metal dichalcogenide monolayers are investigated by polarization-resolved photoluminescence experiments with a signal collection from the sample edge. These measurements reveal a strong polarization-dependence of the emission lines. We see clear signatures of the emitted light with the electric field oriented perpendicular to the monolayer plane, corresponding to an inter-band optical transition forbidden at normal incidence used in standard optical spectroscopy measurements. The experimental results are in agreement with the optical selection rules deduced from group theory analysis, highlighting the key role played by the different symmetries of the conduction and valence bands split by the spin-orbit interaction. These studies yield a direct determination on the bright-dark exciton splitting, for which we measure 40 $\pm 1$ meV and 55 $\pm 2$ meV for WSe2 and WS2 monolayer, respectively.

• The paper identifies distinct polarization-dependent emissions, revealing forbidden z-dipole transitions during in-plane light propagation.
• It directly measures bright-dark exciton splitting in WSe2 (40 ± 1 meV) and WS2 (55 ± 2 meV), elucidating key band structure details.
• The findings enhance understanding of anisotropic optical transitions driven by spin-orbit coupling, advancing TMD-based optoelectronic research.

Exploration of Optical Selection Rules in Transition Metal Dichalcogenide Monolayers

This paper presents an in-depth exploration of optical selection rules governing the inter-band transitions in monolayers of transition metal dichalcogenides (TMDs), specifically WSe$_2$, WS$_2$, and MoSe$_2$. The study uses polarization-resolved photoluminescence (PL) experiments to examine the emission characteristics when light propagates parallel to the plane of the monolayer.

The results reveal a significant polarization dependence of the emission lines, leading to empirical validation of theoretical predictions based on group theory related to the symmetries of the conduction and valence bands modified by spin-orbit interactions. Notably, the experiments uncovered emissions corresponding to inter-band transitions forbidden under normal incidence, hence offering new insights into the band structure and exciton dynamics in TMD monolayers.

Key Findings

1. Polarization-Dependent Emission: The research identifies distinct luminescence lines for polarizations in-plane and perpendicular to the TMD monolayer plane. When emission was detected perpendicular to the layer, a new luminescence line emerged, corresponding to a $z$-dipole transition, which is typically forbidden at normal incidence.
2. Bright-Dark Exciton Splitting: The study provides direct measurements of the bright-dark exciton splitting, which are crucial for understanding the band structure and intrinsic optical properties of these semiconductor layers. Specifically, the bright-dark exciton splitting was measured as 40 ± 1 meV for WSe$_2$ and 55 ± 2 meV for WS$_2$. Interestingly, no such dark state signatures were detected for MoSe$_2$, supporting theoretical predictions that the dark exciton states are energetically higher than the bright states in this material.
3. Implications for TMD Monolayer Band Structure: These measurements offer a detailed insight into the anisotropies of the optical transitions in TMDs, affected by the interplay of strong spin-orbit coupling and broken inversion symmetry. This has crucial implications for future semiconductor applications, especially in realizing optoelectronic devices and understanding electro-luminescent properties.
4. Experimental Set-Up and Challenges: The TMD monolayers were encapsulated in hexagonal boron nitride (hBN) to ensure high-quality samples suitable for optical studies, emphasizing the need for precise experimental setups. With high numerical aperture objectives, the setup enabled efficient excitation and collection of luminescence, critical for these polarization-dependent studies.

Theoretical and Practical Implications

The continued investigation of TMD monolayers draws attention to the critical role of symmetry and spin-orbit interactions in defining their optical properties. By understanding subtle inter-band transitions and exciton dynamics, the research provides foundational insights that could lead to advanced functionalities in nanoscale photonic and optoelectronic devices.

Future research could explore the role of strain, electric field, or external perturbations on mixings of bright and dark states, aiming to modulate optical properties actively, which is pivotal for device integration and functionality enhancement. Moreover, resonant excitation studies could refine the understanding of exciton dynamics and interactions further, driving advancements in material science and technology centered around TMDs.