Breaking of valley degeneracy by magnetic field in monolayer MoSe2 (1407.0686v3)

Abstract: Using polarization-resolved photoluminescence spectroscopy, we investigate valley degeneracy breaking by out-of-plane magnetic field in back-gated monolayer MoSe$2$ devices. We observe a linear splitting of $-0.22 \frac{\text{meV}}{\text{T}}$ between luminescence peak energies in $\sigma{+}$ and $\sigma_{-}$ emission for both neutral and charged excitons. The optical selection rules of monolayer MoSe$_2$ couple photon handedness to the exciton valley degree of freedom, so this splitting demonstrates valley degeneracy breaking. In addition, we find that the luminescence handedness can be controlled with magnetic field, to a degree that depends on the back-gate voltage. An applied magnetic field therefore provides effective strategies for control over the valley degree of freedom.

• The paper demonstrates that an out-of-plane magnetic field induces a linear energy splitting of -0.22 meV/T between σ+ and σ− emissions, confirming valley degeneracy breaking.
• It reveals that combining magnetic fields with back-gate voltage tunes valley population imbalance, achieving over 50% circular polarization in photoluminescence.
• The study, validated by polarization-resolved spectroscopy and theoretical analysis, paves the way for practical valleytronic device applications.

Breaking of Valley Degeneracy by Magnetic Field in Monolayer MoSe$_2$

The paper "Breaking of valley degeneracy by magnetic field in monolayer MoSe$_2$" presents an investigative paper on the interaction of magnetic fields with the electronic properties of monolayer molybdenum diselenide (MoSe$_2$). Using polarization-resolved photoluminescence spectroscopy, the authors observe the effects of an external out-of-plane magnetic field on the breaking of valley degeneracy in this two-dimensional semiconductor material. The research explores the potential of magnetic fields as a tool for controlling the valley degree of freedom in transition metal dichalcogenides (TMDs), a property that distinguishes these materials from conventional semiconductors.

Monolayer TMDs like MoSe$_2$ exhibit unique electronic properties due to their non-zero bandgap and reduced dimensionality. They possess distinct valleys at the vertices of their hexagonal Brillouin zone, akin to graphene, but with more pronounced optical properties. The paper demonstrates how an out-of-plane magnetic field breaks this valley degeneracy by causing a linear energy splitting of $-0.22$ meV/T between the luminescence peak energies in $\sigma_+$ and $\sigma_-$ emissions for both neutral and charged excitons. This observation serves as evidence of valley degeneracy breaking through Zeeman splitting, attributed to the valley-dependent magnetic moments inherent to MoSe$_2$.

Significantly, the paper reveals that this valley splitting is not just a direct consequence of the magnetic field; it is modulated by the application of a back-gate voltage. With increasing back-gate voltage, the authors find an increased circular polarization in emitted photoluminescence, which can exceed 50% under certain conditions. This indicates a gate voltage control over valley population imbalance, suggesting interaction between electric fields from gating and magnetic field-induced valley splitting. These findings imply that the combination of electric and magnetic fields could be used to effectively manipulate valley populations in monolayer TMD materials.

The experimental results were supported by measurements on multiple devices, consistently showing the described valley splitting across samples. The authors relate their observations to theoretical models, particularly addressing the role of intercellular and atomic contributions to the magnetic moments associated with Bloch electrons in the valleys. They identify the dominant contribution to Zeeman splitting as arising from the atomic-scale $d$-orbital hybridization, validated by their calculated exciton valley g-factor, which agrees with the intrinsic orbital magnetic moment predictions.

This paper has substantial implications for the development of valleytronic devices, where the valley degree of freedom could play a role analogous to spin in spintronic devices. By showing that both magnetic and electric fields can dictate valley splitting and population, the work advances our understanding of valley control in TMDs, paving the way for practical applications such as novel optoelectronic devices that utilize the valley pseudospin.

Future research directions include exploring other TMD materials under similar experimental conditions to determine the universality of valley manipulation across different TMD and two-dimensional semiconductor systems. Additionally, further theoretical work will be crucial to fully comprehend the band structure and magnetic response, particularly in the context of multiband $\mathbf{k\cdot p}$ theories. These endeavors will enrich our capabilities to leverage the valley degree of freedom in practical device architectures.