Valley Splitting and Polarization by the Zeeman Effect in Monolayer MoSe2 (1409.8538v1)

Abstract: We have measured circularly polarized photoluminescence in monolayer MoSe2 under perpendicular magnetic fields up to 10 T. At low doping densities, the neutral and charged excitons shift linearly with field strength at a rate of $\mp$ 0.12 meV/T for emission arising, respectively, from the K and K' valleys. The opposite sign for emission from different valleys demonstrates lifting of the valley degeneracy. The magnitude of the Zeeman shift agrees with predicted magnetic moments for carriers in the conduction and valence bands. The relative intensity of neutral and charged exciton emission is modified by the magnetic field, reflecting the creation of field-induced valley polarization. At high doping levels, the Zeeman shift of the charged exciton increases to $\mp$ 0.18 meV/T. This enhancement is attributed to many-body effects on the binding energy of the charged excitons.

• The paper demonstrates that a perpendicular magnetic field induces a linear Zeeman shift in valley exciton energies, measured at ∓0.12 to ∓0.18 meV/T.
• The paper shows that valley polarization arises from field-induced emission imbalances, confirming the lifting of valley degeneracy.
• The paper reveals that many-body interactions at high doping levels alter trion binding energies, paving the way for advanced valleytronic applications.

Valley Splitting and Polarization by the Zeeman Effect in Monolayer MoSe₂

This paper presents an investigation into the valley-dependent Zeeman effect in monolayer molybdenum diselenide (MoSe₂). Using magneto-photoluminescence (magneto-PL) spectroscopy, the researchers explore how a perpendicular magnetic field induces changes in the energies of valley excitons, characterized by the lifting of valley degeneracy and the creation of valley polarization.

Research Context and Methodology

Monolayer MoSe₂ features two notable valleys, K and K', in its Brillouin zone, which are otherwise energetically degenerate and intricately linked by time-reversal symmetry. This paper builds on theoretical predictions regarding valley magnetic moments, thereby providing a unique experimental setup for analyzing valleytronic phenomena.

The authors use mechanical exfoliation to prepare monolayer MoSe₂, while electronic dopants are introduced via electrostatic gating. Under variable magnetic fields up to 10 T at low temperatures (10 K), they examine the photoluminescence of neutral and charged excitons. Notably, this research introduces a novel approach by controlling charge density, thereby achieving a detailed characterization of valley electronic states.

Key Findings

1. Valley Splitting and Zeeman Shifts: The paper affirms the linear relationships between magnetic field strength and energy shifts in both neutral and charged excitons, with Zeeman shifts measured at ∓0.12 meV/T for low doping and ∓0.18 meV/T for high doping. The opposite signs of the shift for K and K' valleys confirm the lifting of valley degeneracy.
2. Valley Polarization: Field-induced modifications in emission intensities indicate the formation of equilibrium valley polarization. The resulting imbalance in charge distribution across valleys is significant when considering the valleytronic applications of these materials.
3. Many-Body Effects on Trion Binding Energy: Enhanced Zeeman shifts at high doping levels suggest significant many-body interaction effects, modifying the trion binding energy due to elevated carrier densities.

Analysis and Theoretical Implications

While confirming theoretical models based on two-band tight-binding descriptions, this paper extends the understanding of magnetic moment contributions from atomic orbitals, carrier spins, and wavefunctions. The results fit well within the framework of existing theoretical predictions, offering empirical support to hypothesized valley-dependent magnetic phenomena.

The findings reveal that intervalley trions, stabilized by exchange interactions, dominate the emission, shedding light on the intricate dynamics between valley configurations and magnetic field influences. This has profound implications for valley-selective optoelectronic applications, suggesting possibilities for enhanced valley control methodologies.

Prospects for Future Research

The immediate implications of this work help pave the way for advanced valleytronic systems, offering intriguing possibilities like the control of intervalley processes and the development of valley-based quantum information technologies. Future research could explore non-linear field effects or expand to other transition metal dichalcogenides (TMDCs) with different valence band structures, probing further into temperature effects and spin-orbit coupling implications. Additionally, leveraging these findings for the synthesis of polymers or composites integrating monolayer MoSe₂ represents a promising path toward cutting-edge optoelectronic devices.

In conclusion, the insights presented in this paper advance the comprehension of valley-dependent phenomena under applied magnetic fields, offering theoretical validation and practical routes toward exploiting the valley degree of freedom in modern materials science.