Real-Time Valley Exciton Monitoring

• Real-Time Monitoring of Valley Excitons is the dynamic tracking of excitonic states with a valley quantum number in 2D semiconductors using polarization-resolved techniques.
• Time-resolved photoluminescence and two-dimensional coherent spectroscopy capture ultrafast valley dynamics, revealing key information about population, polarization, and decoherence processes.
• Integration with heterostructures, defect engineering, and chiral metasurfaces demonstrates practical control strategies that support quantum information protocols and high-speed optoelectronics.

Real-time monitoring of valley excitons refers to the direct and dynamic measurement of the population, polarization, and coherence properties of excitonic states that carry a valley quantum number in two-dimensional (2D) materials, notably transition metal dichalcogenide (TMDC) monolayers and heterostructures. This capability underpins research and technology developments in valleytronics, where the valley degree of freedom serves as an information carrier. Real-time monitoring leverages polarization selection rules, time-resolved photoluminescence (PL), advanced coherent spectroscopy, and control via both external fields and structured excitation, to capture and manipulate valley exciton dynamics on ultrafast timescales.

1. Valley Excitons: Quantum Structure and Optical Selection Rules

Valley excitons are Coulomb-bound electron–hole pairs formed at the band extrema (K or –K valleys) in the Brillouin zone of 2D semiconductors. Their existence is guaranteed by the broken inversion symmetry and strong spin–valley coupling in TMDCs such as WSe₂, MoSe₂, or MoS₂. Each valley carries an additional pseudospin quantum number, and the valley index acts as a robust label for the excitonic state. The electronic states at K and –K valleys possess opposite pseudospins, dictating chiral optical selection rules:

• Right-handed circularly polarized light (σ⁺) selectively excites exciton states in the +K valley.
• Left-handed circular polarization (σ⁻) selectively excites –K valley excitons.

The initialization of the valley state thus follows directly from the polarization of incident light (Jones et al., 2013).

The quantum state of an exciton under linearly polarized excitation is a coherent superposition of |K⟩ and |–K⟩:

$$|\psi\rangle = \frac{1}{\sqrt{2}} (|K\rangle + e^{i\phi}|-K\rangle),$$

where φ is the controllable relative phase. Valley pseudospin behaves as a SU(2) two-level system, conveniently represented on a Bloch sphere, with pure valley-polarized states at the poles and coherent superpositions on the equator.

2. Dynamical Monitoring: Time-Resolved and Polarization-Resolved Techniques

Dynamic tracking of valley exciton populations and coherences relies on state-of-the-art optical spectroscopy.

Time-resolved photoluminescence (TRPL) with circularly polarized excitation provides valley-selectivity in both formation and detection. In monolayer WSe₂, neutral excitons exhibit ultrafast PL decay (τ_X⁰ ≈ 4 ps), while trion emission persists for tens of picoseconds (Wang et al., 2014). The degree of circular polarization in the emission directly reflects the valley polarization:

$$P_c = \frac{I_{\sigma^+} - I_{\sigma^-}}{I_{\sigma^+} + I_{\sigma^-}},$$

allowing real-time extraction of valley population imbalance.

Further, polarization-resolved PL under linearly polarized excitation demonstrates direct correspondence between excitation and emission polarization—evidence for valley coherence. The orientation of the PL signal follows the incident polarization, confirming SU(2) valley pseudospin manipulation (Jones et al., 2013).

Advanced approaches, such as two-dimensional coherent spectroscopy (2DCS), enable direct measurement of valley coherence times. An alternating helicity pulse sequence transfers optical coherence into intervalley excitonic coherence, with the zero-quantum linewidth yielding the valley coherence decay rate (Γ_v), from which the coherence time is

$t_v = \hbar / \Gamma_v,$

with measured values ~100 fs for monolayer WSe₂ (Hao et al., 2015).

3. Scattering, Decoherence, and Many-Body Effects

The stability of valley exciton populations and coherence is primarily limited by intervalley scattering and decoherence mechanisms. The dominant processes include:

• Electron–hole exchange interaction: Acts as an effective in-plane magnetic field (Ω), causing valley pseudospin precession. At finite center-of-mass momentum Q,

$$\mathbf{\Omega}(Q) = 2J_Q (\cos 2\phi, \sin 2\phi, 0)/\hbar,$$

where J_Q is linear in |Q|, leading to rapid dephasing of the valley coherence ensemble (Hao et al., 2015).

• Coulomb exchange and exciton–exciton interactions: At high excitation densities, these interactions decrease the intervalley scattering time (down to ~20 ps) due to exciton heating and many-body screening (Mitioglu et al., 2015). Exciton–exciton exchange further drives density-dependent valley depolarization, with decay rate scaling as $1/\tau_v \propto J_{xx} n_X / \hbar$ (Mahmood et al., 2017).

The measured ultrafast intervalley depolarization, particularly in neutral excitons, places constraints on the timescales for coherent valley manipulation and readout. Strategies such as reducing excitation density, engineering interlayer excitons with long lifetimes, or creating defect-bound excitons enable substantial extension of valley polarization lifetime into the nanosecond or even microsecond regime (Rivera et al., 2016, Moody et al., 2018).

4. Real-Time Control with Advanced Photonic and Electronic Structures

Progress in real-time valley exciton monitoring has benefited from the integration of monolayer TMDCs into complex heterostructures and nanophotonic environments:

• Heterostructures and Interlayer Excitons: Vertical stacks such as WSe₂/MoSe₂ yield interlayer excitons with valley lifetimes ~40 ns, orders of magnitude longer than monolayer counterparts. The spatial dynamics can be directly imaged, with valley drift–diffusion modeling capturing the evolution and ring formation of the polarization pattern, reflecting density-dependent exchange interactions (Rivera et al., 2016). van der Waals heterostructures with precise momentum alignment achieve >80% valley polarization and suppressed depolarization (Zhang et al., 2019).
• Defect Engineering: Electron beam irradiation introduces chalcogen vacancies in WSe₂, creating defect-bound excitons with recombination lifetimes approaching 200 ns and valley polarization persisting for ≥1 μs. This provides both a robust information carrier and a platform for engineered quantum emitters (Moody et al., 2018).
• Chiral Metasurfaces and Structured Light: Integration with dielectric chiral metasurfaces enables optical addressability and real-time monitoring of valley-selectivity via photonic design. Structured light (e.g., optical vortex beams) offers external tunability of exciton momentum, allowing the dynamic probing of valley relaxation and spin-flip scattering rates through steady-state polarization-resolved PL techniques (Guddala et al., 2018, Pattanayak et al., 2022, Pattanayak et al., 2022).
• Waveguide Coupling: Direct access to spin-dark and momentum-dark exciton states via out-of-plane dipole transitions is achieved using integrated photonic waveguides. This supports efficient collection and resonant population of dark excitons, which promise extended valley lifetimes (Wu et al., 2020).

5. Non-Hermitian Dynamics and Topological Signatures

Recent theoretical developments emphasize the non-Hermitian character of valley excitons in driven-dissipative systems. Incorporating optical pumping (gain) and intrinsic decay (loss) into the excitonic Hamiltonian leads to parity-time (𝒫𝒯) symmetry breaking and nontrivial topological phenomena (Wang et al., 29 May 2024):

$$H_{ex}({\bf Q}) = \begin{bmatrix} iP/2 & J(Q/K)e^{-2i\phi} \ J(Q/K)e^{2i\phi} & -iP/2 \ \end{bmatrix}$$

This framework predicts the emergence of anomalously valley-polarized excitonic states with elliptically polarized emission—distinct from the Hermitian (coherent, linearly polarized) expectation. In the 𝒫𝒯-broken regime (typically at small momenta), valley polarization supersedes coherence, consistent with widespread experimental observation of strong circular dichroism in helicity-resolved emission. The appearance of exceptional points—where polarization axes of eigenstates become parallel—leads to spectral and emission anomalies exploitable for momentum-resolved valley state readout.

Furthermore, nonzero Berry curvature arises for excitons in the 𝒫𝒯-broken regime, resulting in topological excitonic Hall transport. This topological signature is accessible via emission mapping under gradients of chemical potential or temperature, and constitutes a new diagnostic and control channel for valleytronic applications.

6. Applications, Challenges, and Technical Implications

Real-time monitoring of valley excitons has profound implications:

• Quantum information protocols: The ability to initialize and read out valley states on ultrafast timescales, combined with extended lifetimes achieved by defect engineering, heterostructure design, and excitation engineering, supports the use of valley degrees of freedom as qubits or memory elements.
• Valley Hall effect and transport: Dynamic tracking of valley exciton distribution and polarization enables direct observation of Hall currents and nonlocal effects, relevant for optoelectronic circuits.
• High-speed optoelectronics: Ultrafast optical manipulation—via the optical Stark or Bloch–Siegert effects—permits sub-50 fs switching, underpinning valleytronic logic at multiterahertz frequencies (Slobodeniuk et al., 2022).

Technical challenges remain, including mitigating ultrafast decoherence due to exchange interaction, distinguishing among various excitonic species (bright, dark, intervalley, defect-bound), overcoming spectral wandering, and maintaining high-fidelity initialization and detection under device-relevant conditions.

The development of advanced photonic and electronic integration—chiral metasurfaces, waveguide coupling, hBN encapsulation, precision alignment—provides a rapidly evolving toolkit for addressing these challenges, advancing both the understanding and exploitation of real-time valley exciton dynamics in 2D semiconductors.