Valley Excitons in TMDs

• Valley excitons in TMDs are quasiparticles formed by electron–hole pairs bound at inequivalent momentum valleys, exhibiting spin–valley locking and distinct optical selection rules.
• Experimental methods like polarization-resolved photoluminescence and Kerr rotation reveal binding energies (0.3–0.7 eV) and range from ultrafast (1–10 ps) to extended valley lifetimes in engineered heterostructures.
• These insights underpin opto-valleytronic applications such as valley-encoded excitonic interconnects, electrically tunable circuits, and valley Hall devices that enable room-temperature exciton transport.

Valley excitons in transition metal dichalcogenides (TMDs) are quasiparticles formed from electron–hole pairs bound by strong Coulomb interactions, where the electron and hole quantum states reside at distinct momentum-space valleys (typically the inequivalent K and K′ points in the Brillouin zone). The emergence of spin–valley locking, robust Coulomb effects, and distinct optical selection rules in TMDs enables the initialization, manipulation, and detection of exciton populations with well-defined valley indices ("valley polarization"). This valley degree of freedom is associated with Berry curvature and nontrivial selection rules, enabling phenomena such as the valley Hall effect, long-range exciton transport, and the optical readout of exciton valley quantum numbers. Recent advances cover both monolayer systems and van der Waals heterostructures, including room-temperature demonstrations of valley-polarized exciton transport and the exploitation of interlayer excitons for opto-valleytronics.

1. Fundamental Theory of Valley Excitons in TMDs

In monolayer group-VIB TMDs (MX₂; M = Mo, W; X = S, Se), the electronic band structure is characterized by direct bandgaps at K and K′ valleys. Broken inversion symmetry and strong spin–orbit coupling (SOC) result in spin–valley locking, yielding four fundamental exciton species: two bright (optically allowed, intra-valley) and two dark (spin- or momentum-forbidden, typically inter-valley) states (Yu et al., 2015, Hoang et al., 2021).

The minimal two-particle Hamiltonian for a valley exciton is

$$\hat{H}_\text{exc} = -\frac{\hbar^2}{2\mu}\nabla^2 - V_\mathrm{Coul}(r)$$

where the binding energy $E_b$ is typically 0.3–0.7 eV for monolayer intralayer excitons (Yu et al., 2015), and the effective dielectric screening is determined by substrate and encapsulation. Optical selection rules are valley-contrasting: right-circular (σ⁺) light excites K, left-circular (σ⁻) light excites K′ valley states.

The valley pseudospin can be represented as a pseudospin-½ describing the coherence and polarization between K and K′ population states. Exchange interactions, particularly the long-range electron–hole exchange, drive k-dependent pseudospin splittings (longitudinal–transverse splitting) (Glazov et al., 2015), with the BL Bloch sphere representation widely adopted for valley coherence concepts (Dufferwiel et al., 2018).

2. Intralayer vs Interlayer Excitons and Heterostructures

Intralayer excitons are formed by electron–hole pairs localized within the same monolayer, exhibiting strong oscillator strength and rapid radiative recombination. Exchange-driven intervalley scattering yields valley depolarization lifetimes in the 1–10 ps range at low temperature, preventing long-range valley transport (Huang et al., 2019).

Interlayer excitons in type-II heterostructures (e.g., MoS₂/WSe₂) are spatially indirect: electrons and holes reside in different atomic layers. The spatial separation decreases wavefunction overlap, suppresses exchange, and extends both population and valley lifetimes to hundreds of picoseconds or nanoseconds. For instance, MoS₂/WSe₂ interlayer excitons exhibit population lifetimes τₚₒₚ ≈ 1 ns and valley polarization up to P_circ ≈ 35% at low T, persisting as P_circ ≈ 5% at room temperature (Huang et al., 2019).

The interlayer exciton Hamiltonian takes a similar form,

$$\hat{H}_\mathrm{inter} = -\frac{\hbar^2}{2\mu}\nabla^2 - V_\mathrm{Coul}^\mathrm{inter}(r)$$

with reduced binding energy due to the interlayer spacing but lifetime extended by suppressed exchange. Photoluminescence peak emission is typically at wavelengths ~1130 nm (~1.05 eV).

3. Berry Curvature, Valley Hall Effect, and Anomalous Transport

Berry curvature $\Omega_z(\mathbf{k})$ acts as a valley-dependent effective magnetic field in K and K′ valleys, having equal magnitude and opposite sign. In the presence of an in-plane external force $\mathbf{F}$ (electrostatic, strain-gradient, or drift), valley excitons acquire an anomalous transverse velocity: $$\mathbf{v}_\perp = \frac{1}{\hbar} \mathbf{F} \times \mathbf{\Omega}(\mathbf{k})$$ This results in valley Hall transport, where excitons of opposite valley indices accumulate on opposite flanks transverse to their drift direction.

The low-temperature and room-temperature valley Hall effect has been demonstrated for interlayer excitons in MoS₂/WSe₂ heterobilayers. Polarization-resolved PL mapping shows that the PL intensity I_{σ+} and I_{σ–} peaks are displaced by up to Δ⊥ ≈ 0.41 μm (4 K) and Δ⊥ ≈ 0.30 μm (300 K), with propagation speeds v_drift ≈ 3 × 10² m/s (Huang et al., 2019).

4. Optical Manipulation, Readout, and Measurement of Valley Polarization

Initialization: Valley polarization is optically generated using circularly or linearly polarized light, exploiting the valley-contrasting selection rules (Yu et al., 2015). Linear polarization excites coherent superpositions, while circular polarization creates population imbalances (valley polarization).

Readout: Emission is resolved into σ⁺ and σ⁻ channels, and the degree of circular polarization, DOP or P_circ(x, y), is defined as: $$P_\text{circ}(x, y) = \frac{I_{\sigma^+}(x, y) - I_{\sigma^-}(x, y)}{I_{\sigma^+}(x, y) + I_{\sigma^-}(x, y)}$$ Confocal PL mapping tracks the spatial evolution of valley populations, allowing direct quantification of valley-polarized transport and the valley Hall separation (Huang et al., 2019, Ubrig et al., 2017).

Experimental Techniques: Methods include polarization-resolved photoluminescence, pump–probe Kerr rotation (Plechinger et al., 2017), and transient absorption. Kerr rotation directly tracks exciton valley pseudospin imbalance and its decay.

5. Valley Depolarization and Lifetime Engineering

Monolayer intralayer (direct) excitons are subject to fast depolarization via the long-range exchange interaction ("Maialle–Silva–Sham mechanism" (Glazov et al., 2015)), yielding τ_v ≈ 1–10 ps at low T. This is insufficient for functional valleytronic transport or logic. In contrast, interlayer, defect-localized, or hybridized excitons (formed via defect centers, strain, or moiré engineering) display dramatically prolonged τ_v—ranging from hundreds of ps (interlayer) up to μs for defect-bound excitons (Moody et al., 2018, Li et al., 2019).

The valley lifetime τ_v can thus be systematically extended by:

• Reducing electron–hole overlap (spatially separating carriers).
• Leveraging defect localization to suppress exchange.
• Engineering strain to induce hybridization with dark or defect-localized excitonic states, enhancing valley polarization by factors of 3–5 and increasing τ_v by up to two orders of magnitude (Kumar et al., 16 Feb 2025).

6. Opto-Valleytronic Applications and Room-Temperature Operation

Long-lived valley polarization and robust interlayer valley Hall transport at room temperature are foundational for TMD-based opto-valleytronic devices (Huang et al., 2019). Specific strategies and implications include:

• Valley-encoded excitonic interconnects: Valley Hall separation can route excitonic signals without charge current, suitable for all-optical logic or non-von Neumann architectures.
• Electrically tunable circuits: Interlayer excitons possess permanent out-of-plane dipole moments, enabling field-controlled drift, trapping, or dynamic routing.
• Patterned valley routers and valley beam-splitters: Strain or electrostatic potential landscapes can serve as valley-dependent circuit elements.
• Integration with photonic crystals and cavities: Strong coupling to photonic modes enables manipulation and readout of valley excitons with enhanced coherence and polarization control (Dufferwiel et al., 2018).
• Device metrics: Achievable propagation distances reach hundreds of nanometers, DOP values for interlayer excitons approach 35% (cryogenic) and remain ≈5% (room temperature), and valley Hall separations >300 nm have been measured at 300 K.

Compared to monolayer systems where rapid depolarization annihilates valley contrast at room temperature, TMD heterobilayers and interlayer excitons are unique in preserving both population and valley coherence, making them leading candidates for functional valleytronic platforms.

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References

• Room temperature interlayer exciton valley polarization and valley Hall effect (Huang et al., 2019)
• Valley excitons in two-dimensional semiconductors (Yu et al., 2015)
• Spin and valley dynamics of excitons in transition metal dichalcogenides monolayers (Glazov et al., 2015)
• Valley Dynamics of Excitons in Monolayer Dichalcogenides (Plechinger et al., 2017)
• Magnetically-Sensitive Valley Polarization Reversal and Revival of Defect-Localized Excitons in WSe2-WS2 (Li et al., 2019)
• Microsecond Valley Lifetime of Defect-Bound Excitons in Monolayer WSe$_2$ (Moody et al., 2018)
• Strain engineering of valley-polarized hybrid excitons in a 2D semiconductor (Kumar et al., 16 Feb 2025)