Valley Excitons in TMDs: Physics & Applications

• Valley excitons in TMDs are tightly bound electron–hole pairs with a unique valley pseudospin, enabling selective optical addressing via circular polarization.
• Strong Coulomb interactions and reduced dielectric screening yield high binding energies up to 1 eV, which underpin robust valley-dependent optical transitions.
• External controls through dielectric, magnetic, and photonic engineering allow precise manipulation of valley excitons for advanced optoelectronic and valleytronic applications.

Valley excitons in transition metal dichalcogenides (TMDs) are bound electron–hole pairs whose internal state—specifically, their valley degree of freedom—offers a unique pseudospin distinct from electronic charge and real spin. In monolayer TMDs such as MoS₂, WS₂, WSe₂, and MoSe₂, these valley excitons are tightly bound due to reduced dielectric screening and large carrier effective masses, and they exhibit robust optical selection rules and strongly valley-dependent interactions. The interplay between valley-contrasting optical selection rules, strong Coulomb binding, long-range exchange, and symmetry-protected mechanisms underpins both fundamental valley dynamics and numerous applications in optoelectronics and valleytronics.

1. Electronic Structure and Valley Index

Monolayer TMDs possess direct band gaps at two nonequivalent corners of the hexagonal Brillouin zone: the $K$ and $K'$ points. These valleys serve as a good quantum number for quasiparticle excitations, conferring a "valley pseudospin" $\tau = \pm 1$ to electrons, holes, and excitons (Yu et al., 2015). Time-reversal symmetry enforces that the valleys $\pm K$ are related, but spin–orbit coupling further locks spins to valley, especially for states near the valence band edge, via spin–valley locking. The resulting band-edge excitons are thus labeled by their center-of-mass momentum, spin, and valley indices.

The structure of these excitons is affected by both the strong Coulomb attraction (driven by the 2D environment, which leads to binding energies up to 1 eV), and valley-dependent selection rules: optical transitions at $K$ ($K'$) couple exclusively to right ($\sigma^+$) [left ($\sigma^-$)] circular polarization (Yu et al., 2015, Caruso et al., 2021). Valley excitons may be selectively created, manipulated, or probed via polarized light.

2. Optical Selection Rules and Valley Addressability

Interband transitions in TMD monolayers obey strict valley selection rules arising from threefold lattice symmetry and time-reversal. The selection rules dictate:

• $K$ valley: couples to $\sigma^+$ (right-circular) polarized photons.
• $K'$ valley: couples to $\sigma^-$ (left-circular) polarized photons.

This valley–optical selectivity is formalized via field modes, $E_{R,L} \propto \bm{e}_\pm = (x \pm i y)/\sqrt{2}$ (Tokman et al., 2015). As a result, circularly polarized excitation selectively creates population in one valley, and linearly polarized excitation generates coherent superpositions, initializing valley coherence (Yu et al., 2015, Wang et al., 2016, Dufferwiel et al., 2018). The valley index is thus both addressable and detectable via the polarization of light.

3. Coulomb Interaction, Exciton Binding, and Exchange Effects

Monolayer TMDs host tightly bound neutral excitons ($X_0$), with unusually large binding energies due to strong Coulombic attraction and limited dielectric screening (Yu et al., 2015, Sun et al., 2016, Hong et al., 2021). The realistic interaction is often described using a screened 2D Keldysh potential, $V(\bm{q}) \sim 2\pi e^2/(\epsilon |\bm{q}|)$, where $\epsilon$ encodes the environmental screening.

The electron–hole exchange interaction induces both valley-independent energy shifts and valley-off-diagonal couplings. The exchange Hamiltonian for bright (spin-allowed) excitons takes the form (Glazov et al., 2015, Yu et al., 2015): $$\mathcal{H}_X(\mathbf{K}) = \begin{pmatrix} 0 & \alpha (K_x - i K_y)^2 \ \alpha (K_x + i K_y)^2 & 0 \end{pmatrix} = \frac{\hbar}{2}\; (\bm{\Omega}_{\mathbf{K}} \cdot \bm{\sigma})$$ where $\alpha(\mathbf{K})$ is the exchange coupling constant derived either via macroscopic electrodynamics (linked to the exciton radiative decay rate $\Gamma_0$) or $\mathbf{k} \cdot \mathbf{p}$ perturbation (Glazov et al., 2015). This long-range exchange is responsible for rapid intervalley mixing and relaxes valley polarization on sub-10 ps timescales, as confirmed experimentally by ultrafast photoluminescence and Kerr rotation techniques (Glazov et al., 2015, Sun et al., 2016, Dogadov et al., 22 Jul 2025).

4. Valley Dynamics: Coherence, Decoherence, and Control

The valley pseudospin of an exciton evolves under the effect of the exchange interaction, disorder, and scattering processes. The density matrix dynamics can be encoded in a pseudospin precession: $$\frac{\partial \mathbf{S}_{\mathbf{K}}}{\partial t} + \mathbf{S}_{\mathbf{K}} \times \bm{\Omega}_{\mathbf{K}} = \bm{Q}\{\mathbf{S}_{\mathbf{K}}\}$$ where $\mathbf{S}_{\mathbf{K}}$ is the pseudospin vector and $\bm{\Omega}_{\mathbf{K}}$ is the exchange field (Glazov et al., 2015). In the Dyakonov–Perel regime (strong scattering), valley polarization decays exponentially at a rate proportional to $\langle \Omega_{\mathbf{K}}^2 \tau_2 \rangle$. Experimentally, bright exciton valley polarization decays rapidly—$\sim 7$ ps in WSe₂—competing with short exciton lifetimes ($<2$ ps) (Sun et al., 2016, Glazov et al., 2015).

Valley coherence, prepared via linearly polarized light, is theoretically protected on the equator of the pseudo-Bloch sphere; its subsequent dephasing is due to the exchange field (which causes in-plane pseudospin precession) and extrinsic decoherence. Notably, the valley coherence can be externally tuned using out-of-plane magnetic fields, which introduce a Zeeman splitting of energy $g\mu_B B$, enabling coherent rotation of valley pseudospin by experimentally observable angles up to $30^\circ$ at $B = 9$ T (Wang et al., 2016, Dufferwiel et al., 2018).

5. Intervalley Coupling and Depolarization Mechanisms

Valley depolarization arises from a combination of processes:

• Phonon-assisted intervalley scattering: Efficiently transfers carriers between $K$ and $K'$, especially on subpicosecond timescales. This causes rapid loss of the A exciton circular dichroism and the appearance of an oppositely signed B exciton CD signal (Dogadov et al., 22 Jul 2025).
• Coulomb-mediated exchange and Dexter-like processes: Double spin-flip exchange and incoherent Dexter coupling between excitons in opposite valleys further drive valley depolarization with a temperature-dependent timescale (few ps) (Dogadov et al., 22 Jul 2025).
• Single spin-flip (Rashba spin–orbit): Particularly efficient for conduction band electrons (and hence the B exciton), accelerating valley depolarization through electric-field-induced spin hybridization (Dogadov et al., 22 Jul 2025).
• Intrinsic symmetry-protected states: Certain finite-momentum ("momentum-forbidden") dark excitons away from high-symmetry axes are immune from exchange-induced mixing, thus retaining high valley polarization, as established via ab initio Bethe–Salpeter calculations and symmetry analysis (Lo et al., 2020, Lo et al., 2021).

6. Dielectric, Magnetic, and Photonic Control of Valley Excitons

The excitonic dispersion and radiative decay of valley excitons are highly sensitive to the dielectric environment. The exchange-induced splitting and group velocity of longitudinal (L) and transverse (T) modes become tunable by:

• Dielectric patterning: Modifies Coulomb screening, induces waveguiding of L-branch excitons, and yields refractive behavior akin to Snell–Descartes law at dielectric interfaces (Yang et al., 2021).
• Magnetic field engineering: Inhomogeneous magnetic fields from magnetized nanostructures (e.g., in proximity to hBN) give rise to a valley-dependent Zeeman shift, spatially separating exciton populations by valley, creating valley-selective confinement that is optically addressable via circular polarization (Chaves et al., 7 Mar 2024).
• Optical cavities and metasurfaces: Embedding TMD monolayers inside microcavities realizes valley-coherent exciton-polaritons with enhanced and tunable radiative properties, valley coherence times, and the ability for nonthermal manipulation under strong coupling (Dufferwiel et al., 2018). Metasurface coupling yields valley-induced routing and separation both in real space and $k$-space, enabling photonic–valleytronic interfaces (Sun et al., 2018).
• Quantum-electrodynamical many-body effects: The full electromagnetic interaction, via Bethe–Salpeter and Schwinger–Dyson techniques, dynamically breaks the valley degeneracy and induces a macroscopically large exciton splitting (∼170 meV), equivalent to an effective Zeeman field ∼1400 T (Marino et al., 2017).

7. Valley Excitons in Device Physics and Advanced Applications

Valley excitons provide opportunities for:

• Valley-based information encoding (valleytronics): Utilizing the valley index as a robust information channel with ultrafast optical addressability (Yu et al., 2015, Dufferwiel et al., 2018).
• Valley Hall effect (VHE): Valley-polarized excitons and trions mediate the photoinduced VHE, with electrically detected Hall voltages dependent on Berry curvature inherited from constituent particles. Spatial mapping allows discrimination between neutral (excitonic) and charged (trionic) contributions (Ubrig et al., 2017).
• Hybrid photonic–valleytronic devices: E.g., excitonic waveguides, optoelectronic switches, quantum light sources—realized through environment-tunable, valley-coherent exciton–polaritons, metasurface manipulation, or dielectric waveguiding (Yang et al., 2021, Dufferwiel et al., 2018, Sun et al., 2018).
• Quantum information: Entanglement of excitons in $K$ and $K'$ valleys via linearly polarized single-photon absorption, with robust entanglement observable through photoluminescence polarization and suppressed photocurrent fluctuations (Tokman et al., 2015).
• Layer degree of freedom: In few-layer TMDs, coupling spin, valley, and layer indices creates new exciton types (e.g., "layer-excitons") with persistent high binding energy and tunable optical response (Das et al., 2019).

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Valley excitons in TMDs thus represent a distinctive quasiparticle platform, combining strong Coulombic binding, valley-pseudospin physics, and robust optical selection rules. Their manipulation and control—enabled by external fields, nanophotonic structures, and precision ultrafast techniques—are foundational to emerging concepts in valleytronics, hybrid optoelectronics, and quantum information science.