Exceptional Excitons

Non-Hermitian physics is reshaping our understanding of quantum systems by revealing states and phenomena without Hermitian counterparts. While non-Hermiticity is typically associated with gain-loss processes in open systems, we uncover a fundamentally different route to non-Hermitian behavior emerging from non-equilibrium correlations. In photoexcited semiconductors, the effective interaction between electrons and holes gives rise to a pseudo-Hermitian Bethe-Salpeter Hamiltonian (PH-BSH) that governs excitonic states in the presence of excited populations. Within this framework, we identify a previously unknown class of excitonic quasiparticles - exceptional excitons - corresponding to exceptional points embedded inside the electron-hole continuum. Exceptional excitons emerge at the onset of population inversion, and represent the strongly renormalized counterparts of the system’s equilibrium excitons. They are spatially localized, protected against hybridization with the continuum, and remain long-lived even in regimes where conventional excitons undergo a Mott transition. Crucially, exceptional excitons appear only when the PH-BSH is evaluated with non-thermal, resonantly generated carrier populations that support an excitonic superfluid. Ab initio results for monolayer WS_2 explicitly demonstrate this scenario and show that exceptional excitons can be realized with existing ultrafast pumping techniques. We also identify distinctive optical and photoemission signatures that enable their unambiguous detection.

💡 Research Summary

This paper introduces a fundamentally new route to non‑Hermitian physics that does not rely on engineered gain‑loss reservoirs but instead emerges intrinsically from many‑body correlations in a photo‑excited semiconductor. The authors formulate a pseudo‑Hermitian Bethe‑Salpeter Hamiltonian (PH‑BSH) that incorporates the non‑equilibrium electron and hole occupations f (k) through the asymmetric Pauli‑blocking factor (f v (k) − f c (k)) multiplying the screened Coulomb kernel K. In the low‑density, thermal regime the eigenvalues of the PH‑BSH are real and correspond to the familiar bound excitons. As the excitation density increases past the Mott threshold, the Pauli‑blocking factor changes sign for some k‑states, the effective electron‑hole attraction becomes repulsive, and the exciton eigenvalues split into complex‑conjugate pairs (E ± = E_R ± iE_I). This signals the conventional excitonic Mott transition: the bound exciton dissolves into the electron‑hole continuum.

The central insight of the work is that when the carrier distribution is not thermal but is instead generated by resonant pumping that creates an excitonic superfluid (a BCS‑like condensate of electron‑hole pairs), the situation changes dramatically. In this regime the occupations are given by f_sf (k) = P |φ (k)|², where φ (k) are the low‑energy solutions of a self‑consistent excitonic‑insulator equation (Eq. 2). Using first‑principles GW‑BSE calculations for a monolayer of WS₂, the authors demonstrate that such a superfluid distribution can be realized with realistic ultrafast laser pulses (≈100 fs, fluence ≈25 µJ cm⁻², photon energy resonant with the A‑exciton).

When the PH‑BSH is evaluated with the superfluid occupations, the exciton eigenvalue Eₓ = μ_c − μ_v acquires an algebraic multiplicity of two while the two corresponding eigenvectors coalesce into a single vector Ψ_sf. This is the hallmark of a second‑order exceptional point (EP): the Hamiltonian becomes defective, the eigenvalues become degenerate and real, and the eigenvectors merge. By interpolating between the thermal and superfluid distributions with a control parameter α (f = (1 − α) f_th + α f_sf), the authors track the evolution of the complex‑conjugate pair E ±. As α→1 the imaginary parts of E ± shrink to zero with a square‑root dependence, while the real parts converge to the same value. Three quantitative coalescence indicators—vector similarity ΔΨ(k), normalized overlap |Ψ* − Ψ|, and determinant of the eigenvector matrix |Det Ψ|—all approach their EP limits (ΔΨ→0, overlap→1, determinant→0), providing unambiguous proof of eigenvector collapse.

The resulting EP corresponds to a new quasiparticle the authors name “exceptional exciton”. Unlike ordinary excitons that disappear at the Mott transition, exceptional excitons persist as bound states embedded within the electron‑hole continuum. They remain spatially localized, are protected from hybridization with the continuum, and retain long lifetimes even when the system is deep in the population‑inverted regime. Their optical signatures include a sharp absorption peak at a real energy (the EP energy) accompanied by a small but finite imaginary part that yields asymmetric gain/loss line shapes. In time‑resolved ARPES, the EP manifests as a real‑energy feature inside the renormalized band gap with a characteristic asymmetric broadening, allowing direct experimental observation.

The paper also discusses practical experimental conditions. For WS₂, the critical density for population inversion is n_c ≈ 5 × 10¹² cm⁻². Pump frequencies slightly above the equilibrium A‑exciton energy (≈2.06 eV) are required to generate carrier distributions close enough to the superfluid limit to reach the EP basin. The authors’ real‑time HSEX simulations confirm that the superfluid distribution f_sf can be achieved with standard resonant pulses, and that the EP appears robust against realistic uncertainties in the carrier distribution.

In summary, the work demonstrates that non‑Hermitian exceptional points—specifically exceptional bound states (EBIC)—can arise naturally in driven quantum materials through many‑body correlations, without any external gain‑loss engineering. The identification of exceptional excitons opens a new interdisciplinary avenue linking non‑Hermitian topology, excitonic Bose‑Einstein condensation, and ultrafast semiconductor optics, and provides concrete predictions for optical and photoemission experiments that are within reach of current ultrafast spectroscopy technology.