Defect-Bound Exciton Complexes (A^-X)

• Defect-bound exciton complexes (A^-X) are excitonic states formed when an electron–hole pair is captured by a charged lattice defect, exhibiting altered binding energies and optical signatures.
• Advanced spectroscopic techniques and ab initio methods (e.g., GW corrections and Bethe–Salpeter equation) quantify how defect structures modify exciton binding and emission properties.
• These complexes enable tunable single-photon sources and quantum emitters in materials like TMDCs and perovskites, paving the way for innovations in optoelectronics and quantum nanophotonics.

Defect-bound exciton complexes, commonly denoted as $A^-X$, are optically active quasiparticle states in which an exciton (an electron–hole pair) is spatially localized at an atomic-scale lattice defect—frequently a charged impurity such as a donor or acceptor. Such complexes are prevalent in a broad range of semiconductors and quantum materials, including transition metal dichalcogenides (TMDCs), III-VI monochalcogenides, halide perovskites, hexagonal boron nitride (hBN), and silicon. The local defect imposes an electrostatic potential and provides discrete electronic states that can trap the exciton, often profoundly modifying its binding energy, wave function, and optical selection rules relative to bulk-like free excitons. Recent advances in spectroscopy and ab initio theory have revealed quantitative correlations between atomic defect structure and the emission properties of $A^-X$ complexes, cementing their role as essential entities in optoelectronics, valleytronics, and quantum nanophotonics.

1. Formation Mechanisms and Electronic Structure

Defect-bound exciton complexes originate from the interaction between a localized defect and the surrounding excitonic cloud created by photoexcitation or carrier injection. In the archetypal scenario, the defect (donor $D^+$ or acceptor $A^-$) generates a localized electronic state with energy $E_{\mathrm{def}}$, lying within the band gap or contiguous to the edges of the host conduction/valence bands. Excitation processes (e.g., valence band electron transition into the defect level) can lead to a charged defect center, which subsequently attracts the complementary carrier (hole or electron) via Coulomb interaction and forms the bound exciton state.

The binding can be conceptualized as a two-step process (Zhang, 2017):

1. Generation of a charged impurity state (e.g., $A^-$ by capture of an electron);
2. Coulomb capture of the oppositely charged carrier—leading to the full $A^-X$ bound complex.

The optical transition energy is reduced compared to the isolated defect state by the exciton binding energy: $E_{A,ex} = E_{\rm{def}} - E_A$ where $E_A$ is the Coulomb binding energy for the hole to the defect. Detailed many-body treatments show that the wave function of $A^-X$ involves mixed orbital character and spatial extension that encodes the specific topology and chemistry of the defect (Skiff et al., 6 May 2025, Alaerts et al., 30 May 2025).

2. Many-Body Effects and Exciton Binding Energy Renormalization

The presence of a defect significantly alters many-body interactions, most notably the excitonic binding energies and quasiparticle spectral positions. Standard DFT treatments, while useful for ground states, underestimate binding energies due to limited treatment of electron–hole correlations. Accurate calculation of defect-bound excitation spectra requires incorporation of GW corrections for quasiparticle renormalization and Bethe–Salpeter equation (BSE) solutions for excitonic effects (Bockstedte et al., 2010, Attaccalite et al., 2011).

For example, in SiC with carbon vacancies, GW corrections increase the effective Coulomb repulsion (Hubbard $U$) by ~0.3 eV relative to DFT, and BSE yields an excitonic red shift $E_{e{-}h} \approx 0.23\ \rm{eV}$ for the defect-bound optical threshold (Bockstedte et al., 2010). In monolayer TMDCs, the binding energies of defect-bound excitons often approach or exceed those of free excitons, and spatial localization further modifies oscillator strengths and radiative lifetimes (Refaely-Abramson et al., 2018, 2207.13472).

For perovskites and layered semiconductors, spectroscopy directly resolves discrete free and defect-bound excitonic peaks, with the binding energy difference defining the localization energy (e.g., $16\ \mathrm{meV}$ in CH$_3$NH$_3$PbI$_3$) (March et al., 2016).

3. Thermal Stability, Dissociation, and Comparison with Trionic Complexes

Thermal stability and dissociation behaviors of defect-bound exciton complexes are determined by the interplay of spatial localization, dielectric screening, and the defect potential. Analytic and Monte Carlo studies in TMDCs demonstrate that while the optical recombination line of $A^-X$ is much more red-shifted compared to trions ($X^-$), its overall three-body binding (dissociation) energy is \textit{lower}, making defect-bound complexes less robust to heating (Ganchev et al., 2014, Jadczak et al., 2016). Specifically, trions persist at higher temperatures (observable up to 240 K in WS$_2$), while donor-bound excitons dissociate above $\sim$80 K.

This counterintuitive property arises because the binding energy responsible for the optical shift reflects only two-particle (carrier–impurity) interactions, while the stability against thermal excitation involves the full three-body configuration (Ganchev et al., 2014). Dielectric environment further tunes the binding landscape: increased screening disproportionately weakens trion and $A^-X$ binding, altering their dissociation pathways (Kylänpää et al., 2015).

4. Optical Signatures, Spatial Localization, and Valley/Spin Hybridization

Defect-bound exciton complexes exhibit distinct optical fingerprints—sharp, low-energy emission lines in photoluminescence or scanning tunneling luminescence, often hundreds of meV below the free exciton (Huberich et al., 17 Oct 2025). Spatial mapping reveals nanoscale energy shifts correlated with local band bending and electrostatic potential fluctuations near charged defects (e.g., CH$_{\mathrm{S}}^-$ in MoS$_2$), providing atomically resolved correlations between defect structure, electronic states, and emission energy (Huberich et al., 17 Oct 2025).

Defects also induce hybridization and mixing with bulk excitons, reducing the valley-selective circular dichroism and modifying selection rules (Refaely-Abramson et al., 2018). In monolayer TMDCs, strong coupling between defect-bound and pristine excitons leads to valley depolarization and altered polarization plateaus at low temperatures.

For materials with topological band structures, defect-bound excitons localize onto ring-shaped in-gap states, resulting in wave functions with extended spatial profiles, reduced Coulomb interaction, and complex nodal structures sensitive to orbital composition and underlying topology (Skiff et al., 6 May 2025). These factors make defect-bound excitons key candidates for engineered quantum emitters with unique emission properties.

5. Theoretical Frameworks and Computational Treatment

Quantitative modeling of defect-bound exciton complexes requires advanced theoretical schemes. Many-body ab initio methods combine GW quasiparticle corrections and BSE for electron–hole interactions. For disordered or dilute systems, the T-matrix approach to disorder-averaged Green’s functions provides a computationally tractable route to capturing exciton–defect bound states without supercell-size limitations (Chan et al., 21 May 2025). The poles in the retarded Green’s function signal the formation of $A^-X$ complexes, which manifest as satellite peaks in both optical absorption and photoluminescence spectra.

Stark tuning of $A^-X$ complexes involves calculating the dipole moment change and polarizability of the defect-bound exciton; the large spatial extent of the bound state renders its emission energy and spectral shift highly susceptible to external or local fields, as illustrated for the T center in silicon (Alaerts et al., 30 May 2025).

Relevant theoretical relations include: $$E_{\rm exc} = (\varepsilon^{\rm QP}_{\rm defect} - E_{\rm ref}) - E_{e{-}h}$$

$$G(\omega)^{-1} = G_0(\omega)^{-1} - \Sigma^\mathrm{T}(\omega)$$

$\Delta E = \Delta \mu \cdot F$

where $G$ is the Green’s function, $\Sigma^T$ the disorder-averaged self-energy, $\Delta \mu$ the dipole moment change, and $E_{e{-}h}$ the excitonic binding energy.

6. Device Implications, Quantum Engineering, and Future Prospects

Defect-bound exciton complexes have emerged as central entities for quantum photonics and optoelectronic device engineering. Their unique emission characteristics—sharp, localized lines tunable by atomic defect type, electric field, and dielectric environment—enable deterministic creation of single-photon sources and control of quantum light emission (Huberich et al., 17 Oct 2025). Manipulation of defect type and distribution (e.g., via doping, irradiation, or chemical functionalization) provides a pathway for tailoring local excitonic landscapes, benchmarking device quality, and developing hybrid organic–inorganic platforms (Greben et al., 2019).

Flat-band materials and topological semiconductors offer expanded parameter space for controlling defect-bound excitonic dynamics and many-body interactions, facilitating the exploration of new quantum phases and correlated states (2207.13472, Skiff et al., 6 May 2025). Advances in spectroscopic resolution and atomically precise defect engineering are further paving the way for scalable quantum emitters and functional photonic circuitry based on $A^-X$ complexes.

7. Outstanding Challenges and Outlook

Although the fundamental physics of defect-bound exciton complexes is increasingly well understood, challenges remain regarding the quantitative prediction of binding energies, spatial widths, and field sensitivities—especially in systems with complex or topologically nontrivial bands. Discrepancies between theory and experiment in Stark shift measurements, for example, may arise from large polarizabilities and sensitivity to local field effects and disorder (Alaerts et al., 30 May 2025). Future work will require improved integration of atomistic, many-body, and disorder treatments, alongside advanced spectroscopic and scanning probe techniques to further elucidate the full scope of defect-bound excitonic phenomena in quantum materials.