Pierre Lechifflart*,
Raisa-Ioana Biega and
Linn Leppert
*
MESA+ Institute for Nanotechnology, University of Twente, 7500 AE, Enschede, The Netherlands. E-mail: p.lechifflart@utwente.nl; l.leppert@utwente.nl
First published on 29th September 2025
Three-dimensional metal halide double perovskites such as Cs2AgBiBr6 exhibit pronounced excitonic effects due to their anisotropic electronic structure and chemical localization effects. Their two-dimensional derivatives, formed by inserting organic spacer molecules between perovskite layers, were expected to follow well-established trends seen in Pb-based 2D perovskites, namely, increasing exciton binding energies with decreasing layer thickness due to enhanced quantum and dielectric confinement. However, recent experimental and computational studies have revealed anomalous behavior in Ag/Bi-based 2D perovskites, where this trend is reversed. Using ab initio many-body perturbation theory within the GW and Bethe–Salpeter Equation frameworks, we resolve this puzzle by systematically comparing experimental structures with idealized models designed to isolate the effects of octahedral distortions, interlayer separation, and stacking. We find that structural distortions, driven by directional Ag d orbital bonding, govern the momentum-space origin and character of the exciton, and are the primary cause of the observed non-monotonic trends. Furthermore, we explore how interlayer distance and stacking influence band gaps and exciton binding energies, showing that, despite different chemistry, the underlying confinement physics mirrors that of Pb-based 2D perovskites. Our results establish design principles for tuning excitonic properties in this broader class of layered, lead-free materials.
Layered organic–inorganic halide perovskites are quasi-twodimensional (2D) derivatives of the three-dimensional (3D) halide perovskites, which consist of alternating layers of corner-sharing metal–halide octahedra and organic molecules, which can be assembled in myriad of different structures, depending on the composition, structure, and bonding interactions of the organic and inorganic sublattices.16 Since the electronic coupling between metal–halide octahedra is disrupted by the organic sublattice in these materials, their photophysical properties are dictated by quantum and dielectric confinement effects17 and thus vary strongly with interlayer distance (which can be controlled through the length of the molecular cation constituting the organic sublattice),18 the dielectric constant of the organic sublattice,19,20 the stacking pattern of adjacent inorganic layers,21 and most notably, the thickness of the inorganic sublattice,22,23 typically denoted by n, the number of metal–halide octahedra in the out-of-plane direction. For example, in lead-based layered perovskites, A2A′n−1PbnX3n+1, where A is, e.g., butylammonium (BA) or phenethylammonium (PEA), pronounced changes in the optical band gap and exciton binding energies have been reported based on experiments and computational modelling,24–26 supported by microscopic theories of quantum and dielectric confinement effects in these materials.23,27,28 These studies show that the exciton binding energy decreases significantly with increasing n, approaching the exciton binding energy of bulk ABX3 with an exponential dependence on n.
Layered derivatives of Cs2AgBiBr6 were first reported in 2018 as (BA)4 AgBiBr8 (corresponding to n = 1 and denoted by 1exp in the following) and (BA)2 CsAgBiBr7 (n = 2 and denoted by 2exp).29 First-principles density functional theory (DFT) calculations of these materials showed that dimensional reduction leads to a transition from an indirect (n ≥ 2) to a direct band gap (n = 1) due to the two-dimensional symmetry of the lattice, the effect of spin–orbit coupling and structural distortions.29,30 This observation is reminiscent of the indirect – direct transition observed in some transition metal dichalcogenides upon exfoliation to the monolayer limit.31 In Ref. 29 1exp and 2exp were shown to both exhibit sharp particle-like features in their optical absorption spectra, at similar energies. Furthermore, polycrystalline powders of 1exp and 2exp had almost identical (yellow) color. These findings suggested the puzzling observation that confinement effects are less pronounced in these systems compared to their Pb-based counterparts.
Similar conclusions were drawn by Pantaler et al. for (PEA)4 AgBiBr8 (n = 1) and (PEA)2 CsAgBiBr7 (n = 2),32 based on experimentally obtained exciton binding energies and rationalized with first-principles calculations using the Bethe–Salpeter Equation (BSE) with electronic band energies from DFT.32 Full GW + BSE calculations of experimental structures of 1exp and 2exp were reported by Palummo et al. who predicted exciton binding energies of 700 meV for 1exp and 970 meV for 2exp,33 and similar absorption onsets, in line with experimental results,34,35 but without providing an explanation for these counterintuitive trends.
Here, we show that confinement effects in 2D Ag/Bi perovskites are similar to those in Pb-based 2D perovskites and provide an explanation for their anomalous exciton binding energy trends. In stark contrast to their Pb-based counterparts, excitonic properties of 2D Ag/Bi perovskites are highly sensitive to structural distortions, which differ between systems with n = 1 and n = 2. As a consequence, excitons in n = 1 and n = 2 Ag/Bi double perovskites arise from different reciprocal space points and have different character. We demonstrate this by systematically investigating the electronic bandstructures and excitonic effects using first-principles calculations based on DFT, and the GW and BSE approaches, and use model systems to disentangle the effects of the molecular A site, structural distortions, interlayer distance, and interlayer stacking. Furthermore, our calculations demonstrate the rich diversity of electronic and excitonic properties that can be achieved by varying interlayer distance and stacking motifs, for example with different organic sublattices.
We start by calculating the electronic structure, optical absorption spectra, and exciton binding energies of 1exp and 2exp. The electronic properties were first calculated with DFT using the Perdew–Burke–Ernzerhof (PBE) functional36 as implemented in QuantumESPRESSO,37–39 including spin–orbit coupling self-consistently. For these calculations, we used experimental structures determined using X-ray crystallography at 100 K from ref. 29, as shown in Fig. 1a. Both 1exp and 2exp are 2D perovskites of the Ruddlesden–Popper form, i.e., with a shift along half the in-plane diagonal between adjacent perovskite layers. Each layer contains alternating corner-sharing Ag and Bi octahedra. As noted before, the Ag–Br octahedra in 1exp and 2exp are strongly distorted as compared to those in cubic Cs2AgBiBr6.29 Terminal Ag–Br bonds, i.e., those that are in the vicinity of the organic sublattice, are shorter, whereas both equatorial and bridging Ag–Br bonds are elongated as compared to the Ag–Br bonds in Cs2AgBiBr6. A more detailed discussion of these structural distortions can be found in the SI.
We define the interlayer distance in these and all other structures mentioned in the following as d = (dOOP − 2dBr–Br)/2, where dOOP is the out-of-plane distance between equivalent layers, and the width of the inorganic layer is defined as the average distance between terminal Br atoms dBr–Br, as indicated in Fig. 1a. Using these definitions, the interlayer distance of both 1exp and 2exp is d ∼ 7.8 Å.
We then used the GW + BSE approach to calculate the electronic band gaps and linear optical absorption spectra of Cs2AgBiBr6, 1exp, and 2exp, as shown in Fig. 1b. These calculations were performed with the BerkeleyGW package, using PBE eigenvalues and eigenfunctions, including spin–orbit coupling (SOC), to construct the G0W0 self-energy, followed by solution of the BSE. We find that 1exp has a direct gap at Γ, whereas 2exp and Cs2AgBiBr6 are indirect gap semiconductors, in agreement with previous calculations and models.29,30,33,35 G0W0@PBE + SOC direct band gap energies are reported in Table 1. Fig. 1b shows that while Cs2AgBiBr6 exhibits one excitonic peak arising from the X point,40,41 1exp has two distinct excitonic peaks below the onset of the independent-particle absorption, separated by approximately 0.5 eV. These correspond to two excitonic states, arising from transitions at Γ (lower energy) and A (higher energy), respectively.
System | G0W0@PBE direct gaps (eV) | ε∞ | Exciton binding energy (meV) | Exciton | ||||
---|---|---|---|---|---|---|---|---|
A | Γ | B | Dark | Bright | Origin | Extent (Å) | ||
1exp | 3.47 | 2.96 | 3.97 | 3.03 | 736 | 654 | Γ | 8.14 |
2exp | 3.00 | 3.10 | 3.27 | 3.63 | 893 | 734 | A | 8.24 |
1model | 3.06 | 2.78 | 3.80 | 3.22 | 664 | 608 | Γ | 14.6 |
2model | 3.02 | 2.76 | 3.64 | 3.77 | 592 | 513 | Γ | 11.0 |
Cs2AgBiBr6 | 2.16 (X) | 2.23 | 2.96 (L) | 5.41 | 260 | 181 | X | 7.52 |
2exp also shows two distinct peaks coming from two different excitonic states, separated by approximately 0.6 eV. This time, the lower-energy peak comes from transitions at A, while the higher-energy one comes from transitions at Γ. More evidence for this inversion is shown in Table 1 and Fig. 2 and discussed later. The onset of absorption of 1exp and 2exp is at similar energies, in agreement with experimental observations.29 However, we note that our G0W0@PBE + BSE calculations underestimate the energy of the experimental peaks by ∼0.5–0.8 eV, which is typical for G0W0 calculations of halide perovskite band gaps based on semilocal DFT.42,43 Our absorption spectra are in good agreement with computational results by Palummo et al., with differences arising from the use of evGW and different numerical parameters in ref. 44. All relevant computational parameters and convergence tests, as well as a discussion of the differences with ref. 44 can be found in the SI.
To understand the counterintuitive trends in the band gaps and exciton binding energies of 1exp and 2exp, we constructed several model systems (see SI). First, we replaced the organic cations in the experimental structures with Cs while preserving their structural distortions. Since Cs-derived states do not contribute near the band edges, the resulting band structures remain nearly identical to those of 1exp and 2exp. The reduced dielectric screening due to the absence of organic molecules increases exciton binding energies but preserves the qualitative trends observed in the experimental systems (Table S2).
Conversely, these trends change in the model structures 1model and 2model, where the organic cations are replaced by Cs and all octahedral distortions are removed. These structures feature uniform Ag–Br and Bi–Br bond lengths, identical to those in Cs2AgBiBr6 (Fig. 2c). Their DFT-PBE + SOC band structures (Fig. 2a) show nearly degenerate valence band maxima at Γ and A, derived from Ag dz2 and dx2−y2 orbitals, and a direct band gap at Γ with similar orbital character. Br p contributions to the band edges are similar across all structures and omitted from further discussion (Fig. 2b). In contrast, the shorter terminal Ag–Br and longer equatorial and bridging Ag–Br bonds of 2exp lead to significant changes in the bandstructure, in particular a pronounced lowering of the valence band at Γ and the conduction band at B, leading to an indirect band gap in 2exp.29,30 Thus our first main result is that octahedral distortions qualitatively change the band-edge positions, leading to a shift of the lowest-energy direct transition from Γ in 1exp to A in 2exp.
We compute exciton binding energies for the lowest excitons in 1model and 2model using G0W0@PBE + SOC and BSE (Table 1). Our second key result is that the binding energies decrease with increasing layer thickness n, consistent with quantum confinement in 2D perovskites, though they remain larger than in Pb-based analogs. This effect is also evident in the absorption spectra, with a redshift of ∼0.25 eV in 1model relative to 2model (Fig. S3). The spatial extent of the exciton, estimated from the average electron–hole separation,46 is larger in the model structures, consistent with enhanced dielectric screening and reduced exciton binding (see Table 1 and SI for details).
These results demonstrate that the anomalous trends in exciton binding energies in the experimental systems arise from a change in their momentum-space origin: the lowest-energy exciton in 2exp arises from a direct transition at the A point, whereas in 1exp it derives from Γ. This shift is induced by octahedral distortions – as discussed in detail in ref. 30 and results in a qualitatively different exciton due to symmetry and orbital-character differences at the A and Γ points. We have previously observed a similar, but composition-driven, transition in 3D Cs2AgBi(IxBr1−x)6, where the lowest-energy direct transition shifts from L to Γ with increasing iodine content due to changes in Ag d orbital hybridization.45
Having established the role of structural distortions, we now turn to the effect of interlayer distance and stacking pattern, i.e., Ruddlesden–Popper (RP) vs. Dion–Jacobson (DJ) stacking, on excitonic properties. In real 2D halide perovskites, interlayer spacing is typically controlled via organic cations, which also contribute significantly to dielectric screening.47,48 This means that any variation in interlayer distance using different molecules necessarily conflates geometric and dielectric effects. To disentangle these contributions, we use idealized model structures in which Cs replaces the organic spacers and all octahedral distortions are removed. In this case, the dielectric screening is significantly reduced and varies with interlayer distance, because the long-range Coulomb interaction is no longer screened.
We vary the interlayer spacing d for 1model and 2model in both RP and DJ stacking (Fig. 2c and d). The resulting direct band gaps and exciton binding energies are shown in Fig. 3. In all cases, we observe that increasing d leads to stronger exciton binding and wider gaps, linearly in RP and as a fractional power law in DJ stacking. The lowest-energy direct transition remains at Γ, and 1model consistently shows higher binding energies than 2model, reinforcing that the anomalous trends in the experimental systems stem from octahedral distortions rather than confinement effects.
At large interlayer distances, the stacking motif has no effect on exciton binding, as interlayer interactions vanish and the excitons are confined to a single 2D layer. At smaller separations, electron and hole wavefunctions become more delocalized across layers, reducing both quantum and dielectric confinement and thereby lowering the exciton binding energy. In this regime, stacking becomes important: DJ stacking consistently yields lower binding energies than RP, regardless of layer thickness. This is due to the in-plane alignment of terminal Br atoms in DJ structures, which enhances Br p-orbital overlap as the layers approach. At very small distances, this overlap becomes so pronounced that the exciton binding energy drops below that of 3D Cs2AgBiBr6, where Br atoms are shared rather than stacked. This effect is likely an artifact of fixed atomic positions in our simulations; in reality, octahedral tilting would reduce Br–Br overlap. These trends agree with recent results on Pb-based 2D perovskites with n = 1,49 confirming that excitons in both systems are shaped by similar quantum and dielectric confinement effects, despite their differing binding strengths and spatial extent.
In conclusion, we have used ab initio GW + BSE calculations of experimental and model structures to investigate the effects of structural distortions on the optoelectronic properties of 2D Ag/Bi double perovskites. These distortions of Ag–Br bonds are driven by dimensional confinement and lead to a different direct band gap location for the experimentally synthesized materials with n = 1 and n = 2 perovskite layers. Because of their different orbital characters, the electronic bands at these two points form different exciton states. This work provides a crucial interpretation of the unexpected trend in exciton binding energy in these systems, highlighting the important role of structural distortions in particular in 2D materials where directional bonding interactions determine the energy and symmetry of interband transitions. We expect similar effects in other 2D perovskites in which metal d orbitals contribute to the band edges, such as 2D Ag/Sb, Ag/In, and Ag/Fe double perovskites.30 Furthermore, we believe that the relationship between Ag–halide bond distortions and exciton self-trapping which has recently been reported for several 3D double perovskites50,51 warrants further investigation. Finally, our systematic calculations also shed light on the evolution of exciton binding energies with respect to changes in stacking patterns and interlayer distances.
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