pith. sign in

arxiv: 2605.21449 · v1 · pith:UEX6RY5Enew · submitted 2026-05-20 · ❄️ cond-mat.mtrl-sci

Hybrid Improper Ferroelectricity and Moir\'e Superlattices-induced Exciton Quantization in Layered 2D Halide Perovskite

Sanika S. Padelkar , Sharidya Rahman , Mattia Belotti , Naufan Nurrosyid , Craig Forsyth , Alasdair Mckay , Tam Nguyen , Thi Vu Mung
show 5 more authors
Lan Nguyen Naeimeh Mozaffari Alexandr N. Simonov Aftab Alam Jacek J. Jasieniak
This is my paper

Pith reviewed 2026-05-21 03:04 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords 2D halide perovskitehybrid improper ferroelectricitymoiré superlatticeexciton quantizationphotoluminescencepiezoelectricitytwinning
0
0 comments X

The pith

Hybrid improper ferroelectricity drives moiré superlattice formation in 2D perovskite, quantizing excitons at low temperature.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that solution-grown crystals of the 2D Ruddlesden-Popper perovskite (PA)2FAPb2I7 form an inadvertent moiré superlattice through pseudo-merohedral twinning induced by hybrid improper ferroelectricity. The ferroelectric order stems from trilinear coupling between two primary zone-boundary structural modes and a secondary polar mode, which breaks inversion symmetry while creating a small rotational misalignment of about 5.17 degrees between layers. This misalignment generates a moiré pattern that confines excitons periodically at 123 K, producing an equidistant ladder of photoluminescence peaks, whereas at room temperature the structure disorders into an incommensurate phase with broadened emission. A general reader would care because the finding explains the origin of unusual secondary light emission in these materials and points to ways of using built-in ferroelectricity to engineer quantum effects without manual layer twisting.

Core claim

The central discovery is that hybrid improper ferroelectricity in (PA)2FAPb2I7, involving trilinear mode coupling of X2+ and X3− with Γ4−, produces a polar displacement that breaks inversion symmetry and causes pseudo-merohedral twinning with a 5.17° twist between layers. This creates a moiré superlattice whose commensurate phase at low temperature imposes a periodic potential that quantizes excitons into a ladder of equally spaced photoluminescence lines, while the incommensurate phase at higher temperature broadens the emission. The same symmetry breaking yields a large piezoelectric response of about 20 pm/V.

What carries the argument

Trilinear coupling between X₂⁺, X₃⁻ zone-boundary modes and the Γ₄⁻ polar mode that induces the rotational misalignment and resulting moiré superlattice.

If this is right

  • The material achieves a high piezoelectric coefficient d33 of approximately 20 pm/V among 2D perovskites.
  • The moiré superlattice enables temperature-switchable exciton quantization between a periodic ladder and broadened emission.
  • This mechanism resolves the source of anomalous secondary photoluminescence peaks in layered 2D perovskites.
  • Pathways open for integrating twistronics, photoferroelectrics, and piezo-optoelectronics in these compounds.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Engineering similar improper ferroelectricity in other compositions could allow deliberate control of moiré angles without external twisting techniques.
  • The quantized exciton states might be used to create narrow-linewidth emitters or for studying exciton-polariton physics in a ferroelectric host.
  • Comparison with artificially twisted bilayers could test whether the ferroelectric-driven misalignment produces equivalent confinement effects.

Load-bearing premise

The equidistant photoluminescence ladder at 123 K is caused by the periodic potential from the moiré superlattice rather than by defects or exciton-phonon interactions.

What would settle it

High-resolution diffraction or scanning probe measurements that confirm the 5.17 degree interlayer rotation only in samples showing the sharp PL ladder at 123 K, but not in those with only broad emission, would support the moiré origin.

Figures

Figures reproduced from arXiv: 2605.21449 by Aftab Alam, Alasdair Mckay, Alexandr N. Simonov, Craig Forsyth, Jacek J. Jasieniak, Lan Nguyen, Mattia Belotti, Naeimeh Mozaffari, Naufan Nurrosyid, Sanika S. Padelkar, Sharidya Rahman, Tam Nguyen, Thi Vu Mung.

Figure 1
Figure 1. Figure 1: Synthesis of the (PA)𝟐FAPb𝟐I𝟕 single crystals. (a) Schematic presentation of the experimental setup and conditions used for the synthesis. (b) SEM￾EDS elemental mapping of the exfoliated (PA)2FAPb2I7 single crystal along with the atomic concentrations of Pb and I. (c) 1H and (d) 13C NMR spectra of the (PA)2FAPb2I7 solution in DMSO￾d6 highlighting the signals associated with PA+ and FA+; labels above and be… view at source ↗
Figure 2
Figure 2. Figure 2: Phase transitions and Phonon dynamics in (PA) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Piezo force microscopy of (PA)2FAPb2I7 and summary of piezoelectric coefficients. (a) AFM topography of delaminated bulk (PA)2FAPb2I7 perovskite on a Si substrate. Thickness is roughly about 100 nm. (b-c) Corresponding PFM amplitude along out-of-plane and in-plane direction respectively. Strong piezoelectricity can be witnessed in the vertical direction while weak but discernible piezo response can be ensu… view at source ↗
Figure 4
Figure 4. Figure 4: Optical characterization and Exciton-phonon coupling in 2D (PA)2FAPb2I7 perovskite flakes. (a) Temperature-dependent PL spectra of exfoliated single crystal at lower temperature, highlighting the emergence of equidistant PL emission peaks (𝑋1, 𝑋2, 𝑋3, 𝑋4, and 𝑋5) (b) Power-dependent PL spectra of exfoliated single crystal measured at 93 K indicating spectral splitting (𝑋1 and 𝑋1 ′ ) (c) (left plot) Functio… view at source ↗
Figure 5
Figure 5. Figure 5: Moiré exciton formation in twisted layers of 2D (PA)𝟐FAPb𝟐I𝟕 perovskite flakes. (a) Temperature-dependent Integrated PL Intensity for PL peak 𝑋1 and 𝑋5 of exfoliated single crystal (PA)2FAPb2I7. (b) Polarisation angle-resolved PL spectra measured at RT for exfoliated single crystal (PA)2FAPb2I7 sample with varying analyzer angle. (c-d) Polarisation-resolved PL intensity (panel c) and peak energy (panel d) … view at source ↗
Figure 1
Figure 1. Figure 1: ICP-MS calibration plots for (a) 209Pb and (b) 127I Symbols represent experimental data, and dashed lines represent corresponding linear fits. The calibration dependence for figure (a) is Intensity [count s−1 ] = (1.8013104 ± 188.6) C𝑃𝑏 [ppb] + (819.7 ± 8205); R2 = 0.9995; and for figure (b) is Intensity [count s−1 ] = (1.535104 ± 352.3) C𝐼 [ppb] + (1.1423104 ± 1.5333104 ); R2 = 0.9987 Nuclear magnetic res… view at source ↗
Figure 2
Figure 2. Figure 2: Crystal structure of (PA)2FAPb2I7 in Pnma and Pna21 space groups derived from the single-crystal XRD analysis [PITH_FULL_IMAGE:figures/full_fig_p031_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Temperature-dependent XRD profile of (PA)2FAPb2I7 single crystals from 373 K to 123 K with black dashed lines, emphasizing the peak position at RT (b) Differential Scanning Calorimetry (DSC) Curve reveals a phase transition around Curie temperature (T𝑐 ) ca. 349 K, at which point (PA)2FAPb2I7 undergoes a transformation from piezoelectric phase at RT to paraelectric above T𝑐 (c) Zoomed-in-view of the XR… view at source ↗
Figure 4
Figure 4. Figure 4: (a-b) Out-of-plane and (c-d) in-plane PFM Phase images of bulk and atomically thin layers of the samples shown in main text. Clear Phase contrast is obtained compared to the Si substrate for both the bulk and thin layers in both vertical and horizontal direction [PITH_FULL_IMAGE:figures/full_fig_p039_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: PFM of another 2D (PA)2FAPb2I7 bulk perovskite to ensure repeatability. (a) AFM topography of bulk and multilayer perovskite on Si substrate. Thickness ranges between 100nm to 165nm. (b-c) Corresponding out-of-plane and (d-e) in-plane PFM amplitude and phase, revealing RT piezoelectricity. f Height and amplitude line profile along the green dotted line shown in (a), (b) and (d). Piezo response varies with … view at source ↗
Figure 6
Figure 6. Figure 6: Evidence of ferroelectricity in 2D (PA)2FAPb2I7: (a) AFM Topography of a exfoliated bulk perovskite sample with thickness of around 100nm, (b-c) Vertical and horizontal piezo amplitude of the selected region in a, obtained from piezo-response force microscopy (PFM) measurements. Similar piezo response is obtained to that of the sample in main text. (d-e) Corresponding PFM phase images and (f, g) correspond… view at source ↗
Figure 7
Figure 7. Figure 7: Ferroelectric switching in another 2D perovskite sample to ensure repeatability. (a) AFM topography of 2D (PA)2FAPb2I7 consisting of bulk and atomically thin layers. (b) Corresponding out￾of-plane PFM amplitude. (c-d) Out-of-Plane PFM phase at +5 and -5V respectively. (e-f) Line Profile along the dotted line in (a) and (b) showing the AFM and PFM amplitude profile. Thin layer obtained is 7L [PITH_FULL_IMA… view at source ↗
Figure 8
Figure 8. Figure 8: (a-b) AFM topography and corresponding PFM amplitude of a bulk (ca. 130nm) 2D (PA)2FAPb2I7 perovskite at +5V. (c-d) AFM and PFM Line profile along the green dotted line in a and b. Negligible background response can be recorded from the substrate [PITH_FULL_IMAGE:figures/full_fig_p043_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: PFM of 2D perovskite (PA)2FAPb2I7 using a stiffer cantilever. (a) Topography of a bulk perovskite. (b-c) corresponding out-of-plane and (d-e) in-plane PFM amplitude and phase captured using a stiff cantilever (DDESP-FM-V2) with K=6 N/m. Similar PFM amplitude and phase variations can be obtained compared to the previously used cantilever. This helps to rule out electrostatics [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 10
Figure 10. Figure 10: Photoluminescence spectra of single crystal, exfoliated single crystal bulk and atomically thin layers of (PA)2FAPb2I7 perovskite at room temperature [PITH_FULL_IMAGE:figures/full_fig_p045_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: X-Ray diffraction profile of single crystal and exfoliated single crystal, indicating contraction of lattice upon exfoliation of quasi-2D piezoelectric (PA)2FAPb2I7 single crystal flakes. Supplementary Note 10 The steady-state PL properties of the as-obtained exfoliated single crystals and atomically thin layers of (PA)2FAPb2I7 are further studied to investigate the anomalous emissive dynamics of (PA)2FAP… view at source ↗
read the original abstract

2D Ruddlesden-Popper perovskites are compelling platforms for quantum-confined optoelectronics. However, polar order in iodide composition remains rare under ambient conditions, and the mechanistic origin of anomalous photoluminescence in this class of perovskite is still speculative. Here, we demonstrate that solution-grown $(PA)_2FAPb_2I_7$ single crystals develop an inadvertent moir\'e superlattice through pseudo-merohedral twinning, driven by hybrid improper ferroelectricity in which trilinear mode coupling between two primary zone-boundary modes ($X_2^+$ and $X_3^-$) and a secondary $\Gamma_4^-$ polar displacement simultaneously breaks inversion symmetry and imposes a ca. 5.17{\deg} rotational misalignment between adjacent layers. This symmetry breaking activates one of the highest piezoelectric coefficients $d_{33}$ (ca. 20 pm/V) reported among 2D perovskites. This misalignment generates a moir\'e superlattice that undergoes a thermally driven commensurate-incommensurate transition, switching between a periodic confinement potential that quantizes excitons into an equidistant photoluminescence ladder at 123 K and a disordered incommensurate phase with broadened emission at 298 K. These emissions are attributed to moir\'e-confined excitons, resolving a longstanding debate on anomalous secondary photoluminescence in layered 2D perovskites and opening pathways to twistronics, photoferroelectrics and piezo-optoelectronic devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that solution-grown (PA)2FAPb2I7 single crystals develop hybrid improper ferroelectricity via trilinear coupling of primary X2+ and X3− zone-boundary modes with a secondary Γ4− polar displacement. This simultaneously breaks inversion symmetry, yields a high d33 piezoelectric coefficient of ~20 pm/V, and drives pseudo-merohedral twinning that imposes a ~5.17° rotational misalignment between layers. The resulting moiré superlattice undergoes a thermally driven commensurate-incommensurate transition, producing an equidistant photoluminescence ladder from moiré-confined excitons at 123 K and broadened emission at 298 K, thereby resolving the origin of anomalous secondary PL in layered 2D perovskites.

Significance. If the central attribution of the PL ladder to moiré quantization holds after rigorous exclusion of alternatives, the work would provide a mechanistic link between hybrid improper ferroelectricity and emergent moiré physics in halide perovskites, while highlighting an unusually large piezoelectric response for the 2D RP family. The integration of structural mode analysis, twinning observations, and temperature-dependent optics is a notable strength; the result could open routes to twistronics and piezo-optoelectronic devices in this materials class.

major comments (2)
  1. [Abstract and PL results] Abstract and PL results: the claim that the equidistant ladder at 123 K arises specifically from periodic moiré confinement (rather than phonon replicas, stacking-fault states, or random potential fluctuations) is load-bearing for the resolution of the anomalous-PL debate, yet the provided text supplies no quantitative comparison of observed spacing to the expected moiré period, no calculated confinement potential depth, and no temperature-dependent diffraction data that would correlate the commensurate-incommensurate transition with the optical change.
  2. [Structural characterization section] Structural characterization section: the reported 5.17° misalignment and its origin in the trilinear X2+/X3−/Γ4− coupling require explicit error bars, the precise diffraction or simulation method used to extract the angle, and a demonstration that the misalignment is absent in control crystals lacking the ferroelectric distortion.
minor comments (2)
  1. [Symmetry analysis] Clarify whether the mode-coupling analysis is derived from first-principles calculations or group-theory tables, and add the relevant reference or supplementary derivation.
  2. [Figure captions] Figure captions for PL spectra should state the excitation wavelength, power density, and fitting procedure used to extract the ladder spacing.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We have addressed each of the major comments in detail below and made revisions to the manuscript where appropriate to strengthen our claims.

read point-by-point responses

  1. Referee: [Abstract and PL results] Abstract and PL results: the claim that the equidistant ladder at 123 K arises specifically from periodic moiré confinement (rather than phonon replicas, stacking-fault states, or random potential fluctuations) is load-bearing for the resolution of the anomalous-PL debate, yet the provided text supplies no quantitative comparison of observed spacing to the expected moiré period, no calculated confinement potential depth, and no temperature-dependent diffraction data that would correlate the commensurate-incommensurate transition with the optical change.

    Authors: We agree with the referee that providing quantitative support for the moiré confinement interpretation is crucial to distinguish it from alternative explanations. In the revised manuscript, we have expanded the PL results section to include a direct comparison between the observed PL ladder spacing and the moiré period calculated from the layer misalignment angle. We have also added a theoretical estimate of the confinement potential depth based on the periodic potential induced by the moiré superlattice. For the temperature-dependent diffraction, we have incorporated additional discussion linking the optical transition to the expected commensurate-incommensurate transition temperature, supported by our structural data. These revisions clarify the mechanistic link and are detailed in the updated abstract and results sections. revision: yes

  2. Referee: [Structural characterization section] Structural characterization section: the reported 5.17° misalignment and its origin in the trilinear X2+/X3−/Γ4− coupling require explicit error bars, the precise diffraction or simulation method used to extract the angle, and a demonstration that the misalignment is absent in control crystals lacking the ferroelectric distortion.

    Authors: We thank the referee for pointing out these details that enhance the clarity and rigor of our structural findings. In the revised version, we have included explicit error bars on the reported 5.17° misalignment angle. We have specified the method used for its determination, which involved analysis of single-crystal X-ray diffraction patterns and reciprocal space simulations. Furthermore, we have added comparative data from control samples that do not exhibit the hybrid improper ferroelectric distortion, confirming the absence of the rotational misalignment in those cases. This supports the causal link to the trilinear mode coupling. These updates are now present in the structural characterization section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on experimental structure and symmetry analysis

full rationale

The paper's central chain—from hybrid improper ferroelectricity via trilinear X2+/X3−/Γ4− coupling to the ~5.17° misalignment, moiré formation, and temperature-dependent PL ladder—is presented as a direct consequence of observed pseudo-merohedral twinning and first-principles mode analysis. No derivation reduces a 'prediction' to a fitted parameter by the paper's own equations, nor does any load-bearing step rely on self-citation chains or ansatz smuggling. The attribution of the 123 K equidistant ladder to moiré confinement is framed as an interpretation of measured emission and diffraction data rather than a tautological redefinition. The work is therefore self-contained against external benchmarks of crystal symmetry and optical spectroscopy.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the central claim rests on standard assumptions of crystal symmetry analysis and mode coupling in perovskites plus experimental attribution of PL features.

pith-pipeline@v0.9.0 · 5884 in / 1144 out tokens · 44243 ms · 2026-05-21T03:04:08.825040+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    Oh, Y. S. & others. Experimental demonstration of hybrid improper ferroelectricity and the presence of abundant charged walls in (Ca,Sr)3Ti2O7 crystals. Nat. Mater. 14, 407–413 (2015)

    work page 2015

  2. [2]

    A., Nowadnick, E

    Smith, K. A., Nowadnick, E. A., Fan, S. & others. Infrared nano -spectroscopy of ferroelastic domain walls in hybrid improper ferroelectric Ca3Ti2O7. Nat. Commun. 10, 5235 (2019)

    work page 2019

  3. [3]

    & others

    Du, Q. & others. Stacking effects on electron –phonon coupling in layered hybrid perovskites via microstrain manipulation. ACS Nano 14, 5806–5817 (2020)

    work page 2020

  4. [4]

    Sung, S. H. & others. Torsional periodic lattice distortions and diffraction of twisted 2D materials. Nat. Commun. 13, 7826 (2022)

    work page 2022

  5. [5]

    & others

    Cao, Y. & others. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018)

    work page 2018

  6. [6]

    Dean, C. R. & others. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013)

    work page 2013

  7. [7]

    & others

    Jin, C. & others. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019)

    work page 2019

  8. [8]

    Zhang, L., Zhang, X. & Lu, G. Predictions of moiré excitons in twisted two -dimensional organic – inorganic halide perovskites. Chem. Sci. 12, 6073–6080 (2021)

    work page 2021

  9. [9]

    & Kim, Y

    Seol, D., Kim, B. & Kim, Y. Non -piezoelectric effects in piezoresponse force microscopy. Current Applied Physics 17, 661–674 (2017)

    work page 2017

  10. [10]

    & others

    Xue, F. & others. Multidirection piezoelectricity in mono - and multilayered hexagonal α -In2Se3. ACS Nano 12, 4976–4983 (2018)

    work page 2018

  11. [11]

    & Flores-Ruiz, F

    Garduño-Medina, A., Vázquez-Delgado, M., Diliegros-Godines, C., García-Vázquez, V. & Flores-Ruiz, F. Measurements outside resonance with piezoresponse force microscopy. in AIP Conference Proceedings vol. 2416 (AIP Publishing, 2021)

    work page 2021

  12. [12]

    & Obradors, X

    Gomez, A., Puig, T. & Obradors, X. Diminish electrostatic in piezoresponse force microscopy through longer or ultra-stiff tips. Appl. Surf. Sci. 439, 577–582 (2018)

    work page 2018

  13. [13]

    P., Robins, L

    Killgore, J. P., Robins, L. & Collins, L. Electrostatically -blind quantitative piezoresponse force microscopy free of distributed-force artifacts. Nanoscale Adv. 4, 2036–2045 (2022)

    work page 2036

  14. [14]

    & Kim, Y

    Kim, S., Seol, D., Lu, X., Alexe, M. & Kim, Y. Electrostatic -free piezoresponse force microscopy. Sci. Rep. 7, 41657 (2017)

    work page 2017

  15. [15]

    & others

    Rahman, S. & others. Enhanced piezoresponse in van der Waals 2D CuCrInP2S6 through nanoscale phase segregation. Nanoscale Horiz. (2025)

    work page 2025

  16. [16]

    P., Mihalyi -Koch, W

    Hautzinger, M. P., Mihalyi -Koch, W. & Jin, S. A -site cation chemistry in halide perovskites. Chemistry of Materials 36, 10408–10420 (2024)

    work page 2024

  17. [17]

    & others

    Rahmany, S. & others. The impact of piezoelectricity in low dimensional metal halide perovskite. ACS Energy Lett. 9, 1527–1536 (2024)

    work page 2024

  18. [18]

    Frost, J. M. & others. Atomistic origins of high-performance in hybrid halide perovskite solar cells. Nano Lett. 14, 2584–2590 (2014)

    work page 2014

  19. [19]

    & others

    Li, C. & others. Formability of ABX3 (X = F, Cl, Br, I) halide perovskites. Acta Crystallogr. B 64, 702– 707 (2008)

    work page 2008

  20. [20]

    & others

    Wang, X. & others. Moiré band structure engineering using a twisted boron nitride substrate. Nat. Commun. 16, 178 (2025). 56

    work page 2025

  21. [21]

    & others

    Feng, Y. & others. Thickness-dependent evolution of piezoresponses and a/c domains in [101]-oriented PbTiO3 ferroelectric films. J. Appl. Phys. 128, (2020)

    work page 2020

  22. [22]

    & others

    Feng, Y. & others. Thickness -dependent evolution of piezoresponses and stripe 90 domains in (101) - oriented ferroelectric PbTiO3 thin films. ACS Appl. Mater. Interfaces 10, 24627–24637 (2018)

    work page 2018

  23. [23]

    Kelley, K. P. & others. Thickness and strain dependence of piezoelectric coefficient in BaTiO3 thin films. Phys. Rev. Mater. 4, 24407 (2020)

    work page 2020

  24. [24]

    & Yamamoto, T

    Konabe, S. & Yamamoto, T. Piezoelectric coefficients of bulk 3R transition metal dichalcogenides. Jpn. J. Appl. Phys. 56, 98002 (2017)

    work page 2017

  25. [25]

    & Shenoy, V

    Dong, L., Lou, J. & Shenoy, V. B. Large in -plane and vertical piezoelectricity in Janus transition metal dichalchogenides. ACS Nano 11, 8242–8248 (2017)

    work page 2017

  26. [26]

    & others

    Wang, Y. & others. Piezoelectric responses of mechanically exfoliated two -dimensional SnS2 nanosheets. ACS Appl. Mater. Interfaces 12, 51662–51668 (2020)

    work page 2020

  27. [27]

    & others

    Yang, J. & others. Coexistence of piezoelectricity and magnetism in two -dimensional vanadium dichalcogenides. Physical Chemistry Chemical Physics 21, 132–136 (2019)

    work page 2019

  28. [28]

    & others

    Jiang, X. & others. Strong piezoelectricity and improved rectifier properties in mono - and multilayered CuInP2S6. Adv. Funct. Mater. 33, 2213561 (2023)

    work page 2023

  29. [29]

    L., Muensit, S

    Guy, I. L., Muensit, S. & Goldys, E. M. Extensional piezoelectric coefficients of gallium nitride and aluminum nitride. Appl. Phys. Lett. 75, 4133–4135 (1999)

    work page 1999

  30. [30]

    & Kar -Narayan, S

    Calahorra, Y. & Kar -Narayan, S. Piezoelectricity in non -nitride III –V nanowires: Challenges and opportunities. J. Mater. Res. 33, 611–624 (2018)

    work page 2018

  31. [31]

    H., Ullah, H., Shafique, A., Kim, H

    Pham, T. H., Ullah, H., Shafique, A., Kim, H. J. & Shin, Y.-H. Enhanced out-of-plane electromechanical response of Janus ZrSeO. Physical Chemistry Chemical Physics 23, 16289–16295 (2021)

    work page 2021

  32. [32]

    & Krishnan Jagadamma, L

    Sekhar Muddam, R., Sinclair, J. & Krishnan Jagadamma, L. Piezoelectric charge coefficient of halide perovskites. Materials 17, (2024)

    work page 2024

  33. [33]

    & others

    Yamashita, Y. & others. A review of lead perovskite piezoelectric single crystals and their medical transducers application. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 69, 3048–3056 (2022)

    work page 2022

  34. [34]

    & others

    Shi, E. & others. Extrinsic and dynamic edge states of two -dimensional lead halide perovskites. ACS Nano 13, 1635–1644 (2019)

    work page 2019

  35. [35]

    & Tan, L

    Hong, J., Prendergast, D. & Tan, L. Z. Layer edge states stabilized by internal electric fields in two - dimensional hybrid perovskites. Nano Lett. 21, 182–188 (2020)

    work page 2020

  36. [36]

    Wright, A. D. & others. Electron -phonon coupling in hybrid lead halide perovskites. Nat. Commun. 7, 11755 (2016)

    work page 2016

  37. [37]

    R., Dahod, N

    Paritmongkol, W., Powers, E. R., Dahod, N. S. & Tisdale, W. A. Two origins of broadband emission in multilayered 2D lead iodide perovskites. J. Phys. Chem. Lett. 11, 8565–8572 (2020)

    work page 2020

  38. [38]

    & others

    Lin, M.-L. & others. Correlating symmetries of low -frequency vibrations and self -trapped excitons in layered perovskites for light emission with different colors. Small 18, 2106759 (2022)

    work page 2022

  39. [39]

    & others

    Ni, L. & others. Real -time observation of exciton –phonon coupling dynamics in self -assembled hybrid perovskite quantum wells. ACS Nano 11, 10834–10843 (2017)

    work page 2017

  40. [40]

    & others

    Biswas, S. & others. Exciton polaron formation and hot -carrier relaxation in rigid Dion –Jacobson-type two-dimensional perovskites. Nat. Mater. 23, 937–943 (2024)

    work page 2024

  41. [41]

    & Tan, P.-H

    Krahne, R., Lin, M.-L. & Tan, P.-H. Interplay of phonon directionality and emission polarization in two - dimensional layered metal halide perovskites. Acc. Chem. Res. 57, 2476–2489 (2024)

    work page 2024

  42. [42]

    & others

    Castelli, A. & others. Revealing photoluminescence modulation from layered halide perovskite microcrystals upon cyclic compression. Advanced Materials 31, 1805608 (2019). 57

    work page 2019

  43. [43]

    & others

    Blancon, J.-C. & others. Extremely efficient internal exciton dissociation through edge states in layered 2D perovskites. Science (1979). 355, 1288–1292 (2017)

    work page 1979

  44. [44]

    Kinigstein, E. D. & others. Edge states drive exciton dissociation in Ruddlesden –Popper lead halide perovskite thin films. ACS Mater. Lett. 2, 1360–1367 (2020)

    work page 2020

  45. [45]

    & others

    Tongay, S. & others. Defects activated photoluminescence in two -dimensional semiconductors: Interplay between bound, charged and free excitons. Sci. Rep. 3, 2657 (2013)

    work page 2013

  46. [46]

    & others

    Jin, F. & others. Exciton polariton condensation in a perovskite moiré flat band at room temperature. Sci. Adv. 11, eadx2361 (2025)

    work page 2025

  47. [47]

    & others

    Xiao, S. & others. Polarization -dependent multiphoton -excited self -trapped emission in alloyed 0D Rb7Bi3Cl16 metal halides via Sb3+ doping. Small Science 2500261 (2025)

    work page 2025

  48. [48]

    & others

    Förg, M. & others. Moiré excitons in MoSe2 -WSe2 heterobilayers and heterotrilayers. Nat. Commun. 12, 1656 (2021)

    work page 2021

  49. [49]

    Seyler, K. L. & others. Signatures of moiré -trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019)

    work page 2019

  50. [50]

    & others

    Tran, K. & others. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019)

    work page 2019

  51. [51]

    & others

    Rossi, A. & others. Anomalous interlayer exciton diffusion in WS2/WSe2 moiré heterostructure. ACS Nano 18, 18202–18210 (2024)

    work page 2024

  52. [52]

    & Weng, H

    He, Z. & Weng, H. Giant nonlinear Hall effect in twisted bilayer WTe2. NPJ Quantum Mater. 6, 101 (2021)

    work page 2021

  53. [53]

    Howieson, G. W. & others. Incommensurate –commensurate transition in the geometric ferroelectric LaTaO4. Adv. Funct. Mater. 30, 2004667 (2020)

    work page 2020

  54. [54]

    & MacDonald, A

    Wu, F., Lovorn, T. & MacDonald, A. Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers. Phys. Rev. B 97, 35306 (2018)

    work page 2018

  55. [55]

    & others

    Rivera, P. & others. Observation of long -lived interlayer excitons in monolayer MoSe2 –WSe2 heterostructures. Nat. Commun. 6, 6242 (2015)

    work page 2015