Emerging perovskite monolayers

The library of two-dimensional (2D) materials has been enriched over recent years with novel crystal architectures endowed with diverse exciting functionalities. Bulk perovskites, including metal-halide and oxide systems, provide access to a myriad of properties through molecular engineering. Their tunable electronic structure offers remarkable features from long carrier-diffusion lengths and high absorption coefficients in metal-halide perovskites to high-temperature superconductivity, magnetoresistance and ferroelectricity in oxide perovskites. Emboldened by the 2D materials research, perovskites down to the monolayer limit have recently emerged. Like other 2D species, perovskites with reduced dimensionality are expected to exhibit new physics and to herald next-generation multifunctional devices. In this Review, we critically assess the preliminary studies on the synthetic routes and inherent properties of monolayer perovskite materials. We also discuss how to exploit them for widespread applications and provide an outlook on the challenges and opportunities that lie ahead for this enticing class of 2D materials. Metal-halide and oxide perovskites are a rich playground for fundamental studies and applications. This Review focuses on the opportunities opened by reducing the dimensionality of these materials to two-dimensional monolayers.

energies up to hundreds of millielectronvolts. The unit cell size can be varied through molecular engineering of the organic chains. This affects the overall physics and key electronic properties such as the bandgap and exciton binding energy. In particular, because the organic spacers between two adjacent unit cells of RP-phase halide perovskites are often connected by weak interaction such as van der Waals forces, individual perovskite layers can be isolated from their bulk crystals in the way that graphene has been. In the past, a number of comprehensive reviews on thinly layered halide perovskites have been reported [13][14][15] . By scaling down the physical thickness to the monolayer limit, the intrinsic properties become accessible and it is possible to gain a deeper understanding of the structure-property relationship and how this changes as the number of unit cells is increased.
Unlike traditional 2D inorganic materials, monolayer perovskites are composed of a soft lattice and a dynamically disordered framework 16 . This makes them particularly susceptible to external stimuli, such as interface strain, temperature, pressure and electric fields. They are open to chemical functionalization, which grants access to a plethora of new 2D materials with tailorable features, going beyond the structural diversity of bulk analogues. Importantly, the broken inversion symmetry at the interfaces of ferroelectric species can enhance the Rashba splitting 17 , with which the charge carrier lifetime and the magnetic and electronic structure can be manipulated 18 . Currently, ultrathin sheets of halide perovskites have been prepared by either mechanical cleavage from the stacked RP-phase crystals 19 or by bottom-up synthetic approaches from molecular building blocks, such as chemical vapour deposition and epitaxial growth 20,21 . The latter routes are also applicable for growing single layers of oxide perovskites 22 , the latest member in the monolayer family. For a long time, oxide perovskites were thought to have a critical minimum thickness down to five unit cells, below which the lattice of the film would collapse 23 . Recently, an oxide perovskite monolayer was however successfully exfoliated by ion-exchange methods from DJ-phase bulk materials 24 . The inorganic slab was composed of three layers. It is noteworthy that 3D oxide perovskites cover insulators to semiconductors as well as metals and superconductors.

Box 1 | A brief history of perovskite materials
The progenitor of perovskite materials, CaTiO 3 , was discovered in the Ural Mountains by Gustav Rose in 1839. It was named in honour of the mineralogist Lev Aleksevic von Perovski 91 . The general chemical formula of perovskites is ABX 3 , where A and B are both cations and A is generally larger than B, and X is usually an oxide or a halide anion. The replacement of ionic species led to a myriad of perovskites with distinct features and properties. These include ferroelectricity, superconductivity, strong optical absorption, low exciton-binding energy and so on.
Since the 1940s, oxide perovskites have found their way in the field of catalysis, sensing, electrical and optical devices 3,92 . For example, BaTiO 3 is a classic ferroelectric material with high dielectric constant. Since the 1950s, it has been widely used in capacitors and condensers. The discovery of superconductivity in the La-Ba-Cu-O cuprate system at ∼30 K was an important milestone in 1986. It triggered the search for superconducting materials with a higher critical temperature (T c ) within the oxide perovskite family 26 . Among the cuprates, the substitution of La with Y caused a big leap forward pushing T c up to 93 K only one year later 93 . In 1988, compositional engineering enabled even highertemperature superconductors without any need for rare-earth elements. For example, with BiSrCaCu 2 O x , it is possible to achieve a T c of 105 K (ref. 94 ). The more recent discovery of superconductivity in a 2D electron system that spontaneously emerges at the LaAlO 3 /SrTiO 3 (001) and SrTiO 3 /KTaO 3 (111) polarized interfaces brought this old topic back into the spotlight 69,95 . The history of halide perovskites dates back to 1893, when CsPbX 3 was first discovered 16 . From the 1920s to 1950s, many others were prepared, such as CsSnX 3 and CsGeX 3 . The discovery of intrinsic photoconductivity 96 in lead-based halide perovskites (CsPbCl 3 and CsPbBr 3 ) attracted considerable attention and marked the start for novel thin-film electronic devices. Early structural studies on layered perovskites date from the 1960s 25 25 . c, The discovery of superconductivity at ∼30 K in La 2−x ba x CuO 4 unleashed a flood of work in the search for higher-T c superconductivity in perovskite structures 26 . d, The successful intercalation of layered halide perovskites crystals paved the way for the exfoliation of atomically thin sheets 27 . e, Discovery of a series of layered tin-based halide perovskites with controllable layer thickness. A trend from semiconducting to metallic-like behaviour is observed with increasing number n of the perovskite layer 28 . f, Solution-based growth of a perovskite with a thickness of a single unit cell. The structural relaxation in monolayers causes a change in the bandgap compared with the gap of the bulk counterpart 35 . The insets show an optical image of (bA) 2 Pbbr 4 sheets (left) and an atomic force microscopy image of several single layer square-shaped sheets (right). g, Large-size halide perovskite monolayers with different well thicknesses, such as a different n, were successfully fabricated by mechanical cleavage from bulk crystals. The exfoliated sheets offer tunable optoelectronic features due to their mouldable structure 19 . The inset shows an atomic force microscopy image corresponding to single layer (1L)-thick (bA) 2 (MA)Pb 2 I 7 . h, Epitaxial-growth of free-standing SrTiO 3 and biFeO 3 films down to the monolayer. The ultrathin and highly crystalline films are transferrable onto a variety of different substrates (such as silicon, holey carbon) 22 . The insets show cross-sectional (bottom) and low-magnification plane-view (top) annular dark-field images at high angle of a two-unit-cell freestanding SrTiO 3 film. i, The fabrication of lateral heterostructures containing monolayer halide perovskite semiconductors. Diverse conjugated organic ligands, metals and halides are mixed to tune the optoelectronic properties of these more complex 2D architectures 37 . The insets show the optical (left) and photoluminescence (right) images of a (bA) 2 PbI 4 -(bA) 2 Pbbr 4 lateral heterostructure. Credit: panels adapted with permission from: f, ref. 35 , AAAS; g, ref. 19 , Springer Nature Ltd; h, ref. 22 , Springer Nature Ltd; i, ref. 37 , Springer Nature Ltd.
The research on exotic 2D correlated electronic phases in these oxides is, however, still in its infancy.
In this Review, we provide an up-to-date overview of pioneering advances in this exciting arena of perovskite-type 2D materials with a focus on their synthesis, characterization and fundamental physical properties. In particular, we highlight the opportunities to manipulate the properties of perovskite monolayers and offer our insights into the future directions and challenges towards new materials, new device concepts and innovative applications in this emerging field. Due to the widely tailorable chemical and physical properties, the developments on monolayer perovskites are bound to stimulate fruitful interactions between the currently distinct scientific communities working on perovskites and 2D materials. The tremendous potential that the merger of these two material classes holds may not be fully appreciated yet.

Structural versatility
The perovskite structure originates from calcium titanium oxide (CaTiO 3 ), a mineral discovered in 1839 (Box 1). This crystal structure exhibits exceptional flexibility through ionic substitutions, structural defects and superstructures, resulting in hundreds of halide and oxide perovskites with layered or non-layered geometries ( Fig. 1) [25][26][27][28] . The layered perovskites can be further divided into the RP phases, the DJ phases and the Aurivillius phases (exclusively for oxide perovskites), which adopt the general formulas of A′ 2 A n−1 B n X 3n+1 , A′A n-1 B n X 3n+1 and (Bi 2 O 2 )(A n-1 B n O 3n+1 ), respectively 16 . Compared with RP phases, DJ-phase layered perovskites possess strong interlayer interactions because they have only one divalent interlayer cation A′ per formula unit 29 . When X is an oxide anion, the classical examples of oxide perovskites consist of alkaline, alkaline-earth or rare-earth cations at the A sites, and transition or p-block metals at the B sites. When X is a halide anion (such as Cl − , Br − or I − ), A′ is a bulky aromatic or aliphatic alkylammonium spacer, such as butylammonium (BA) and 2-phenylethylammounium (PEA), and B is a divalent metal cation from group XIV (for example, Pb² + , Sn² + , Ge² + and so on) in RP-phase hybrid halide perovskites 30 . The hybrid perovskite superlattices contain multiple units or quantum wells. The organic moieties act as insulator or barrier to confine charge carriers in each inorganic layer. The introduction of monovalent cations A, such as Cs + , methylammonium (MA) or formamidinium (FA), modulates the thickness of the quantum well and n (n = 1, 2, 3…) refers to the number of [MX 6 ] 4− octahedral layers. Note that, when n is greater than 5, hybrid perovskite layers usually undergo a spontaneous degradation towards more thermodynamically stable mixtures including thinner perovskite layers and 3D perovskites 16 . For n → ∞, the layered perovskite evolves into a rigid 3D network with formula ABX 3 , where the aristotype, undistorted structure can be defined in a cubic unit cell with B atoms at the centre of the cube, A cations at the corners and X anions at the middle of the faces.

Synthesis of perovskite monolayers
Inspired by the research on atomically thin 2D crystals, such as graphene, transition metal dichalcogenides (TMDs) and black phosphorus 2 , mechanical exfoliation has been deployed for van der Waals stacked perovskite bulk crystals to achieve perovskite monolayers. Also the direct growth of monolayers in liquids or on substrates has been pursued to control precisely the thickness n and the a hybrid perovskite 27 . However, the extraction of perovskite monolayers was not achieved until recently 19,22,35,37 , owing to both technical difficulties and the disproportionate attention paid to halide perovskites for photovoltaics.
In 1986, Maruyama and co-workers reported the first layered halide perovskite (CH 3 (CH 2 ) 8 NH 3 ) 2 PbI 4 (ref. 27 ) and marked the start of the synthesis of state-of-the-art 2D hybrid perovskites. Mitzi and co-workers carried out systematic synthesis studies of layered halide perovskite semiconductors with designable organic moieties and tunable electrical properties during the 1990s 28 . The work of Miyasaka and colleagues in 2009 represents another important step forward by exploiting the photovoltaic function of bulk organic-inorganic hybrid perovskite (CH 3 NH 3 PbI 3 ) 97 . It sparked extensive research of halide perovskites as light-absorbing layers in photovoltaic devices. A decade later, the initial efficiency of 3.8% of perovskite solar cells reached an impressive 25.5% in a single junction and 29.5% as perovskite/silicon tandem devices 98 . Layered halide perovskites also offer other interesting photonic, electronic and spin related properties. However, these mostly stem from spin-coated polycrystalline thin films and thick single crystals.
The fabrication of and control over perovskite monolayers is an important recent research direction in the field of perovskite materials. Recently, pioneering studies on ultrathin perovskite halides and oxides have revealed their potential 19,22,35,37 , being more prone to property changes upon external stimuli and molecular engineering than their bulk counterparts. Monolayers can be incorporated into various electronic devices in which the inherent characteristics of the perovskite can be fully exploited, leading to the discovery of a rich spectrum of novel properties.

Fig. 1 | Perovskite types.
Schematic of the general structure of perovskites with non-layered AbX 3 , layered RP phase A′ 2 A n−1 b n X 3n+1 or DJ phase A′A n−1 b n X 3n+1 . Here, the case of n = 1, 2 and 3 is shown but n can go up to 5 (ref. 16 ).
crystal structure. For example, molecular beam epitaxy (MBE) and chemical vapour deposition are employed to grow highly crystalline single sheets of non-layered perovskites. The chosen synthesis method has an impact on the surface morphology, which in turn affects the overall behaviour of the perovskite monolayers. Device fabrication through mechanical exfoliation and transfer are the most successful techniques to obtain high-quality monolayer nanocrystals from either native layered structures or from starting material grown on top of a substrate. Properties inherent to the 2D materials, such as the quantum Hall effect and superconductivity, have been observed on exfoliated flakes, but were either not observable or suppressed in samples prepared by other approaches 31 . Both mechanical exfoliation and MBE usually enable 2D material growth with a clean surface and well-defined morphology, whereas the chemical method based on bottom-up growth in solution often causes surface contamination of the isolated sheets. Therefore, compared with solution-prepared perovskite monolayers, the mechanically exfoliated sheets and those obtained by MBE are more suitable for device assembly and the exploration of new properties.
Top-down exfoliation. Pioneering attempts to isolate single-and few-layer hybrid halide perovskites from bulk material resorted to mechanical cleavage ( Fig. 2a) 32,33 . Compared with rigid layered inorganic materials, the combination of an elastic crystal lattice and weak interlayer interactions makes layered halide perovskites (with mainly n = 1) easier to delaminate into thin sheets with large sizes, high crystallinity and surface cleanness. These parameters are critical for fundamental studies and fabrication of high-performance electrical and optical devices based on single flakes. However, the relatively weak in-plane ionic bonds usually cause structural cracks and yield uneven flakes with reduced lateral size as well as thickness fluctuations. Recently, micrometre-scale uniform monolayers with a controlled number of inorganic layers n (n = 1-4) have been exfoliated from large crystals of an RP-phase halide perovskite 19 .
Mechanical cleavage is not suited for DJ-phase halide perovskites, because the organic spacers (for example, 3-(aminomethyl)piperidinium) between the quantum wells are linked with ionic bonds, which are much stronger than van der Waals forces 12 . However, the DJ-phase oxide perovskites can be exfoliated into monolayers through an ion-exchange approach. The replacement of larger interlayer cations (such as Cs + and K + ) with smaller cations, such as protons, breaks the strong interlayer interaction and creates a new layered solid, which is crucial for the subsequent exfoliation 24,34 . This exfoliation procedure is mainly conducted in dispersion. It enables excellent solution processability of the exfoliated sheets.
Despite the disturbed surfaces from residual chemicals and large distribution of lateral sizes (mainly below 5 µm) and thickness (down to few nanometres), the as-prepared thin films are useful for large-area optoelectronic devices.
Bottom-up synthesis. Wet-chemical approaches offer an alternative route towards the production of widely tunable and well-defined monolayers (Fig. 2b). Direct growth of atomically thin sheets in solution has been demonstrated in a ternary co-solvent system composed of acetonitrile, chlorobenzene and N,N-dimethylformamide 35 . It yields square-shaped (BA) 2 PbBr 4 flakes with a random thickness (from monolayer to few layer) and lateral dimensions up to 8 μm.
The selection of different solvents can alter the balance between dissolution and crystallization of the specific halide perovskite. One of the most fascinating merits of solution growth methods is the freedom of spectral tunability by molecular design. It allows the incorporation of large conjugated organic moieties into the crystal lattice. For example, large tetra-thiophene-based monoammonium cations trigger the formation of halide perovskite sheets down to single-unit-cell thickness 36 . The introduction of steric groups into the organic ligands aids in restricting sheet growth to the lateral dimension and prevents the self-aggregation of 2D sheets into 3D crystals. This technique has been applied to synthesize complex monolayer lateral heterostructures with sharp interfaces and well-defined edges through a solution-phase sequential growth mechanism 37 . In a colloidal synthesis process, the addition of organic spacers with long alkylammonium chains enables ultrathin lead-and tin-based hybrid perovskite nanosheets (n = 1, 2) with excellent thickness homogeneity 38 . However, the thickness control fails for the growth of sheets with higher n (n = 3, 4, 5…) and sheets of mixed thickness are obtained instead.
In addition, solution-based synthesis is available for non-layered, molecularly thin sheets with a rigid ABX 3 network, such as CsPbX 3 (X = Cl − , Br − , I − ) 39,40 , in which the cations at the A site can be further replaced by organic molecules. For example, ultrathin methylammonium lead halides (MAPbX 3 ) sheets with thickness down to 1.3 nm can be prepared through precise control of the solvent evaporation rate 41 . So far, the major drawbacks of solution-based growth methods are the large distribution of thicknesses and lateral sizes of the 2D sheets, which might be a limiting factor for device assembly. In addition, surface contamination and structural defects such as grain boundaries, phase impurities and a considerable dislocation density affect the intrinsic properties of solution-processed perovskite monolayers. MBE is an alternative strategy to grow uniform thin films on compatible substrates with controlled thickness and structural precision at the atomic level. This technique is particularly suited for the preparation of ultrathin sheets of non-layered perovskites, in which, strong bonds between the layers usually prevent the isolation of individual sheets. In particular, the combination of epitaxial growth and selective etching enables the fabrication of freestanding single-crystalline oxide perovskite membranes, including SrTiO 3 and La 0.7 Sr 0.3 MnO 3 , with lateral dimensions on the millimetre scale and thicknesses of a few unit cells 42 . A key process step consists of the deposition of a water-soluble sacrificial Sr 3 Al 2 O 6 film before the growth of the target oxide perovskite. Ultrathin sheets can then be released in water and transferred onto any desired substrate or 2D material for multifunctional electronic devices. By carefully controlling the sacrificial buffer layer, further reduction of the perovskite thickness down to the extreme monolayer limit (one unit cell) is achievable 22 . The optimized conditions are applicable for the growth of single-crystal large-sized SrTiO 3 and BiFeO 3 membranes with variable thickness from one to four unit cells. MBE can not only be deployed for the growth of oxide perovskites but also be used to grow inorganic halide perovskites 43 . However, this method usually requires high temperatures and flux energies that are incompatible with the organic components of hybrid perovskites. Although organic molecular beam deposition has been developed for the growth of organic semiconducting layers 44 , the different growth mechanism and kinetics for organic layers and inorganic units, and the large lattice mismatch during their sequential growth, strongly hamper the synthesis of hybrid perovskite monolayers.

tunable electronic and optical properties
The flexibility in modifying the structure and composition endows perovskite materials with tunable electronic and optical properties ( Table 1) [45][46][47] . The bandgap is one of the most significant parameters for semiconductors. Its size has implications for the types of possible application. For example, the narrow-bandgap perovskite semiconductors are widely used for applications related to photon absorption or emission 48 . The recently reported hybrid halide perovskites have relatively small bandgaps between 1.1 eV and 1.8 eV, whereas inorganic halide and oxide analogues usually exhibit larger intrinsic bandgaps exceeding 2 eV (ref. 49 ), which are interesting for light-emitting diodes and lasers. Some oxide species such as Sr 2 Nb 3 O 10 have even wider bandgaps (for example, 3.9 eV) corresponding to ultraviolet photon energies 24 . However, not all bandgaps are available through direct synthesis and band structure engineering is critical for achieving desired bandgaps and physical characteristics. So far, many techniques, including alloying, heating, anion exchange, electronic doping, and applying external stimuli, are used to modulate the bond length and bond angle of perovskite lattices, thereby manipulating the band structure 50,51 .
The thickness reduction when moving from bulk to monolayers broadens the bandgap due to quantum confinement. Especially in halide perovskite monolayers, the optical bandgap further increases as the quantum well thickness decreases (Fig. 3a) 52 . For example, the optical bandgap of exfoliated (BA) 2 (MA) n−1 Pb n X 3n+1 evolves from 1.85 eV to 2.42 eV by lowering n from 5 to 1 (ref. 53 ). Although the trend is in good agreement with that of thin films, the bandgap is redshifted by as much as 300 meV for n values between 3 and 5. By adding or removing monovalent cations, that is, increasing or decreasing n, the thickness of the inorganic layer of the unit cell or quantum well is altered, which has a dramatic influence on the properties. As an example, the electrical properties of tin-based organic-inorganic halides alter as a function of n from intrinsically semiconducting when n = 1 to the heavily doped and 'metallic like' when n = ∞. Such a transition may result from the disorder of organic fragments within the structure 28 . In this class of materials, the charge carriers are tightly confined in the inorganic layers sandwiched between the insulating organic layers forming a natural superlattice 54 . The spatial confinement and the dielectric mismatch between the organic and inorganic layers causes the formation of excitons with a Bohr radius that exceeds the well thickness 55 . This results in an exceptionally high binding energy (Fig. 3b) 56 . These electronic and excitonic properties are easily tuned as the spatial confinement is varied via n. Likewise, the exciton-binding energies of all-inorganic halide perovskites increase dramatically as n decreases (n ≤ 3). In spite of the absence of organic layers, the value of monolayer Cs 2 PbI 4 (181.7 meV) is almost three times larger than that of the bulk phase (CsPbI 3 , 59.1 meV) 57 . Nonlinear optical processes are possible in the hybrid dielectric-confined systems that host excitons with strong binding energies and also possess transitions with large oscillator strength 58,59 . Unfortunately, bulk samples suffer from grain boundaries and defect states limiting the coherence of 2D excitons 11 . These issues can be avoided in thinner single crystalline layers. Nonlinear optical studies on such 2D nanosheets have revealed thickness-dependent third-harmonic generation, which is suppressed in bulk polycrystalline halide perovskites, due to signal depletion and phase-matching conditions. The delaminated flakes with reduced thickness exhibit a third-order susceptibility, χ (3) , as high as 1.12 × 10 −17 m 2 V −2 and conversion efficiencies are five orders of magnitude larger compared with other 2D materials 60 . The excitonic properties of exfoliated halide perovskites, especially those of monolayers consisting of only a single unit cell (~2.4 nm), can easily be manipulated through the dielectric environment it surrounds 33 . This can be the substrate or an encapsulating layer (if available) with dielectric properties distinct from the bulk crystal. Dielectric screening from the supporting substrate can be particularly prominent for halide perovskite monolayers, as evidenced by drastic changes in bandgap and exciton properties in TMDs 61 . For instance, in molecularly thin (BA) 2 PbBr 4 sheets, the change in the dielectric environment causes an increase of the exciton binding energy to 490 meV, almost one-third larger compared with the binding energy in the corresponding layered bulk perovskite 33,55 . Absorption and photoluminescence studies suggest the formation of edge states in exfoliated perovskite single crystals with unit cells for which n is larger than 2 (Fig. 3c,d). This is the result of the distortion of the lattice, the formation of chemically induced surface states and the resulting self-trapping of excitons. These states at the grain boundaries of monolayers promote the dissociation of photogenerated excitons into long-lived free carriers that are protected from non-radiative recombination. This intrinsic dissociation process is not observed in other quantum-confined systems. In contrast to thicker perovskites, excitons in exfoliated layers with n ≤ 2 decay through the usual processes. There can be no doubt that halide perovskite monolayers represent a fertile playground for further photophysical investigations.
Their optoelectronic properties depend not only on the quantum well thickness, such as n, but also the stiffness of the lattice. The soft and ionic nature of the layers makes these ultrathin sheets susceptible to larger lattice deformations upon external mechanical, optical, thermal and electrical stimuli compared with bulk  53 . d, Comparison of the photoluminescence spectra recorded on an exfoliated crystal, at the edge of the exfoliated crystal and on the corresponding thin film of (bA) 2 (MA) 2 Pb 3 I 10 . The spectrum obtained from the edge of the flake exhibits photoluminescence features of both the thin film and the exfoliated crystal, suggesting a common origin of the photoluminescence from layer edge states in exfoliated crystals and the photoluminescence of a thin polycrystalline film with n > 2 (ref. 53 ). e, Order-disorder transition induced by laser illumination in an encapsulated perovskite monolayer. Surface relaxation gives rise to a shift of the photoluminescence line. This is reversible upon laser annealing in vacuum at higher power 19 . f, Shift of the photoluminescence line when going from bulk (bA) 2 (MA) n−1 Pb n I 3n+1 to a single quantum well or monolayer with n ranging from 1 to 4 (ref. 19 ). Credit: panels adapted with permission from: a,c,d, ref. 53 , AAAS; b, ref. 52 , National Academy of Sciences (right y axis); b, ref. 56 , under a Creative Commons license CC bY 4.0 (left y axis); e,f, ref. 19 , Springer Nature Ltd. materials. A reversible shift in excitonic energies is generated upon laser irradiation in large-sized monolayers encapsulated by a layer of hexagonal boron nitride (Fig. 3e) 19 . This unique behaviour arises from dynamic surface relaxation and compression effects in these highly deformable monolayers. Such effects are far less pronounced in their thicker multilayer parent compounds. We note that the hexagonal boron nitride prevents photoinduced degradation of the exfoliated flakes. Unlike other inorganic 2D materials, thin sheets of halide perovskite undergo crystal lattice relaxation, which might be driven by the strong structural distortions in bulk hybrid halide perovskites 33 . The resulting in-plane lattice expansion in monolayer perovskite (~0.1 Å for (BA) 2 PbBr 4 ) is responsible for the blueshift of both bandgap and photoluminescence emission, compared with the bulk counterpart. The emission characteristics are easily modulated by changing the halide composition or layer thickness (Fig. 3f) 35,62 . Moreover, the substitution of Pb with Ge and Sn lowers the bandgap range from 2.5-3.5 eV to 1.7-2.5 eV ref. 63 ). The incorporation of large semiconducting conjugated organic spacers into the inorganic matrix leads to charge transfer at the organic-inorganic interface on the timescale of a few picoseconds 36 . Such large conjugated ligands can also enhance the thermal and environmental stability of the isolated perovskite quantum wells.
In contrast to halide perovskite monolayers, the study of oxide perovskite monolayers remains at a nascent stage. Bulk crystals and thin films of this material family have already unveiled rich physical phenomena since the late 1980s, including high-temperature superconductivity, multiferroic behaviour and colossal magnetoresistance, due to electron-electron interactions and correlations in the constituent transition metal ions 22,26 . However, it is not well understood how these effects would transform when approaching the monolayer limit. So far, only two archetypical examples out of many possible candidates have been experimentally realized since 2019 22 . Previous studies on BiFeO 3 thin films suggest a thickness-dependent magnetic moment 64 (Fig. 4a) as well as an electric-field-tunable optical transmission (Fig. 4b) 65 . Ultrathin freestanding BiFeO 3 sheets, which are not subjected to epitaxial strain, exhibit lattice distortions and a giant polarization, because of a transition of the lattice from the R to the T-like phase when approaching the 2D limit 22 . Near interfaces, unusual 2D electron phases can arise due to the strong ionic character of oxide perovskites 66 . In ferroelectric crystals with broken spatial inversion symmetry, energy bands split as a result of Rashba spin-orbit coupling (Fig. 4c) 18 . This effect allows for the detection of spin currents as well as the conversion of charge current to spin current and vice versa, using the direct and inverse Edelstein effects without the need for ferromagnetic contacts or an external applied magnetic field (Fig. 4d,e) 67 . Through the application of a gate voltage across the interface, it is possible to manipulate the electron occupation as well as the asymmetry of the quantum well. This control over the interfacial potential drop alters the strength of the Rashba parameter and allows tuning of the magnitude of the Rashba spin-orbit splitting. For example, SrTiO 3 is a wide bandgap insulator that hosts a two-dimensional electron gas (2DEG) at the surface with a giant Rashba splitting producing two subbands separated with an energy gap of 90 meV and two concentric circular Fermi surfaces containing electron spins with opposite chiralities 68 . Interfacial superconductivity was discovered at SrTiO 3 /LaAlO 3 heterointerfaces, where the use of back-gating can control electrostatically the superconductor-metal-insulator transition (Fig. 4f) 69 . At SrTiO 3 /γ-Al 2 O 3 heterointerfaces, this 2DEG displays an electron mobility of up to 1.4 × 10 5 cm 2 V −1 s −1 (ref. 47 ). The combination of high mobility and long spin lifetime 70 are important prerequisites for efficient spin-charge conversion. A spin-charge conversion efficiency ten times larger than what has been reported in topological insulators such as HgTe and α-Sn has been reported in these 2DEGs 71 . This makes SrTiO 3 -based 2DEGs an appealing platform for the design of all-electrical spintronic devices. We note that according to density functional theory, similar properties can be expected in bismuth aluminate (BiAlO 3 ). It has been suggested that the polar distortion in this ferroelectric perovskite oxide in conjunction with a sizeable Rashba spin splitting 72 may enable the full conversion between spin and charge through polarization switching in a reversible manner. While Rashba splitting has been a well-known effect at the interfaces of oxide perovskites, the use of monolayer perovskites instead of the surface of a bulk layer offers additional degrees of freedom and considerably expands the toolbox of the spintronics community. For instance, the Rashba effect can be modulated by the structural distortions associated with diverse surface terminations. The charge conduction, spin transport and Rashba strength parameter can be far more easily manipulated by extrinsic parameters, including substrates (for example, suspended, encapsulated), contacts and heteroatom doping. Such ultrathin perovskite layers can also be used as a tunnel barrier in a junction, where the spin Hall effect appears because of the non-centrosymmetric nature of the barrier 73 . Spin polarization can also be controlled through chemical design 74 . The integration of chirality into perovskite structures can be achieved by embedding chiral organic and inorganic compo-nents 75 . This provides attractive venues in fields such as chiroptics, biosensing, quantum computing and for devices with non-volatile memory functionality. We note for the sake of completeness that large Rashba splittings not only occur in oxide perovskites but also have been observed in layered halide perovskite with energy splittings as large as (40 ± 5 meV) enriching this field further with the possibility of achieving ferroelectric control over spin textures 17 .

Potential device applications
As described in the previous section, different synthesis methods result in perovskite monolayers with diverse thickness, size, composition and controllability, which have a direct impact on their potential utilization. Monolayer perovskites grant the possibility to design and fabricate vertical/lateral heterostructures and artificial superlattices in any desirable fashion 37 . The molecular engineering offers a myriad of opportunities to tailor the optical, electronic and chemical properties in addition to the possibilities available through structural modifications and external dielectric screening 76 . Oxide perovskite monolayers are predestined for the use as catalysts due to their tunable structures and defect chemistry, while halide perovskite monolayers are attractive for photovoltaic applications, although their study for this purpose is at an early stage. Beyond that, also advanced photodetectors, batteries and other devices based on polariton interactions are conceivable, as described in more detail below (Fig. 5).
Photodetectors. Monolayer perovskites with moderate bandgaps are good candidates for photodetectors, because of efficient light adsorption, charge extraction and the absence of grain boundaries. The versatile band structure engineering methods, which can be deployed on halide or oxide perovskites, allow devices with light detection across a broad range of the electromagnetic spectrum. Moreover, in combination with conventional 2D materials (such as MoS 2 , WSe 2 and so on) the surface and interface properties can be modified to improve the photocarrier extraction 15 . As an example, a heterostructure device consisting of a monolayer tungsten disulfide (WS 2 ) and a thickness-tunable hybrid halide perovskite (MA) n+1 Pb n I 3n+1 has been shown to exhibit remarkable photosensing and charge separation capabilities 77 . Indeed, the p-n junction  with atomically sharp interfaces has a type-II band alignment (type I for thicker perovskite samples), which leads to an excellent photoresponsivity on the order of 10 4 AW −1 and an ultrafast photoresponse (64 μs). The photosensing ability of pristine halide perovskite has recently been demonstrated down to the monolayer level 19 . The internal quantum efficiency was 34% for a monolayer (BA) 2 (MA) 3 Pb 4 I 13 and 19% for the bulk crystal. The higher efficiency is attributed to the enhanced charge-collection efficiency in molecularly thin sheets. Moreover, the devices show ultralow dark current and on/off current ratios as high as 10 5 . The fortunate combination of excellent detection capability with the deformable nature of perovskite monolayers can potentially be brought in perfect synergy in smart photodetectors responding to external stimuli.

Batteries.
Oxide perovskites and their derivatives can serve as efficient and stable catalysts in metal-air batteries, where oxygen reduction and evolution reactions (ORR/OER) play crucial roles. For example, LaMnO 3+δ and LaNiO 3 particles exhibit significant intrinsic activity in ORR, which is comparable with a noble metal catalyst (such as Pt/C) 78 . The ORR performance of oxide perovskites is correlated with the amount of O 2 σ*-antibonding and the degree of B-site transition metal-oxygen covalency. Given that the ORR performance of these materials mostly depends on the surface area, oxide perovskite monolayers with completely exposed active sites can further boost the device performance. Some types of oxide perovskite, such as La 0.5 Li 0.5 TiO 3 , also have excellent lithium-ion conductivity up to 1 × 10 −3 Ω −1 cm −1 (ref. 79 ). Embedded oxide monolayers with fast Li + diffusion at the interface are promising ion conductors for rechargeable all-solid-state batteries.
Devices based on polariton effects. The optical and excitonic characteristics of 2D halide perovskites are also promising to benefit from polaritons in the strong light-matter interaction regime 80 .
The exciton-phonon interaction in (PEA) 2 PbI 4 is one order of magnitude larger than in gallium arsenide (GaAs) quantum wells 81 . Hence, monolayer halide perovskites are attractive active layers in electrically driven quantum well microcavity devices for polariton laser emission, which operate in the regime of strong coupling between excitons and photons 82 . Additional opportunities in electro-optics and nonlinear optics may arise by tuning the excitonpolariton interaction through chemical composition engineering of monolayer halide perovskites. The remarkable rise in power conversion efficiency of metal halide bulk perovskite photovoltaic cells can be largely attributed to favourable charge-carrier mobilities. Electrical transport studies on monolayers should therefore be an important target to unveil the fundamental charge transport mechanism. Currently, most studies still concentrate on field-effect transistors fabricated on spin-coated polycrystalline thin films. The measured carrier mobility ranges from 0.1 to 40 cm 2 V −1 s −1 (ref. 83 ). This value, however, probably underestimates the intrinsic carrier mobility, because of the defects and grain boundaries in the polycrystalline samples 84,85 . Although the use of halide single crystals can reduce the number of grain boundaries, at room temperature, the mobility is also limited by ion migration of the perovskite layers and the importance of the Fröhlich interaction 6 . Unfortunately, the incorporation of monolayer halide perovskites into field-effect transistors faces electrical contact issues. The insulating organic molecules on the surfaces act as a tunnelling gap and suppress the injection of electrons. An obvious strategy to try to achieve good electrical contacts is replacing the standard gold contacts with other metals, such as aluminium, titanium, silver, platinum and others to modulate the height of the Schottky barrier (Φ SB ) 86   layer (such as MoO x ) between the metal and the perovskite layer. The oxide interlayer reduces the Schottky barrier height, but does introduce an extra tunnel barrier 87 . Hence, an optimization of the competition between the desirable reduction of the Schottky barrier and the increase of the overall barrier thickness is required. Also graphene can be used as interlayer material. Even though it is a Dirac semimetal, the Fermi level or chemical potential can easily be adjusted by applying a gate bias, thereby effectively reducing the barrier height. Such additionally inserted layers can also protect the perovskite from ambient degradation.

Outlook
In contrast to the tremendous progress made in bulk perovskite crystals, the journey of exploring monolayer perovskites has just started. So far, only a few types of monolayers have been prepared, although numerous perovskites are stable in the 2D regime. It is of primary importance to develop new protocols to grow high-quality layered crystals and wafer-scale monolayers with high phase purity, sharp thickness control, tailorable composition and uniform crystal orientation. However, this requires a better understanding of the crystallization kinetics and thermodynamics of crystal nucleation. In addition, it is crucial to address the challenge of material instability under ambient conditions, especially for the halide perovskite monolayers. Attempts to isolate monolayers from bulk crystals should not be limited to sticky tape delamination or cleavage. Other exfoliation techniques, including shear-induced delamination, supercritical fluid-assisted exfoliation and ball milling, are worthwhile pursuing to make perovskite nanosheets. The resulting products can be dispersed in appropriate solvents that are attractive for printing technologies. On the other hand, epitaxial growth offers a fresh hunting ground to customize the lattice structure of monolayer perovskites through precise layer-by-layer deposition, which may lead to large-area films and interesting heterojunctions, such as Janus monolayers. Apart from the required tour de force in synthesis, an intense research thrust to disclose the fundamental physics of perovskite monolayers and the structure-property relationship, and to exploit their potential in prospective, innovative device concepts, is needed. For example, hybrid perovskite monolayers are direct-bandgap semiconductors with a 'built in' quantum well confinement potential and a remarkably strong light-matter interaction 15 . Bilayer devices allow the spatial separation of electrons and holes in the two quantum wells by applying a perpendicular electric field, so that interlayer excitons can form (Fig. 6a). The reduced overlap of the electron and hole wavefunctions increases the excitonic lifetime. Inorganic halide perovskite monolayers form a large family of 2D semiconductors possessing different bandgaps and work functions. By combining two of them or a single one with a TMD monolayer (MX 2 , where M = Mo, W and X = S, Se, Te), it is possible to create a type-II band alignment as shown in Fig. 6b 88 ; in such a configuration, electrons and holes will also occupy separate layers, causing a permanent electric dipole moment. Moreover, it should be possible to create a moiré superlattice potential via rotational misalignment or different lattice constants of perovskite heterobilayers. The induced moiré potential can trap interlayer excitons to create an ordered array of quantum dot-like emitters as well as enhance the effects of exciton-exciton interactions that contribute to the optical nonlinearity. Perovskite ionic lattices are also inherently more sensitive to strain than TMDs and external forces are bound to have a larger influence on the moiré potential landscape of perovskite heterobilayers. This may offer additional opportunities to manipulate interlayer excitons and the exciton moiré mini-bands as well as control the exciton-exciton interactions by external electric and magnetic fields in these systems.
In certain types of oxide perovskite, the coexistence of tunable Rashba splitting and superconductivity in 2DEGs predestine these compounds for the identification and fundamental study of Majorana fermions 67 , the key players in one of the paradigms towards quantum computation. Because of the completely exposed surfaces, monolayer oxide perovskites provide great ease to generate, control and convert spin current, the key ingredients for low-power spintronics. At present, monolayer-based perovskite devices are rather simplistic. Their integration with other 2D inorganic materials (such as boron nitride) or organic semiconductors (such as 2D metal-organic frameworks) will probably boost their usefulness, performance and functionality similar to what has happened in recent years with other 2D materials with the advent of van der Waals stacking. Ingenuity will coincide with the agony of choice. We posit that this class of new 2D material holds enormous potential for the future development of multidisciplinary research combining electronics, photonics and spintronics.