Picoperovskites: Diverse Perovskite Systems

• Picoperovskites are perovskite-derived systems encompassing s–p cubic compounds, one-dimensional nanowires, and He-filled frameworks, each with distinct structural and electronic features.
• They exhibit phenomena such as ligand-hole formation, exciton localization, and pressure-tuned phase stability, which are crucial for applications like superconductivity and photonics.
• Research emphasizes precise control over synthesis conditions—including pressure, temperature, and nanoconfinement—to access metastable states and tailor perovskite-derived functionalities.

Searching arXiv for papers on picoperovskites and related usages of the term. Picoperovskites is a term applied in recent literature to several perovskite-derived systems rather than to a single crystal-chemical class. The term has been used for s–p $ABX_3$ cubic perovskites in which the low-energy electronic states are built from a main-group cation $s$ orbital hybridized with anion $p$ orbitals, for one-dimensional metal halide perovskite nanowires encapsulated inside single-walled carbon nanotubes (SWCNTs), and for helium-intercalated A-site-vacant perovskites in which He occupies the A-site cavity and acts as an ultra-small, non-bonding occupant (Benam et al., 2021, Tomoscheit et al., 22 Jul 2025, Racioppi et al., 2023). Extreme-pressure work on PbTiO$_3$ further uses the term in a design-oriented sense for miniaturized or nanoscale perovskites, emphasizing how pressure–temperature trajectories, metastability, and decomposition can govern accessible phases (Farraj et al., 7 Nov 2025).

1. Terminological scope and structural settings

Recent usage separates picoperovskites into three principal structural contexts.

Usage in the literature	Definition	Representative systems
s–p $ABX_3$ picoperovskites	cubic perovskites in which the low-energy electronic states are built from a main-group cation $s$ orbital hybridized with anion $p$ orbitals	SrBiO$_3$, BaBiO$_3$, BaSbO$_3$, CsTlF$s$0, CsTlCl$s$1, MgPO$s$2, CaAsO$s$3, SrSbO$s$4, RaMcO$s$5
one-dimensional picoperovskites	one-dimensional metal halide perovskite nanowires encapsulated inside SWCNTs	CsPbI$s$6 nanowires confined inside SWCNTs
helium-filled picoperovskites	A-site-vacant perovskite frameworks filled by helium	HeAlF$s$7, HeGaF$s$8, HeInF$s$9, HeScF$p$0, HeReO$p$1, [He]$p$2[CaZr]F$p$3

In the s–p usage, the structural reference is the cubic $p$4 perovskite with corner-sharing $p$5 octahedra and A cations in 12-fold anion-coordinated sites. In the nanotube-encapsulated usage, the defining structural element is a perovskite core with diameter below 1 nm stabilized by a surrounding nanotube “scaffold” that also acts as an encapsulation barrier against environmental degradation. In the helium-filled usage, the parent hosts are A-site-vacant frameworks such as ReO$p$6-type and VF$p$7-type networks, where the perovskite topology is retained but the A site is empty until occupied by He (Benam et al., 2021, Tomoscheit et al., 22 Jul 2025, Racioppi et al., 2023).

This multiplicity of usage is technically consequential. In one case the emphasis is orbital hierarchy and negative charge-transfer physics; in another it is one-dimensional confinement, exciton localization, and photostability; in the third it is pore occupancy, vibrational entropy, and pressure-tuned mechanics. The PbTiO$p$8 study adds a fourth perspective by arguing that miniaturized or nanoscale perovskites (“Picoperovskites”) require careful control of pressure–temperature trajectories because the perovskite framework may be metastable against equilibrium decomposition under combined high $p$9–$_3$0 conditions (Farraj et al., 7 Nov 2025).

2. s–p $_3$1 picoperovskites as an electronic-structure class

Picoperovskites in the s–p sense are cubic perovskites in which the relevant cation orbital is $_3$2 rather than $_3$3, so it couples most strongly to the totally symmetric ligand molecular orbital built from $_3$4–$_3$5 orbitals, namely the O/halogen $_3$6 molecular orbital of the octahedral cage (Benam et al., 2021). The resulting $_3$7–$_3$8 hybridization produces a very large bonding–antibonding splitting that often exceeds the charge-transfer energy, and the symmetry of the $_3$9–$ABX_3$0 coupling makes the $ABX_3$1-dependent hybridization vanish at $ABX_3$2 and peak at $ABX_3$3. The minimal model contains one $ABX_3$4–$ABX_3$5 orbital and three $ABX_3$6–$ABX_3$7 orbitals per anion, for 10 orbitals per formula unit, and is parameterized by the nearest-neighbor hopping $ABX_3$8 and the charge-transfer energy

$ABX_3$9

The corresponding schematic Hamiltonian is

$s$0

A central result is that heavy $s$1 cations drive $s$2 negative through relativistic lowering of the cation $s$3 level. Negative $s$4 means that the anion $s$5-derived $s$6 level lies higher than the cation $s$7 level in the effective model, which favors ligand-hole character. When $s$8 and $s$9 is large enough to push the $p$0–$p$1 antibonding band above the non-bonding $p$2–$p$3 states, holes reside predominantly on the ligands. BaBiO$p$4 and SrBiO$p$5 are placed deep in the $p$6–$p$7 regime; MgPO$p$8, CaAsO$p$9, SrSbO$_3$0, BaSbO$_3$1, and CsTlF$_3$2 are closer to the crossover where $_3$3–$_3$4 and $_3$5–$_3$6 contributions are comparable; RaMcO$_3$7 and CsTlCl$_3$8 are placed near the $_3$9–$_3$0 boundary on the approximate phase diagram, although projected densities of states show strongly $_3$1–$_3$2-like holes (Benam et al., 2021). Representative DFT+MLWF parameters span MgPO$_3$3 with $_3$4 eV and $_3$5 eV, BaBiO$_3$6 with $_3$7 eV and $_3$8 eV, and RaMcO$_3$9 with $_3$0 eV and $_3$1 eV.

This electronic structure underlies the distinction between bond disproportionation and charge disproportionation. Charge disproportionation is formal valence separation on $_3$2 sites, for example

$_3$3

whereas bond disproportionation is a breathing-mode distortion with alternating short and long $_3$4–$_3$5 bonds without large changes in formal $_3$6 valence. In bismuthates with $_3$7, the self-regulating response is written as

$_3$8

or, at the octahedral level,

$_3$9

so the action is largely on the ligands rather than on strongly differentiated Bi valences. The paper explicitly connects strongly negative $s$00 and sizable $s$01 to bond disproportionation and to superconductivity upon hole doping in the bismuthates, with Ba$s$02K$s$03BiO$s$04 reaching $s$05 K and BaPb$s$06Sb$s$07O$s$08 reaching maximal $s$09 K (Benam et al., 2021).

3. One-dimensional metal halide picoperovskites

In the nanotube-encapsulated usage, picoperovskites are one-dimensional metal halide perovskite nanowires encapsulated inside SWCNTs (Tomoscheit et al., 22 Jul 2025). ADF-STEM shows CsPbI$s$10 nanowires confined inside SWCNTs, with a perovskite core diameter of about 0.8 nm within SWCNTs of $s$11 nm diameter. Polarization-resolved Raman spectroscopy identifies an RBM at 128.9 cm$s$12, consistent with a nanotube diameter of 1.36 nm, i.e. a (10,10) SWCNT, and the Raman G/D intensity ratio $s$13 indicates low SWCNT defect density. Optical microscopy and fluorescence imaging reveal aligned bundles with typical lengths around 9 $s$14m and apparent widths $s$15 nm.

The perovskite composition is CsPbI$s$16, and the heterostructures are produced by a melt-filling protocol. Pristine CsPbI$s$17 is prepared from CsI and PbI$s$18 and then combined with oxidized SWCNTs; the sealed mixture is heated to 525 $s$19C for 12 h. For optical characterization, the resulting powder is dispersed in isopropanol/ethanol, sonicated to loosen bundles, and deposited onto Si/SiO$s$20 wafers or TEM grids. DFT models the picoperovskite core as charge-neutral Cs$s$21PbI$s$22 inside a (10,10) CNT. The projected density of states confirms that the valence band is dominated by I-5$s$23 and the conduction band has mixed I-5$s$24/Pb-6$s$25 character, and the combined picoperovskite/CNT band structure is effectively a superposition of the isolated components, indicating negligible hybridization; the picoperovskite band gap remains $s$26 eV (PBE, no SOC), essentially unchanged by encapsulation (Tomoscheit et al., 22 Jul 2025).

Optically, these one-dimensional picoperovskites exhibit bright, linearly polarized photoluminescence with polarization preferentially oriented along the bundle axis. The degree of linear polarization is

$s$27

and the measured angular dependence implies $s$28 and thus $s$29. At 4 K, the picoperovskite PL peak is centered at 2.313 eV and is red-shifted by $s$30 meV relative to a bulk CsPbI reference measured under identical conditions. The dominant low-temperature peak exhibits a large FWHM $s$31 meV and high intensity, characteristic of self-trapped excitons. Temperature evolution reveals multiple peaks, including an E2 component with a linear blueshift of $s$32 meV between 75–300 K, corresponding to $s$33 meV/K, and a total PL amplitude that decreases by more than three orders of magnitude between 4 K and room temperature (Tomoscheit et al., 22 Jul 2025).

Time-resolved PL further distinguishes the one-dimensional system from bulk material. At 4 K, biexponential fits yield a slow component $s$34 ns and a fast component $s$35 ns; at 100 K, $s$36 falls to 208 ns and $s$37 to a few ns; above $s$38 K, lifetimes rapidly decrease to the single-digit nanosecond range, and beyond 200 K only monoexponential fits are feasible. The decay forms are

$s$39

with

$s$40

The long-lived component dominates at 4–50 K, whereas around 75 K the short-lived component overtakes, tracking the emergence of the second steady-state PL peak. The study attributes the long lifetimes and photostability to suppressed nonradiative recombination, one-dimensional confinement and exciton localization, and possibly charge-transfer excitons associated with a type-II-like band edge alignment between picoperovskite and CNT; however, the mechanism remains unresolved, and the paper states that self-trapped exciton localization versus charge-transfer excitons both can explain the long $s$41 and temperature dependence (Tomoscheit et al., 22 Jul 2025).

4. Helium-filled A-site-vacant picoperovskites

In the helium-intercalated usage, picoperovskites are perovskite frameworks with vacant A sites that are filled by an extremely small, inert atom—helium—whose tiny size and high compressibility allow it to occupy the A-site cavity without forming conventional chemical bonds (Racioppi et al., 2023). The parent hosts include ReO$s$42 (Pm$s$43m), ScF$s$44, VF$s$45-type rhombohedral systems such as AlF$s$46, GaF$s$47, and InF$s$48, and the neutral “double perovskite” [CaZr]F$s$49. He is treated structurally as a hard sphere and thermodynamically as a compressible, entropy-bearing species. Structure prediction was performed with XtalOpt v12.1, duplicate removal with XtalComp, and DFT relaxations with VASP 5.4.1 using PBE for crystal structure prediction and optB88-vdW for final relaxations; phonons were computed with Phonopy to confirm dynamical stability (Racioppi et al., 2023).

The thermodynamic description is explicit. For He insertion into an A-site-vacant perovskite MX$s$50, the formation enthalpy is

$s$51

and the free energy change is

$s$52

The central stabilization criterion is that entropy favors He-filled picoperovskites when the accessible volume of He in the perovskite pore exceeds the atomic volume of He in solid helium at the same pressure. Quantitative reference volumes for hcp He are 11.9 \AA$s$53/atom at 1 GPa, 8.4 \AA$s$54/atom at 5 GPa, and 7.0 \AA$s$55/atom at 10 GPa. This criterion explains why HeAlF$s$56 is destabilized entropically at 1 GPa but becomes stabilized above $s$57 K at 10 GPa, whereas HeGaF$s$58 requires very high temperature, above $s$59 K at 5 GPa, for $s$60 (Racioppi et al., 2023).

The predicted stability windows are diverse. HeReO$s$61 is enthalpy-driven and stable at $s$62 GPa across most temperatures, with $s$63 meV/atom at 10 GPa. HeScF$s$64 is favorable at 1 GPa for all temperatures considered and adopts P4/mbm at low pressure before transforming to R$s$65c and then Pnma. HeInF$s$66 becomes enthalpically favored in P6$s$67/m above $s$68 GPa, but $s$69 is negative only below $s$70 K. HeAlF$s$71 and HeGaF$s$72 are primarily entropy-driven at elevated temperature. In the [He]$s$73[CaZr]F$s$74 case, He uptake delays amorphization to $s$75 GPa, and DFT finds a monoclinic P2$s$76/c structure lower in enthalpy than earlier suggestions at 1 GPa (Racioppi et al., 2023).

Helium insertion also produces large mechanical and structural effects. The bulk modulus of AlF$s$77 increases from 46.5 GPa to 131.1 GPa in HeAlF$s$78, summarized in the paper as a change “from tin-like (~47 GPa) to steel-like (~131 GPa).” GaF$s$79 stiffens from 56.3 to 109.0 GPa, whereas ScF$s$80 and InF$s$81 change only modestly because their pores are already large. He hinders pressure-induced octahedral rotations and tilt transitions: in GaF$s$82, the M–F–M angle increases from $s$83 to $s$84 at 1 GPa; in InF$s$85, from $s$86 to $s$87; and in ReO$s$88, He preserves cubic Pm$s$89m and suppresses the Im$s$90 rotation-driven transition. Charge analyses and COOP/COHP indicate that He is essentially neutral and does not form significant covalent He–framework bonding (Racioppi et al., 2023).

5. Pressure–temperature path dependence and the PbTiO$s$91 design problem

The PbTiO$s$92 study does not redefine picoperovskites as a separate crystal-chemical family, but it explicitly frames its results as relevant to miniaturized or nanoscale perovskites (“Picoperovskites”) (Farraj et al., 7 Nov 2025). PbTiO$s$93 is a prototypical oxide perovskite ($s$94) with A = Pb and B = Ti. At ambient conditions it is ferroelectric and tetragonal, space group P4mm, with the polarization arising from Ti 3$s$95–O 2$s$96 hybridization and Pb–O covalency, and its Curie temperature is high, $s$97 K. Under pressure at room temperature, the classic P4mm $s$98 I4/mcm transition near 18–20 GPa is well established; I4/mcm is centrosymmetric (paraelectric) and nonpolar; and second-harmonic generation studies rule out a return to polar symmetry at higher pressures. The present work finds that the nonpolar tetragonal I4/mcm state persists up to at least 100 GPa on cold compression (Farraj et al., 7 Nov 2025).

The same composition follows a different path under combined high $s$99–$p$00. Polycrystalline PbTiO$p$01 compressed in diamond-anvil cells and probed by synchrotron X-ray diffraction persists in I4/mcm from 17 to 100 GPa at 300 K, but under laser heating at 87 GPa it decomposes to PbO and TiO$p$02. DFT calculations show that decomposition becomes enthalpically favored above $p$03 GPa, with reaction

$p$04

and

$p$05

The thermodynamic criterion is $p$06, and the paper emphasizes that temperature then enables diffusion and reaction, lowering $p$07 via the $p$08 term and overcoming kinetic barriers. No TiO$p$09 Bragg peaks were detected, likely because of overlap with PbO peaks and/or amorphization during laser heating, but cotunnite-type TiO$p$10 (Pnma) is identified as the expected thermodynamic product (Farraj et al., 7 Nov 2025).

The decomposition products are themselves structurally and electronically differentiated. Laser heating above $p$11 GPa produces two high-pressure PbO polymorphs, both P4/nmm: compressed $p$12-PbO with a three-dimensional framework topology and a previously unreported $p$13-PbO polymorph with a two-dimensional layered structure. At 87 GPa, $p$14-PbO has $p$15 \AA, $p$16 \AA, $p$17 \AA$p$18, and nearest Pb–Pb distance 2.871 \AA; $p$19-PbO has $p$20 \AA, $p$21 \AA, $p$22 \AA$p$23, Pb–Pb separation 2.996 \AA, and interlayer spacing $p$24 \AA. Upon decompression, both transform to $p$25-PbO (Pbcm). DFT r2SCAN calculations predict that $p$26-PbO metallizes above $p$27 GPa via band-gap closure, whereas $p$28-PbO remains semiconducting from 50–100 GPa with only modest gap reduction from $p$29 eV to $p$30 eV, and $p$31-PbO remains semiconducting with $p$32–1.7 eV up to at least 100 GPa (Farraj et al., 7 Nov 2025).

For picoperovskite design, the paper’s explicit implication is that cold compression can stabilize metastable nonpolar perovskite frameworks to very high pressures, while modest heating at the same pressures can trigger equilibrium decomposition into $p$33 constituents if the reaction becomes enthalpically favored. The source further states that, for miniaturized or nanoscale perovskites (“Picoperovskites”), where surface energies and kinetics can further shift phase stability, these findings argue for careful control of $p$34–$p$35 trajectories to access desired metastable phases or to deliberately synthesize novel high-pressure polymorphs (Farraj et al., 7 Nov 2025).

6. Common themes, misconceptions, and research directions

A first misconception is that picoperovskites denote a single, settled materials class. The literature sampled here uses the term for an orbital class of cubic s–p perovskites, a dimensionality-reduced nanowire-in-tube heterostructure, and a helium-filled A-site-vacant framework; the PbTiO$p$36 work uses it in a miniaturization-oriented design sense (Benam et al., 2021, Tomoscheit et al., 22 Jul 2025, Racioppi et al., 2023, Farraj et al., 7 Nov 2025). A second misconception is that holes in these systems are always cation-centered: in the s–p $p$37 case, negative $p$38 and sufficiently large $p$39 place the low-energy holes on ligand $p$40 states and favor bond disproportionation rather than charge disproportionation (Benam et al., 2021). A third is that exceptionally long photoluminescence lifetimes in one-dimensional picoperovskites already have a unique microscopic explanation: the available data do not conclusively distinguish self-trapped exciton localization from charge-transfer excitons (Tomoscheit et al., 22 Jul 2025). A fourth is that helium-filled picoperovskites are chemically bonded helium compounds in the usual sense: the source instead describes He as an ultra-small, non-bonding occupant that is essentially neutral (Racioppi et al., 2023). A fifth is that high pressure generically restores or enhances ferroelectricity in PbTiO$p$41: the cited work finds no evidence of re-entrant ferroelectricity and instead emphasizes metastable I4/mcm persistence on cold compression and decomposition under heating (Farraj et al., 7 Nov 2025).

Across these usages, several design principles recur. In s–p picoperovskites, the governing parameters are the charge-transfer energy $p$42 and the $p$43–$p$44 hybridization $p$45; strongly negative $p$46 plus sufficiently large $p$47 yields ligand holes and breathing-mode bond disproportionation, with superconductivity upon hole doping in the bismuthates (Benam et al., 2021). In one-dimensional halide picoperovskites, the decisive variables are confinement, nanotube encapsulation, anisotropy, and nonradiative suppression; the practical limitations are the more than three orders of magnitude drop in PL amplitude from 4 K to room temperature, the contraction of lifetimes to few-ns values above $p$48 K, and ensemble averaging over diverse CNT chiralities (Tomoscheit et al., 22 Jul 2025). In helium-filled picoperovskites, accessible pore volume, pressure, and temperature determine whether stabilization is enthalpy-driven or entropy-driven, and He insertion can be used to suppress Glazer tilts and tune stiffness (Racioppi et al., 2023). In PbTiO$p$49-derived design problems, metastability versus decomposition depends on the synthesis path, with cold versus hot compression selecting different states (Farraj et al., 7 Nov 2025).

A plausible implication is that picoperovskites are best understood as a family of perovskite problems posed at extreme limits: extreme orbital hierarchy in s–p compounds, extreme dimensional confinement in nanowire-in-tube heterostructures, extreme pore occupancy in A-site-vacant frameworks, and extreme path dependence under high pressure. Within that broad usage, the common research program is not a single stoichiometry, but controlled access to perovskite-derived states whose symmetry, carrier character, excitonic response, mechanical stiffness, or decomposition pathway becomes unusually sensitive to size, confinement, pore topology, and thermodynamic trajectory.