Extremely low thermal conductivity in rigid layered hybrid perovskites

Abstract

Materials with exceptionally low thermal conductivity are desirable for thermal insulation and waste heat recovery. While foams and aerogels boast ultralow thermal conductivities akin to air, lack of mechanical stiffness in these soft materials necessitates a paradigm shift in materials design that can offer thermal insulation and mechanical rigidity simultaneously. Here, we show that spun-cast layered hybrid organic-inorganic perovskite thin films, azobenzene ethyl ammonium lead iodides, exhibit a record-low thermal conductivity, down to ∼0.04 watts per meter per kelvin at room temperature, while maintaining mechanical rigidity with an elastic modulus of 7.7 gigapascals that surpasses that of most plastics, foams, and aerogels. This unusual combination of ultralow thermal conductivity and high mechanical rigidity is attributed to the specially engineered organic cations in the layered structure. Our finding highlights the potential of molecular engineering in hybrid layered structures to push the extreme of thermal insulation in dense, rigid solids.

INTRODUCTION

Materials with ultralow thermal conductivity are increasingly vital across modern energy technologies, where controlling heat flow directly influences efficiency, stability, and safety (1, 2). In thermal-insulation systems, from building envelopes to refrigeration and high-temperature industrial processes, suppressing thermal transport reduces energy demand and operating costs. In energy-conversion devices, thermal management is equally critical. For example, in high-flux solar modules, a thin film with ultralow thermal conductivity can act as an effective thermal barrier, limiting heat leakage into electronics, reducing thermal stress, and improving power stability (3). Energy-conversion and storage platforms such as fuel cells, hydrogen-production modules, and concentrated solar receivers require protective coatings that minimize parasitic heat loss and shield components operating at elevated temperatures (4). Similarly, in high-energy–density batteries and supercapacitors, thermal insulating interlayers can localize heat, slow intercell thermal propagation, and mitigate thermal runaway, offering a promising route to enhanced system-level safety and reliability (5).

Most crystalline and ceramic solids exhibit thermal conductivities within the range of 1 to 1000 W m⁻¹ K⁻¹ at room temperature, whereas plastics stay on the order of 0.1 W m⁻¹ K⁻¹. Only a handful of dense solids have thermal conductivities even lower than 0.1 W m⁻¹ K⁻¹ (6–11). Notably, two unconventional substances—stacking-disordered WSe₂ (6) and fullerene derivatives (7, 8)—exhibit a record-low thermal conductivity of ∼0.05 W m⁻¹ K⁻¹. Achieving such extreme suppression of thermal transport in fully dense solids is of broad relevance: It could enable more efficient thermal-insulation and energy-conversion technologies while also offering a platform to probe the fundamental limits of thermal transport in solids (1, 2).

In the pursuit of materials with ultralow thermal conductivity, their mechanical properties are also important attributes that cannot be overlooked (12). In applications such as electronics, cryogenics, industrial equipment, photovoltaics, and thermoelectrics, the ideal material that has both ultralow thermal conductivity and high mechanical stiffness is anticipated to offer optimized device performance and long-term durability. However, given a (typically) positive correlation between the thermal conductivity of common materials and their elastic modulus (shown in Fig. 1A and also in fig. S24), achieving both thermally insulating and mechanically stiff in one material is usually challenging (13). For example, plastics [e.g., polymethyl methacrylate (PMMA)] primarily have weak van der Waals interactions among individual chains. These weakly interacting chains result in low packing density and conformational disorders and thereby reduce thermal conductivity; the trade-off is to inevitably lower their mechanical stiffness. By contrast, diamond is extremely rigid due to its strong covalent bonds among carbon atoms, but such strong bonding restricts structural disorder and results in a much higher thermal conductivity. Because ambient air has a much lower thermal conductivity (∼0.026 W m⁻¹ K⁻¹) than any solid, a common strategy for thermal insulation is to create highly porous materials, such as foams and aerogels (14–16), which can achieve thermal conductivity close to that of air, albeit at the expense of their elastic moduli (typically several orders of magnitude lower than those of plastics).

Fig. 1. Engineering principle.

(A) Four representative materials from polymer to diamond, where thermal conductivity increases from low to high (Λ ∼ 0.1 to 2000 W m⁻¹ K⁻¹) and elastic modulus follows the same trend (E ∼ 1 to 1000 GPa) (93). (B) Engineering of organic cations in two-dimensional hybrid organic-inorganic perovskites (2D-HOIPs). Substituting an aliphatic cation with an aromatic one enhances rigidity and simultaneously diminishes heat transfer between cations. Incorporating double rings in the cation further boosts rigidity. Moreover, the elongated length of the cation amplifies the random stacking disorders between the inorganic layers. In addition, if the linkage between the double rings allows for a dihedral torsion, then this extra degree of freedom (df) is also beneficial to suppress thermal transport. These modifications from aliphatic cations are anticipated to decrease thermal conductivity while increasing the elastic modulus, as shown by the two shaded areas. (C) Crystal structure of four 2D-HOIPs with the chemical composition of the organic cations listed on the bottom. From left to right: (BA)₂PbI₄, (PEA)₂PbI₄, (SEA)₂PbI₄, (AEA)₂PbI₄.

Here, we present an exceptionally low thermal conductivity in layered hybrid organic-inorganic perovskites (HOIPs) while retaining their mechanical stiffness. This material exhibits a record-low thermal conductivity only 60% higher than that of ambient air at room temperature and an elastic modulus surpassing that of most plastics, foams, and aerogels. This unique combination of properties is enabled by tailoring their organic cations between the inorganic layers.

RESULTS

Layered HOIP as a platform

Record-low thermal conductivity in dense solids does not generally occur in amorphous materials (11, 17–19). Inorganic amorphous solids such as a-SiO₂ exhibit a well-known minimum thermal conductivity limit (also known as “amorphous limit”) (20) near ∼1 W m⁻¹ K⁻¹, as many vibrational modes become localized and do not transport heat. Polymers and other low-density amorphous molecular solids can reach even lower values (≈0.1 W m⁻¹ K⁻¹), but this originates primarily from weak intermolecular bonding and low packing density, not disorder alone (21).

In contrast, in layered hybrid organic-inorganic structures, the periodic stacking of organic and inorganic layers introduces a superlattice-like phonon band folding and mode hybridization that suppresses phonon group velocities (22, 23). A moderate degree of structural disorder, such as fluctuations in layer spacing or organic cation orientation, can further disrupt the periodicity and introduce additional phonon localization (24–26). This coexistence of partial long-range order and local disorder may enable the suppression of thermal transport beyond what is typically achievable in either fully crystalline or fully amorphous materials (27, 28).

With this context, layered HOIPs with tailored alternating organic-inorganic structures would be an ideal materials platform (29). Their alternating organic-inorganic architecture naturally combines structural rigidity with dynamic disorder: The inorganic metal-halide layers, built from strongly bonded corner-sharing octahedra, ensure long-range crystalline order, while the intercalated organic cations introduce orientational fluctuations and other local dynamic disorders (30, 31). Experimental and modeling studies on layered perovskites indicate signatures of coherent phonon transport and strong disorder-induced suppression of thermal conductivity, consistent with this picture (10, 32). Some previously studied (including our own work) layered hybrid perovskites have demonstrated thermal conductivity as low as that of plastics (10, 31, 33–36). For example, (BA)₂PbI₄ and (PEA)₂PbI₄ exhibit out-of-plane thermal conductivities of ≈0.20 and 0.13 W m⁻¹ K⁻¹, respectively. Moreover, their thermal anisotropy is notably weak (≈1.5 and 3.5) (37, 38), which is orders of magnitude smaller than those of inorganic layered materials such as graphite and MoS₂ (1, 39, 40). More recently, measurements using the vibrational-pump visible-probe technique reported thermal anisotropy ratios in the range of ∼1.6 to 2.7 across several layered hybrid perovskites with similar organic cations (41). This unusual combination of ultralow thermal conductivity and near isotropy in layered materials positions layered HOIPs as a unique materials platform for exploring and engineering extreme thermal insulation.

Engineering principles of organic cations in HOIPs

Here, we focus on tailoring the organic cations in layered structures, which is anticipated as a bottleneck for limiting mechanical rigidity and thermal insulating properties. Figure 1B illustrates the conceptual design of organic cations to be incorporated in layered HOIPs. Compared to their aliphatic counterparts, organic cations containing aromatic rings tend to have greater rigidity due to the stronger CH-π and π-π interactions (33, 42, 43). Thermal transport in layered perovskites is strongly influenced by the vibrational coupling at both organic-inorganic and organic-organic interfaces. Aliphatic chains provide abundant low-frequency vibrational modes (<200 cm⁻¹) that are thermally populated at room temperature and overlap with Pb-I lattice vibrations, facilitating interfacial heat conduction. In contrast, aromatic rings shift most of their vibrational spectrum to high frequencies (>800 cm⁻¹) that remain less populated at room temperature, reducing the number of active modes and thereby lowering both organic-inorganic and organic-organic thermal coupling (see detailed analysis in section S4) (44). These two pivotal roles of aromatic rings, verified through our previous theoretical and experimental work (33, 44), serve as the cornerstone of our engineering principles.

In this work, we introduce organic cations featuring two aromatic rings connected by a double-bond linkage. On one hand, doubling the number of aromatic rings with a strong double bond in between could further elevate the mechanical rigidity; on the other hand, the elongated length of the organic cation could alter the molecular packing and amplify the random stacking disorder between the inorganic layers, thereby suppressing thermal transport. Moreover, the double bond connecting the two rings may allow for a dihedral torsion between rings, by which dynamic disorders would be further increased to diminish thermal transport. Figure 1C shows the selected four organic cations and their atomic structures of the corresponding layered HOIPs: (from left to right) butyl ammonium (BA), phenethyl ammonium (PEA), stilbene ethyl ammonium (SEA), and azobenzene ethyl ammonium (AEA), respectively. Specifically, replacing the first two carbons in the aliphatic chain of BA with a benzene ring leads to PEA, both serving as control cations. In our double-ring design, we used C═C and N═N double bonds as the linkage, leading to two organic cations, SEA and AEA, respectively (see the crystal structure in CIF files).

Thin films of two-dimensional (2D) HOIPs (2D-HOIPs) (here, 2D specifically refers to layered HOIPs with the inorganic layer number n = 1) based on lead iodide and individual organic cations were then fabricated by spin coating the corresponding solutions of hybrid perovskites onto cleaned silicon substrates. The resulting samples were immediately annealed. Film composition and density were characterized by x-ray photoelectron spectroscopy (XPS), wavelength-dispersive x-ray fluorescence (WDXRF), Rutherford backscattering spectrometry (RBS), and hydrogen forward scattering (HFS), which confirm that the films are stoichiometric and fully dense. Film thickness and microstructure were characterized by atomic force microscopy (AFM) and grazing incidence wide-angle x-ray scattering (GIWAXS) techniques. More details regarding the sample synthesis and characterizations are described in Materials and Methods and sections S1 and S8.

Ultralow thermal conductivity in 2D-HOIP films

The out-of-plane thermal conductivity, Λ of four types of thin films described in Fig. 1C, was measured using the ultrafast-laser–based pump-probe time-domain thermoreflectance (TDTR) method (45–48). Figure 2A shows schematics of sample configuration and TDTR measurement with representative experimental data and heat transfer model fitting shown in Fig. 2B. At room temperature, with a film thickness around 150 nm, the measured thermal conductivity of (BA)₂PbI₄, Λ ≈ 0.2 W m⁻¹ K⁻¹, is the highest (Fig. 2C); both thermal conductivity of (PEA)₂PbI₄ and (SEA)₂PbI₄ (Λ ∼ 0.1 W m⁻¹ K⁻¹) is roughly half of that in (BA)₂PbI₄; last, (AEA)₂PbI₄ shows the lowest thermal conductivity of Λ ∼ 0.04 W m⁻¹ K⁻¹ among four. The trend approximately matches our engineering principles of organic cations. We note that the large interlayer distance or the high density of organic-inorganic or organic-organic interface alone does not explain the observed ultralow thermal conductivity in (AEA)₂PbI₄ because (SEA)₂PbI₄ has a similar structure.

Fig. 2. Thermal conductivity measurements.

(A) Schematics of sample configuration and ultrafast-laser–based TDTR measurement. 2D-HOIP thin films were spun cast on the Si substrate and were then subsequently coated with ≈20-nm-thick Cu and ≈80-nm-thick Al. The ultrafast laser beam is divided into pump and probe beams; the pump beam heats the sample surface, and the probe beam measures the surface temperature response upon heating with a controllable time delay between the two beams. (B) Representative experimental data (normalized temperature rise, termed as “ratio,” as a function of delay time between pump and probe beams), fitted with heat transfer model, for four types of 2D-HOIP films. Labels BA, SEA, PEA, and AEA are abbreviations for (BA)₂PbI₄, (SEA)₂PbI₄, (PEA)₂PbI₄, and (AEA)₂PbI₄, respectively. (C) Room-temperature out-of-plane thermal conductivity of 2D-HOIP films with a film thickness ∼ 150 nm. (D) Statistical analysis of the room-temperature thermal conductivity measurements on ∼150-nm-thick (AEA)₂PbI₄ samples processed with different annealing temperatures T_a and on multiple locations of samples. (E) Thermal conductivity (open circle) of (AEA)₂PbI₄ as a function of film thickness with the same annealing temperature of 80°C. The g-parameter (filled circle) that quantifies the lattice paracrystallinity and cumulative lattice disorder is also plotted. (F) Temperature-dependent thermal conductivity of ∼150 nm-thick (AEA)₂PbI₄ (red filled symbols), comparing with other 3D inorganic perovskites [MAPbI₃ in blue (56), with the data point close to the phase transition point removed for clarity, and CsPbBr₃ in green (55)] and inorganic layered crystal [disordered WSe₂ in purple (6)] in open symbols. The gray dashed line is the amorphous limit, ${\mathrm{\Lambda }}_{\text{min}}$, predicted from the Cahill-Pohl minimum thermal conductivity model, incorporating lattice anisotropy. The shaded area represents the prediction from our thermal resistant network model with a simple temperature-dependent treatment, with its boundaries indicating the upper and lower limits of the prediction.

We annealed the 150-nm-thick (AEA)₂PbI₄ films at three different temperatures and repeated the measurements on multiple locations of the films (see more details in section S2). The lowest thermal conductivity observed on one sample approaches 0.03 W m⁻¹ K⁻¹. Figure 2D displays the histogram analysis of all results, showing the consistency, repeatability, and uncertainty of the measured thermal conductivity in (AEA)₂PbI₄ films. The lowest statistically averaged thermal conductivity at room temperature is found in the 150-nm-thick (AEA)₂PbI₄ film annealed at T_a = 80°C. The obtained thermal conductivity is 0.043 ± 0.011 W m⁻¹ K⁻¹, which is only 60% higher than that of ambient air (0.026 W m⁻¹ K⁻¹), representing a record-low thermal conductivity in fully dense solids at room temperature (6, 7). We note that previously reported values of ultralow thermal conductivity were measured in a film thickness typically less than 100 nm [with some thicknesses even less than 10 nm (39, 49)] where vibrational modes with mean-free paths larger than the thickness of film will be suppressed (50); by contrast, the extremely low thermal conductivity we observed was obtained in a much thicker film (∼150 nm) at which thickness contributions from all the extended and propagating vibrational modes should already be accounted for.

Figure 2E shows the measured out-of-plane thermal conductivity of (AEA)₂PbI₄ as a function of film thickness at T_a = 80°C. Thermal conductivity decreases from 0.067 W m⁻¹ K⁻¹ at ∼85 nm to a minimum of 0.041 W m⁻¹ K⁻¹ at ∼150 nm and then increases to 0.07 W m⁻¹ K⁻¹ at ∼200 nm. Although the absolute minimum occurs near 150 nm, films with thicknesses in the ∼125- to 160-nm range consistently exhibit ultralow values (<0.05 W m⁻¹ K⁻¹), demonstrating that this effect is reproducible rather than a sample-specific outlier. The nonmonotonic characteristic points to an underlying structural parameter of importance.

To understand this nonmonotonic thickness dependence, we analyzed the GIWAXS data beyond basic analysis by determining the paracrystalline disorder. We used the Williamson-Hall method (51–53), which assumes cumulative lattice disorder and quantifies the paracrystallinity in the films through the g-parameter (see Materials and Methods and section S8). The analysis reveals a nonmonotonic variation of g with thickness, with the strongest stacking disorder observed for the ∼150-nm-thick films—precisely where the lowest thermal conductivity occurs. This correlation strongly supports the conclusion that enhanced paracrystallinity is responsible for suppressing thermal transport.

The temperature-dependent thermal conductivity of a ∼150-nm-thick (AEA)₂PbI₄ film is shown in Fig. 2F. The thermal conductivity first increases and then decreases with decreasing temperature from 300 to 100 K, showing a peak at ≈150 K. From 100 to 150 K, the increase is dominated by the increasing vibrational population where more vibrational modes are thermally excited and can participate in mode-mode coupling (see section S4). From 150 to 300 K, the temperature dependence of thermal conductivity can be approximately described by $\mathrm{\Lambda }\sim T^{-n}$, with n ≈ 0.77. In conventional dielectric and semiconducting crystals, thermal conductivity is approximately proportional to 1/T, i.e., n ∼ 1, because the thermal transport is mainly dominated by propagating phonon modes with their mean-free paths limited by three-phonon anharmonic scattering processes (6). In a case of strong anharmonicity in the crystal lattice, n will increase (n > 1) when higher-order phonon scattering processes contribute substantially (54). Whereas in many amorphous materials, such as glass, disorder substantially reduces the contribution of extended, propagating modes to thermal transport. Instead, thermal transport is mainly driven by the interactions between nonpropagating, diffusive modes. As a result, thermal conductivity increases with increasing temperature (n < 0) and reaches a plateau at the high temperature limit (n ∼ 0). Hence, the observed temperature dependence in (AEA)₂PbI₄ (n ≈ 0.77) is in between that of 3D inorganic perovskite crystals (n ∼ 1 in MAPbI₃ and CsPbBr₃) (35, 55, 56) and WSe₂ with rotational stacking disorder (glass like, n ∼ 0 at the high temperature limit) (6), implying a competition between two thermal transport channels including both propagating and nonpropagating modes in (AEA)₂PbI₄ (11).

In crystalline solids, thermal transport is typically described by the phonon gas model, where thermal conductivity decreases with increasing temperature due to enhanced phonon-phonon scattering. However, when the phonon mean-free path approaches the Ioffe-Regel limit, vibrational transport becomes diffusive rather than propagating. The hybrid organic-inorganic perovskites studied here operate in this regime: Although the inorganic framework remains crystalline, structural disorder and dynamic molecular motions in the organic cations strongly scatter and localize vibrational energy. This leads to suppressed transport length scales and ultralow thermal conductivity despite retained crystallinity. The observed temperature dependence—an increase at low temperature followed by a decrease at higher temperature—reflects the competition between increasing vibrational population and enhanced scattering from thermally activated molecular dynamics (MD), consistent with transport behavior intermediate between crystalline and amorphous limits (57, 58).

To further assess the transport regime, we compared the measured temperature-dependent thermal conductivity with the amorphous limit, ${\mathrm{\Lambda }}_{\text{min}}$, predicted from the Cahill-Pohl minimum thermal conductivity model, incorporating lattice anisotropy (20, 59). At low temperatures, the measured thermal conductivity lies above this limit, indicating that a substantial fraction of extended, propagating modes still contributes to thermal transport. As the temperature increases and approaches room temperature, however, the measured values fall below ${\mathrm{\Lambda }}_{\text{min}}$, implying that the contribution from extended, propagating modes is strongly suppressed and reduced to a minimum.

Disorder model

One plausible explanation for this unconventional temperature dependence is that the soft lattice and the dynamics of the organic cations enhance anharmonicity. In the case of 2D-HOIPs, although the organic cations are confined between rigid lead-iodide octahedra, which restricts translational motion, their oscillation amplitudes remain substantial, especially the rotational and tilting motion, owing to weak intermolecular interactions. As a result, the cation dynamics occupy an intermediate regime between those of a rigid solid and a freely diffusing liquid, which is referred to the “confined liquid-like” dynamics at elevated temperatures (43, 55, 60, 61). As temperature increases, both stacking and dynamic disorders become more pronounced (19). To quantify the impact of these effects, we apply our previously developed thermal resistance network model (see Materials and Methods), focusing on two dominant types of disorder (Fig. 3A): (i) Spatially dependent random stacking disorder between the inorganic layers, where the inorganic layers (accompanied by the organic cations) have random positional offsets with each other. These random offsets most likely correspond to low-energy states within the potential wells, as shown in Fig. 3B. (ii) Time-dependent dihedral torsion of the organic cations, characterized by a torsional angle $\mathrm{\theta }$ between the two aromatic rings in the AEA and SEA cations. Both the coordination number density n_c and torsional state energy E_tor vary with $\mathrm{\theta }$ (Fig. 3C). The characteristic oscillation frequencies of these disorders are presumably several orders of magnitude lower than those of dominant lattice vibrational modes. Nevertheless, they effectively weaken thermal contacts between cations and thereby suppress thermal transport mediated by nonbonded interactions. Figure 3D shows that the measured thermal conductivity agrees reasonably well with the thermal resistance network model’s predictions considering both stacking disorder and dihedral torsion. Furthermore, our model, even with a simplified temperature-dependent treatment, qualitatively reproduces the temperature-dependent experimental trend, consistent with the fact that both disorders become increasingly active at higher temperatures (see Fig. 2F and more analysis in section S6). These results confirm that stacking disorder and dihedral torsion are the dominant contributors to the ultralow thermal conductivity observed in (AEA)₂PbI₄.

Fig. 3. Theoretical modeling to identify dominant mechanisms for suppressing thermal conductivity.

(A) Two major thermally activated disorders: (i) Random stacking disorder where the inorganic layers (and consequently the organic cations) have random position offset with each other, demonstrated by the yellow translation arrows. (ii) Dihedral torsion between the two rings in the AEA and SEA cations, demonstrated by the blue rotation arrow. The solid and semitransparent images are the pristine and disordered crystal, respectively. (B) Energy potential well as a function of local stacking disorder in the X and Y directions (i.e., the in-plane direction of the layered crystal). The blue region represents the lower energies in the potential well, where random stacking disorders are probable. (C) The coordination number density, n_c, and energy of dihedral torsion state, E_tor, as a function of torsion angle θ. (D) Thermal conductivity modeling including disorders. When the effect of both disorders is ignored, the thermal conductivity of (SEA)₂PbI₄ and (AEA)₂PbI₄ is similar and higher than that of (PEA)₂PbI₄. Considering only the stacking disorder, thermal conductivity of (AEA)₂PbI₄ is substantially suppressed, while that of (SEA)₂PbI₄ decreases slightly, which matches with the size comparison of the regions shown in (B). With additional dihedral torsion, thermal conductivity of both (AEA)₂PbI₄ and (SEA)₂PbI₄ reduces substantially. SEA, PEA, and AEA are abbreviations for (SEA)₂PbI₄, (PEA)₂PbI₄, and (AEA)₂PbI₄, respectively.

We note that even small chemical modifications of organic cations, such as a different double bond, can alter the molecular packing density and dynamics. For example, the N═N bond in AEA is shorter and weaker than the C═C bond in SEA, and its lone-pair electrons could introduce distortions in the bonding geometry (see more discussions in section S6) (62). Our simulations reveal that these bond characteristics in AEA synergistically promote a molecular packing with a much higher probability of stacking disorder and dihedral torsion, leading to substantially reduced coordination number density and thus lower thermal conductance across adjacent aromatic rings in the adjacent cations (i.e., n_c), in (AEA)₂PbI₄ when compared with (SEA)₂PbI₄.

Thermally insulating yet mechanically stiff film

We conducted the elastic modulus measurements in these four perovskite thin films using the contact resonance atomic force microscopy (CR-AFM) method (see Fig. 4A for the schematics and Materials and Methods for the details). Figure 4B shows an example statistical fitting using the normal distribution function in a (AEA)₂PbI₄ sample. The elastic moduli of (AEA)₂PbI₄ thin films with three thicknesses annealed at 80°C are all larger than 7 GPa, with E = 7.67 ± 2.47 GPa for the ∼150-nm-thick film (see the data in section S7). We also found that the elastic modulus of 2D-HOIPs with aromatic components in the cations is usually higher than that with aliphatic counterpart. For example, E ≈ 3.3 GPa for (BA)₂PbI₄, whereas E ≈ 8.3 GPa for (SEA)₂PbI₄ and E ≈ 12.3 GPa for (PEA)₂PbI₄. These fully dense solid thin films have orders-of-magnitude higher elastic modulus than that of porous thermal-insulation materials, such as aerogel (E << 1 GPa) (14, 63), polystyrene or polyurethane foam (E << 1 GPa) (64), nanowood (E ≈ 0.015 GPa) (65), and most plastics (E ∼ 1 to 4 GPa) (64).

Fig. 4. Elastic modulus and materials-screening metric.

(A) Schematics of the CR-AFM method for elastic modulus mapping. (B) A typical statistical analysis of the elastic modulus map measured on a representative (AEA)₂PbI₄ sample (T_a = 80°C, d = 200 nm). (C) A summary of anisotropic thermal conductivities and elastic moduli of thermal insulating candidate materials, categorized into three classes—porous materials, organic and hybrid materials, and inorganic layered materials—to highlight the distinct performance trade-offs and application spaces of each. The open and filled circles represent the cross-plane and in-plane thermal conductivity, respectively. BA, PEA, SEA, and AEA are abbreviations for (BA)₂PbI₄, (PEA)₂PbI₄, (SEA)₂PbI₄, and (AEA)₂PbI₄, respectively. (D) Materials-screening metric $E/\overline{\mathrm{\Lambda }}$ of these thermal insulators at room temperature (see section S9 for the raw data) to evaluate the materials performance applied for flexible multilayer energy applications. The red and blue bars are from this work and literature, respectively. PCBM is a fullerene derivative, [6,6]-phenyl-C₆₁-butyric acid methyl ester. Values for PCBM (7, 94), r-WSe₂ and r-MoSe₂ (6, 9), r-MoS₂ (r means rotational stacking disorder) (39), PMMA (64), polystyrene (PS) foam (64), aerogel (14, 63), and nanowood (65) were taken from references. The error bars only reflect the variation among reported values from different publications or our best estimates for the in-plane thermal conductivity where direct data are unavailable. The individual uncertainties for both the elastic modulus and thermal conductivity are shown in the Supplementary Materials.

Figure 4C summarizes the anisotropic thermal conductivities and corresponding elastic moduli of candidate thermal-insulation materials, categorized into three classes—porous materials, organic and hybrid materials, and inorganic layered materials—to highlight their distinct performance trade-offs and application spaces. Porous materials offer ultralow and isotropic thermal conductivity but lack mechanical integrity; inorganic layered materials exhibit high stiffness and strong thermal anisotropy and are suited for directional heat spreading; while organic and hybrid materials—including the HOIPs studied here—fill a unique position where mechanical compliance, near-isotropic thermal insulation, and processability are essential. This combination is particularly advantageous for practical flexible multilayer device architectures, such as perovskite- or polymer-based solar cells, where heat flow occurs in mixed directions and mechanical compatibility across interfaces is critical. Within this context, we introduce a materials-screening metric $E/\overline{\mathrm{\Lambda }}$ to compare thermally insulating candidate materials at room temperature. This metric serves as a simple and intuitive guide for identifying materials that balance isotropic thermal insulation with mechanical stiffness. For layered materials, we use $\overline{\mathrm{\Lambda }}=\sqrt{{\mathrm{\Lambda }\mathrm{\Lambda }}_{\mathrm{i}}}$ where $\mathrm{\Lambda }$ and ${\mathrm{\Lambda }}_{\mathrm{i}}$ are the out-of-plane and in-plane thermal conductivity, respectively. A full justification for this definition, from both the fundamental standpoints and practical relevance, is provided in section S9. Figure 4D shows the metric values of the 2D-HOIPs investigated in this work, benchmarked against other thin films with ultralow thermal conductivity and representative bulk thermal insulators at room temperature. For clarity, the comparison is limited to materials with thermal conductivities below 0.2 W m⁻¹ K⁻¹. A recent study (66) reported that Ba₃Zr₂S₇ exhibits a high metric value (∼100) under our definition; however, its average thermal conductivity is considerably larger, ∼0.69 W m⁻¹ K⁻¹. By contrast, (AEA)₂PbI₄ achieves the highest metric value among all materials in this ultralow–thermal-conductivity regime.

DISCUSSION

Our engineering principles emphasize two key factors: (i) vibrational coupling across organic-inorganic and organic-organic interfaces and (ii) the combined influence of stacking disorder and organic cation rattling. Aromatic cations, while rigid, also help suppress thermal transport by shifting their vibrational spectra to higher frequencies, thereby weakening vibrational coupling, while dynamic rattling and stacking disorder further suppress the thermal transport. The consistency between thermal conductivity and elastic modulus measurements, together with theoretical analysis, validates this framework and motivates its further refinement.

Through molecular engineering of organic cations, the local bonding environment and molecular packing can be tuned. This control suppresses thermal conductance between organic cations—the bottleneck in the overall heat transfer pathway—while the double aromatic rings maintain mechanical rigidity. The comparison between AEA and SEA illustrates both the power and limitations of the approach. While SEA follows the general engineering principles of introducing rigidity, conjugation, and ring linkages, its molecular packing does not amplify stacking disorder to the same extent as AEA (Fig. 3D). Our phenomenological model qualitatively explains this difference, but first-principles predictive accuracy remains challenging. This highlights that the details of organic cation chemistry and the specific types of disorder they promote play a decisive role in thermal transport and are not yet fully predictable a priori. Rather than undermining the engineering principles, the SEA case underscores the need for deeper exploration of molecular cations that govern disorder in layered perovskites.

Looking forward, our design framework offers broad opportunities for molecular engineering. For example, if a double-ring cation were synthesized with a torsional energy E_tor an order of magnitude lower than that of (AEA)₂PbI₄ at the same torsional angle θ (while maintaining other structural features), then our estimates suggest that the thermal conductivity of the resulting perovskite could approach that of ambient air (see section S10). This prospect highlights the vast potential of chemical synthesis to realize extreme thermal insulation in layered HOIPs.

Previous studies investigating extremely low thermal conductivity have predominantly focused on inorganic layered materials, where either a high density of dissimilar interfaces or random stacking disorder is introduced to create notable thermal resistances. While these materials exhibit ultralow thermal conductivity along the out-of-plane direction, their in-plane thermal conductivity is typically much higher, making them potential candidates for anisotropic heat spreaders (39), not near-isotropic thermal insulators. Synthesizing such thin film coatings requires a high-vacuum deposition chamber and a suitable substrate, with the precise control of stacking disorder posing a substantial challenge. By contrast, layered HOIP films are solution processed, which can be easily adapted for large-area surface coating on a variety of flexible or unconventional substrates in a scalable and cost-effective manner (29, 67).

The extreme suppression of heat conduction in this rigid crystalline perovskite offers a design strategy for energy-efficient coatings and energy-conversion devices. With a thermal conductivity up to five times lower than that of typical polymer or perovskite layers, this material enables thermally decoupled device architectures that combine strong optoelectronic performance with enhanced thermal stability. Its mechanical rigidity and radiation tolerance further position it as a promising candidate for space energy systems, where passive thermal control and material resilience are critical (68). In addition, such crystalline thin films could potentially serve as a solid-state thermal barrier in energy-conversion and storage technologies, reducing parasitic heat loss in fuel cells or solar receivers and mitigating thermal runaway in batteries or supercapacitors. Although not thermoelectric, the underlying design principle of achieving ultralow thermal conductivity in a dense crystalline solid may guide the development of next-generation thermoelectric materials. These materials are particularly envisioned for near–room-temperature thermal insulation [see the thermogravimetric analysis (TGA) result in section S7], where ultralow thermal conductivity under practical conditions is critical.

In summary, we demonstrate a record-low room-temperature thermal conductivity, Λ ≈ 0.043 ± 0.011 W m⁻¹ K⁻¹, in 2D-HOIP films. This extreme thermal conductivity is attributed to the thermally activated stacking and dynamic disorders, benefiting from the rational engineering of organic cations. We show that these solution-processed films are also unexpectedly mechanically stiff, E ≈ 7.67 ± 2.47 GPa, positioning them well for thermal insulating coating applications. Considering the vast compositional and structural space and overall versatility in layered hybrid perovskites, our findings open an avenue of research and serve as an impetus for pushing the extremes in heat conduction while retaining mechanical rigidity.

MATERIALS AND METHODS

Synthesis of hybrid perovskite thin films

Boron-doped p-type single-side–polished (100) Si substrates (University Wafer) with a resistivity of 1 to 10 Ω·cm were cleaned with ultrasonic wave in deionized water, acetone, and then 2-propanol for 15 min each. The substrates were dried under a stream of nitrogen and subjected to the treatment of ultraviolet ozone for 15 min. For (AEA)₂PbI₄ and (SEA)₂PbI₄, the precursor solution was made by dissolving corresponding ammonium iodide salt (AEAI and SEAI) and PbI₂ in N,N′-dimethylformamide (DMF):dimethyl sulfoxide = 4:1 with the molar ratio of 2:1, and the solution was stirred at room temperature for 1 hour. The concentration of Pb²⁺ is varied to change the film thickness. The layered perovskite thin film was obtained by spin coating precursor solution onto the precleaned Si substrate with a two-step spin coating process (2000 rpm for 2 s followed by 4000 rpm for 20 s). At the 13 s in the second step, 0.3 ml of toluene for (AEA)₂PbI₄ or 0.3 ml of chlorobenzene for (SEA)₂PbI₄ was dropped on the spinning substrate. After spin coating, the samples were immediately annealed. For (PEA)₂PbI₄, the precursor solution was made by dissolving PEAI and PbI₂ in DMF with a molar ratio of 2:1, and the solution was stirred at room temperature for 1 hour. The concentration of Pb²⁺ is 0.3 M. The layered perovskite film was obtained by spin coating precursor solution onto a precleaned Si substrate at 5000 rpm for 20 s. After spin coating, the samples were immediately annealed at 80°C for 30 s. All the samples were kept in a nitrogen gas–filled glove box for further use.

Film characterizations

To characterize the elemental composition of the thin films, we conducted XPS and WDXRF. The XPS spectra were obtained using a monochromatic 1486.7-eV Al Kα x-ray source on a PHI VersaProbe II spectrometer with a 0.47-eV resolution. The WDXRF spectra were acquired on a Rigaku ZSX Primus II XRF using a Rh Kα source (20.2161 keV, 0.6147 Å) and a LiF (200) crystal monochromator (4.027 Å). In addition, we carried out an independent analysis of thin film density and composition using RBS and HFS. RBS spectra were acquired at a normal backscattering angle of 160° and an appropriate grazing angle (∼100°; with the sample oriented perpendicular to the incident ion beam). In an HFS experiment, a detector was placed 30° from the forward trajectory of the incident He⁺⁺ ion beam, and the sample was rotated so that the incident beam strikes the surfaces 75° from normal. More details can be found in section S1.

GIWAXS measures the diffracted intensity of an x-ray beam with an incidence angle close to the total external reflection angle of the 2D hybrid perovskite film. Simultaneous measurement of the in-plane and out-of-plane diffraction intensity using a 2D detector allows for the determination of the orientational order parameter and crystallite coherent length of the perovskite films. To quantify the degree of structural disorder in the layered perovskite thin films, we carried out a paracrystallinity and coherence length analysis of the GIWAXS data using the Williamson-Hall method (51–53). In this method, paracrystallinity in the thin films is quantified by the g-parameter, defined as the relative SD of the lattice spacing (g = σ_d/d). In an ideal crystal, successive lattice planes are separated by a constant distance d, whereas in a paracrystal, the disorder in atomic locations is cumulative rather than random lattice distortions. These distortions result in a small perturbation to the long-range order of the lattice and cause higher-order diffraction peaks to broaden progressively with increasing order n. More details can be found in section S8.

TDTR measurements

Thermal conductivity of hybrid perovskite thin films was measured using the TDTR method (see Fig. 2A) (33, 45, 46). Before the TDTR measurements, an ∼80-nm-thick Al thin film and a 20-nm-thick Cu thin film were deposited on the samples via electron-beam evaporation (69). The samples were sealed in a protected Argon gas environment during the measurements. For the TDTR measurements, a mode-locked Ti:sapphire laser (Tsunami, Spectra Physics) generates a train of pulses with a temporal width of ∼200 fs at a repetition rate of 80 MHz. The spectrum of pulses is centered at 785 nm with a full width at half maximum of ≈10 nm. A mechanical delay stage is used to change the optical path difference between the pump and probe beams before they are focused through an objective lens onto the sample surface. The radius of the focused Gaussian laser beams is ≈12 μm. The pump beam is modulated at a modulation frequency f = 1.04 MHz so that the thermoreflectance change at the sample surface could be detected by the probe beam via lock-in detection. The laser power on the sample surface could be adjusted and measured accurately to control the temperature rise within the sample to be less than 10% of the environmental temperature. The samples are allowed to cool down for ≈10 min before each TDTR scan. The low-temperature measurements were carried out in the cryostat ARS-DMX-20-OM with optical access. The reported temperature values represent the sum of the environmental temperature and the steady-state laser-induced temperature rise in the sample. We note here that the measured thermal conductivity is predominantly in the out-of-plane (i.e., through thickness) direction due to a larger Gaussian beam radius (∼12 μm) compared to the thermal penetration depth (∼0.1 μm)—the length scale at which thermal wave penetrates the film in our measurement. Other details regarding optimizing the measurement condition, sensitivity analysis, and uncertainty calculations are presented in section S2. The details regarding the measurement results dependence on laser modulation frequency, laser spot size, and Cu film thickness are also presented in section S2.

Elastic modulus characterization

CR-AFM is a dynamic AFM mode that uses the AFM cantilever resonance to measure the mechanical properties of materials, which has been widely used to quantify the elastic modulus of thin films, 2D materials, and single crystals (70–74). In this study, all CR-AFM measurements were performed with an MFP-3D Infinity AFM (Asylum Research, an Oxford Instrument Company, CA) enclosed by a customized chamber under dry air flow (relative humidity < 3%). Before the AFM measurements, the deflection sensitivity of the AFM cantilever (ZEILR, NanoWorld) was calibrated by force curves on a silicon surface freshly cleaned by Piranha solution (98% H₂SO₄:35% H₂O₂ = 3:1 by volume) (71, 73). The spring constant of the cantilever, $k_{\mathrm{c}}$, was then calibrated by fitting the first free resonant peak to equations of a simple harmonic oscillator to measure the power spectral density of the thermal noise fluctuations in air (75, 76). The ultrasonic actuation of the AFM cantilever was achieved by gluing the perovskite thin film sample to an ultrasound transducer (V133-RM, Olympus NDT); see schematics in Fig. 4 (71–73). The dual actuation resonance tracking approach built in our MFP-3D Infinity AFM was used to track the contact resonance frequency simultaneously during the contact mode topographic imaging, and the total applied force $F$ (including the adhesion force) during the scanning was also recorded (73). The dynamic behavior of the AFM cantilever can be modeled as an Euler-Bernoulli beam oscillating with a mechanical constraint at the tip position to extract the tip-sample contact stiffness $k^{\ast }$ (70, 72, 77). $k^{\ast }$ can then be converted to the reduced modulus (also called indentation modulus) $E^{\ast }$ of the tip-sample contact through contact mechanics models. Here, we used the most–widely used Hertzian contact model for the analysis, where the AFM tip-sample contact is approximated as a spherical indenter with a radius $R$ contacting a flat surface with a total force $F$ (70, 72, 77)

$$k^{\ast }=\sqrt[3]{6\mathit{FR}{E}^{\ast 2}}$$ (1)

$E^{\ast }$ can then be used to derive the material’s elastic modulus by

$$\frac{1}{E^{\ast }}=\frac{1-{\mathrm{\upsilon }}_s^2}{E_s}+\frac{1-{\mathrm{\upsilon }}_t^2}{E_t}$$ (2)

where $E_{\mathrm{s}}$ and $E_{\mathrm{t}}$ are the Young’s moduli and ${\mathrm{\upsilon }}_{\mathrm{s}}$ and ${\mathrm{\upsilon }}_{\mathrm{t}}$ are the Poisson’s ratios of the sample and the tip (silicon in this case), respectively. The tip position on the cantilever and the tip radius $R$ were calibrated by CR-AFM measurements on a sample with known stiffness. More details are described in section S7.

Modeling the roles of disorders in suppressing thermal conductivity

In complex compounds with strong anharmonicity such as layered HOIPs, the thermal conductivity ${\mathrm{\Lambda }}_{\mathrm{L}}$ in the framework of the Wigner transport equation comprises two-channel thermal components: crystal-like (population conductivity from particle-like phonon propagation, ${\mathrm{\Lambda }}_{\mathrm{P}}$) and liquid-like (coherence conductivity from wavelike phonon tunneling, ${\mathrm{\Lambda }}_{\mathrm{C}}$) terms, i.e., ${\mathrm{\Lambda }}_{\mathrm{L}}={\mathrm{\Lambda }}_{\mathrm{P}}+{\mathrm{\Lambda }}_{\mathrm{C}}$ (78). In modeling, ${\mathrm{\Lambda }}_{\mathrm{P}}$ coincides with the Peierls-Boltzmann thermal conductivity in crystals from particle-like phonons, while the wavelike phonon tunneling contributes to ${\mathrm{\Lambda }}_{\mathrm{C}}$ as described by the Allen-Feldman equation for amorphous materials. There are many recent modeling works using first-principles–based method to resolve the two-channel thermal transport mechanisms in complex crystals but with a relatively reasonable number of atoms in the primitive cell (58, 78–87). Layered HOIPs exhibit substantial structural disorder, including stacking faults and layer-spacing variations. Because of the large number of atoms (284) in the primitive cell of these hybrid perovskites in our work and the dynamic disorders present at high temperature, it is prohibitive to compute the thermal transport properties using the ab initio first-principles–based methods (see section S4). Capturing these long-range variations requires simulation domains far larger than the typical supercell size feasible for full-atom ab initio MD simulation.

Empirical potential–based MD simulation might be a good method to provide insights on thermal transport in complex crystalline materials at the high temperature limit. On the basis of extensive literature and our own experience, although MD-predicted density, heat capacities, elastic properties, and phonon density of states agree reasonably well with the experiments in the existing literature (31), we find that MD simulations can only reproduce experimental results of thermal conductivity only in limited cases of hybrid perovskites, and systematic discrepancies emerge when the organic cation becomes complex (e.g., containing aromatic rings). For this reason, we did not attempt to report quantitative thermal conductivities from MD in this study. Instead, we developed a phenomenological model to rationalize the observed reduction in thermal conductivity with increasing structural and dynamic disorder.

Recently, we developed a unified thermal conductivity formula for disordered materials systems, such as polymer glass, liquids, and amorphous solids, based on the concept of Einstein’s random walk across a thermal resistance network (88–91). With properly defined fundamental units for heat transfer in these materials, we demonstrated that their thermal conductivity is dominated by the thermal resistances between neighboring fundamental units. This unified model can also be applied to the heat flow in the cross-plane direction of layered HOIPs because thermal resistances between two weakly bonded ligands dominate the total resistance, if we treat ligands as fundamental units. The local thermal resistance strongly depends on the local distance between neighboring fundamental units. When the distance between two fundamental units is larger than a critical distance, we regard these two units as thermally disconnected (“OFF”). Otherwise, they are strongly connected with a substantial heat transfer capability (“ON”). On the basis of the thermal resistance network, the thermal conductivity Λ is written as

$$\mathrm{\Lambda }=\frac{L}{A}{\displaystyle \sum _i}\frac{1}{R_i}=L\frac{N_{\mathrm{c}}}{A}\overline{h}={\mathit{Ln}}_{\mathrm{c}}\left(2\mathrm{\nu }{C}_{\text{per}}\right)$$ (3)

where L and A are the cell length in the cross-plane direction and cross-sectional area of the cell, respectively. R_i is the local thermal resistance between neighboring fundamental units. $\overline{h}$ is the average thermal conductance between neighboring fundamental units. N_c is the number of connections (“ON” states, also called coordination number) and $n_{\mathrm{c}}$ is the coordination number density, which represents the number of connections between fundamental units per unit area. ν represents the characteristic vibrational frequency of the fundamental units, which can be determined from the melting temperature, molar mass, and molar volume of the ligands. C_per is the molar heat capacity. To account for thermally activated dynamic disorders, we calculated the thermal conductivity at each “snapshot” where atomic positions can be considered as fixed, representing a randomized but thermally accessible configuration of the layer structure, and subsequently averaged these values across all snapshots. This approach is justified as the timescale for dynamic disorder is much longer than thermal transport across fundamental units, which is notably longer than thermal transport within these units. More details of this formula can be found in section S6.

The inorganic layers in the layered hybrid perovskites could slide randomly with respect to each other, and the coordination number density of organic cations would change accordingly. Because of the unique molecular packing in each perovskite, the energy potential wells are distinct among the three perovskites, shown in Fig. 3B, where the blue regions represent the most probable random stacking disorder. We applied the Monte Carlo method to simulate all the possible random stacking disorders and used the average coordination number density (treat them as equal probability) to compute the thermal conductivity with the consideration of stacking disorder.

Because of the presence of two isomers in the AEA and SEA ligands, the two isomers can have trans and cis configuration relative to each other. This feature leads to the known photoisomerization behavior in azobenzene-like molecules (92). The energy fluctuations in the organic cations at room temperature will inevitably give rise to variations in the cation molecule’s conformation, thus varying the coordination number density. As shown in Fig. 3D, the coordination number density $n_{\mathrm{c}}$ of both AEA and SEA will substantially decrease when the dihedral torsional angle between the two isomers $\mathrm{\theta }$ increases slightly. However, the total energy of the conformation state due to torsion increases with the torsional angle. To consider the varying conformations of molecules induced by thermal fluctuation of energy at room temperature, the weighted average coordination number density ${\overline{n}}_{\mathrm{c}}$ can be calculated on the basis of $n_{\mathrm{c}}\left(\mathrm{\theta }\right)$ by assuming that the occupation probability of the energy states at different torsional angles follows the Maxwell-Boltzmann distribution function. Then, the thermal conductivity considering both the stacking disorder and dihedral torsion can be obtained. More details about the application of this formula to layered perovskites can be found in section S6.

Supplementary Materials

The PDF file includes:

Sections S1 to S11

Tables S1 to S12

Figs. S1 to S27

Legend for movie S1

Legends for files S1 and S2

References

Other Supplementary Material for this manuscript includes the following:

Movie S1

Files S1 and S2