To explore our idea, we applied a point force on the surface of centrosymmetric materials (i.e., SrTiO₃ single crystals, cubic crystal system, space group \mathit{Pm}\overline{3}m) to investigate the induced pyroelectric effect. The point force was exerted by the tip of a custom-made micrometer-scale indentation system (Fig. 1B and Fig. S1), which locally breaks the centrosymmetry via the generated strain gradient (Fig. 1C). In our experiments, the micrometer-scale indentation system was equipped with a femtoampere-level current amplifier-filter and a temperature control system. The temperature control system enabled the precise heating and cooling of sample, achieving an absolute precision of ±0.1 K. A conductive micrometer-scale tip applied a localized force on the sample surface while simultaneously collecting the resultant pyroelectric current.

The SrTiO₃ single crystal is an ideal platform for studying the flexoelectric effect, owing to their simple cubic centrosymmetric lattices (which excludes piezoelectricity as well as ferroelectricity and facilitates the flexoelectric analysis) and relatively large dielectric permittivity (χ > 300 at 300 K, which endows the materials with high flexoelectricity). Unlike its sister material BaTiO₃, SrTiO₃ does not exhibit the pyroelectric effect because it has a center of inversion symmetry. However, when the tip loading force breaks the intrinsic centrosymmetry of SrTiO₃, a flexoelectric polarization is generated, and this induced flexoelectric polarization varies with temperature fluctuation (Fig. 1D). As a result, the temperature fluctuation-induced variation of the flexoelectric polarization theoretically enables the FP effect in the centrosymmetric SrTiO₃ single crystal. As shown in Fig. 1E, when a sinusoidally varied temperature stimulus is applied around the contact area on a (001) face of an SrTiO₃ crystal, a marked and stable current that changes in frequency with the temperature is observed under tip force loading. It is worth noting that there is a phase shift of 90° phase difference between the temperature signal and the FP current signal (Fig. 1E). This means that the FP response is not resistive (and thus not a shift current) but rather dielectric in nature, originating from polar displacement. Specifically, if the phase difference between current and temporal temperature gradient is 90°, the polarization (from which the current is the time derivative) is in phase with the temporal temperature gradient.

To solidly demonstrate the validity of the FP effect, we investigated the FP current in response to the temperature fluctuation with controlled period and amplitude. As shown in Fig. 2A, no matter what the period of temperature fluctuation is, the period of FP current is always highly consistent with the period of the temperature, and there is always a phase shift of 90° between them. This consistency of period indicates that the measured signal (FP current) indeed comes from the temperature fluctuation rather than artificial signals nor noise signals. Then, by calculating the integral of the FP current over time, we obtained the corresponding transferred FP charge as a function of the period of temperature fluctuation (Fig. 2B). A clear presence of decreased FP charge with the increased period can be observed. It is easy to understand that as the period becomes larger, the temporal temperature gradient is smaller, resulting in a smaller FP effect. Furthermore, as the amplitude of the temperature fluctuation increases, the FP current also increases accordingly in the same level (Fig. 2C). Through further analysis, we observed a clear linear relationship between the transferred FP charge and the amplitude of temperature fluctuation (Fig. 2D). This linear relationship is consistent with conventional pyroelectric effect, which in turn proves that the measured current indeed originates from the temperature fluctuation and its amplitude highly depends on the temporal temperature gradient.

The FP effect should not be confined to the cubic SrTiO₃ crystal with cubic crystal. We also performed the same experiment on rutile TiO₂ single crystals (tetragonal crystal system, space group P4₂/mnm) and observed analogous FP current when it is under the action of point force (Fig. S2). This indicates the universal nature of FP effect in centrosymmetric materials. Furthermore, the interface pyroelectric effect previously found in metal–semiconductor heterostructures [5] is also excluded here through material design: adopting undoped SrTiO₃ and TiO₂ crystals (considered as insulators) to prevent Schottky barrier formation and build-in field construction [35] at the tip–sample interface, thereby avoiding the possibility of interface pyroelectric effect. Likewise, a potential cubic-to-tetragonal phase transition induced in a SrTiO₃ single crystal under a large hydrostatic pressure (>6 GPa) should not play a role given the centrosymmetric nature of the induced tetragonal phase [36].

The strain gradient induced by a microscale tip–sample contact exhibits a complex spatial distribution in an elastic material. The microscale tip apex can be approximated as a cylindrical plateau (Fig. 3A), and the distribution of strain gradient induced by the tip can be calculated analytically with the Hertzian model and the Boussinesq’s calculation [37]. Figure 3B illustrates the spatial distributions of the calculated strain under loading forces of 0 to 1.4 N for a 58-μm-radius contact area, revealing strain gradients linearly proportional to applied force (Fig. 3C). It is expected that the strain gradients induced by the tip loading force will break local symmetry, thus leading to the manifestation of the pyroelectric effect locally under temperature fluctuations. However, deep theoretical analyses are required to understand the intricate relationship between the complex distribution of the strain gradient and the basic behaviors of the FP effect. Experimentally, we found that the transferred FP charge per cycle increases with force up to ~0.7 N, beyond which saturation occurred (Fig. 3D). This saturation is attributed to the mechanical limits of the microscale indentation system. The SrTiO₃ crystal is exceptionally hard, and at high loads, the tungsten steel tip may undergo blunting or plastic deformation. This increases the effective contact area, which in turn reduces the generated strain gradient for a given load. The saturation thus reflects a balance where further force increase is offset by a decreasing strain gradient due to tip deformation, limiting the maximum flexoelectric polarization achievable in this configuration.

The strain gradient induced by tip loading force becomes increasingly significant as tip dimensions decrease to the nanoscale, where the flexoelectric effect is more pronounced [16,28]. This suggests that using a nanometer-scale tip of an atomic force microscope (AFM) rather than a micrometer-scale indentation system may provide a valuable route for strain engineering to enhance the FP effect. To verify this hypothesis, we employed a custom-made pyroelectric atomic force microscope (Pyro-AFM), which integrates an AFM system with a femtoampere-level current amplifier-filter and a temperature-controlled stage (±0.1 K). A conductive AFM tip applied a localized force on the sample surface while simultaneously collecting the resultant FP current. A schematic of the Pyro-AFM setup and a scanning electron microscope (SEM) image of the AFM tip are shown in the upper panel of Fig. 4A. Under a tip loading force (~0.52 μN) and a sinusoidal thermal cycling (ΔT = 2.0 K, period = 10 s), a clear sinusoidal FP current synchronized with temperature modulation was observed (Fig. 4A, lower panel). Remarkably, the strain gradient induced by AFM tip yielded a record-breaking pyroelectric coefficient as high as 1.25 × 10⁶ μC·m^–2·K^–1.

To confirm that the enhanced FP effect at the nanoscale follows the same fundamental physics as its microscale counterpart, we verified the key scaling relationships. As shown in Figs. S3 to S5, the FP charge maintains a linear dependence on the temperature amplitude ΔT, and its magnitude varies inversely with the period of thermal cycling, consistent with a current generation mechanism proportional to the temporal temperature gradient dT/dt. This confirms that the giant pyroelectric coefficient observed at the nanoscale stems from a massive enhancement of the strain gradient-induced polarization, not a change in the underlying functional dependence on thermal stimuli.

By demonstrating the consistency of these scaling laws across both micro- and nanoscales, we significantly strengthen the argument that the observed phenomenon is the same fundamental FP effect, merely amplified by the enormous strain gradients achievable at the nanoscale. We thank the reviewer for prompting this crucial verification.

We highlight here 4 main features of the FP effect. First, the pyroelectric coefficient obtained via the FP effect exceeds that of conventional polar materials, even the best ferroelectrics, heterostructures, and 2-dimensional materials (Fig. 4B and Table S1). For example, the pyroelectric coefficient of SrTiO₃ achieved through the FP effect is over 6.9 times larger than that of triglycine sulfate (TGS) and 19 times larger than that of Au/Si, both of which have similar figures of merit. Beyond oxide semiconductors such as SrTiO₃ and TiO₂, there is great potential to enhance the pyroelectric coefficient by exploring materials with a large flexoelectric effect, such as paraelectric phases of polycrystalline ferroelectrics wherein the flexoelectric coefficient is over 3 orders of magnitude larger than that of SrTiO₃ crystal. Second, a high pyroelectric current can be obtained from any material by simply generating a large strain gradient. For instance, a sharp probe with sufficient loading force can be used for bulk materials, or microstructures with sharp contours can be employed for 2-dimensional materials. Third, unlike the conventional pyroelectric effect that is limited to noncentrosymmetric materials, the FP effect is universal. It is allowed in all materials with any symmetry due to the universal nature of strain gradient-induced centrosymmetry breaking. The FP effect not only is observed in SrTiO₃ and TiO₂ but also is applicable to any flexoelectric material, ranging from ferroelectric ceramics [8,9], halide perovskites (MAPbX₃, X = Br, Cl, I) [29,32], 2-dimensional materials (MoS₂ [30] and 3R-MoS₂ [31]), ferromagnetic metal (SrRuO₃ [15]), polymers [19], electrets [20], biological materials such as bones and ear hairs [21], and even frozen water [22] and helielectric nematic state (HN*) materials [33]. Fourth, the FP effect exhibits a strong size effect. As the tip size decreases from the micrometer-scale to the nanometer-scale, the pyroelectric coefficient can even increase by 326 times. This size effect is highly similar to that of flexoelectric effect, which in turn can highlight the important role of the tip loading force-induced flexoelectric polarization in the FP effect. Meanwhile, this huge improvement further indicates that the FP effect plays a role, rather than the previously reported interface pyroelectric effect [5] or the surface pyroelectric effect [38]: If the current is generated by the interface pyroelectric effect or surface pyroelectric effect, it will not increase gigantically as tip dimensions decrease to the nanoscale.

To further demonstrate the universality of the FP effect beyond oxide semiconductors, we investigated a polyvinylidene fluoride (PVDF) polymer film and a silicon wafer, representing a flexible organic system and an elemental semiconductor, respectively. As shown in Fig. S6, clear and phase-locked FP currents were observed under AFM tip loading in both materials. This conclusively shows that the FP effect is a general phenomenon, applicable across a vast range of material classes, from rigid oxides to soft polymers and elemental semiconductors, thereby dramatically expanding the library of candidate materials for pyroelectric applications. Furthermore, our pyroelectric indentation system is straightforward to configure, and the FP effect grows significantly at the nanoscale, a region where the flexoelectric effect is most dominant [16]. This establishes a compelling strain engineering strategy for improving the performance of pyroelectric devices. For example, an integrated pyroelectric harvester can be fabricated by combining an array of nanoscale indenters (e.g., nanowire arrays) [39] with 2-dimensional materials (e.g., single-layer MoS₂ and nanomembranes) [40], thereby enabling a higher efficiency because the FP effect can be designed to increase the existing pyroelectric current in the polar materials. Considering the considerable strain gradients produced by interface lattice mismatch and crystallographic disorder in polycrystalline films [30,31,41], the associated FP effect could significantly enhance the performance of these pyroelectric harvesters, although this area remains largely unexplored. In addition to inorganic pyroelectric energy harvesters, the FP effect is also poised to be key for flexible and stretchable electronics that use organic and polymer materials. Both macroscopic bending of flexible organic devices [20] and nanoscale folding and entanglement of polymeric chains generate sizable strain gradients [41,42], which can modify electronic transport and induce the FP effect under temperature fluctuations; however, the details of how strain gradients and the FP effect influence electronic characteristics of nanoscale systems remain a topic of ongoing debate.

SrTiO₃ and TiO₂ samples were ultrasonically cleaned in ethanol and acetone and then bonded to a conductive substrate using silver paste. The substrate assembly was placed on a DC-powered thermal stage. The temperature of the substrate was precisely controlled by supplying DC power to the thermal stage using a Keithley 2636A Source Meter. A conductive tungsten steel microprobe was vertically pressed onto the surface of the SrTiO₃ sample. The applied pressure was monitored and measured using a force gauge (DS2-2N). For pyroelectric signal measurement, the conductive substrate was connected to the cathode and the probe was connected to the anode of a Keithley B2985A Electrometer/High Resistance Meter. The FP current signals were directly measured using the Keithley B2985A. The basic properties of SrTiO₃ and TiO₂ crystals are listed in Table S2.

The sample was similarly bonded to a conductive substrate using silver paste. Temperature control was maintained via the DC-powered thermal stage positioned beneath the substrate. The AFM (Bluker Dimension Icon) setup was operated in contact mode. A specialized C-AFM Probe Holder, featuring an integrated wire lead at its rear for electrical connection, was employed. The conductive AFM tip was stably engaged onto the sample surface under constant force (0.52 μN). For electrical measurement, the integrated wire lead of the C-AFM Probe Holder was connected to the anode of the Keysight B2985A, while the conductive substrate was connected to the cathode. The Keysight B2985A instrument was used to directly measure the temperature-dependent pyroelectric current flowing through the sample and the AFM tip.

The FP current signals were directly measured using a Keysight B2985A Electrometer/High Resistance Meter. To ensure optimal stability and accuracy for the pA-level and fA-level currents, the instrument was operated in the pA or fA fixed range mode (as opposed to auto-range) to prevent range-switching artifacts during measurement. The integration time was set to the “Short” power line cycle (PLC) setting to provide a suitable balance between measurement noise and temporal resolution for the observed current signals. All measurements were conducted in a shielded probe station to minimize electromagnetic interference.