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Atomically thin 2D materials exhibit strong intralayer covalent bonding and weak interlayer van der Waals interactions, offering unique high in-plane strength and out-of-plane flexibility. While atom-thick nature of 2D materials may cause uncontrolled intrinsic/extrinsic deformation in multiple length scales, it also provides new opportunities for exploring coupling between heterogeneous deformations and emerging functionalities in controllable and scalable ways for electronic, optical, and optoelectronic applications. In this review, we discuss (i) the mechanical characteristics of 2D materials, (ii) uncontrolled inherent deformation and extrinsic heterogeneity present in 2D materials, (iii) experimental strategies for controlled heterogeneous deformation of 2D materials, (iv) 3D structure-induced novel functionalities via crumple/wrinkle structure or kirigami structures, and (v) heterogeneous strain-induced emerging functionalities in exciton and phase engineering. Overall, heterogeneous deformation offers unique advantages for 2D materials research by enabling spatial tunability of 2D materials' interactions with photons, electrons, and molecules in a programmable and controlled manner. 

While surface microstructures of butterfly wings have been extensively studied for their structural coloration or optical properties within the visible spectrum, their properties in infrared wavelengths with potential ties to thermoregulation are relatively unknown. The midinfrared wavelengths of 7.5 to 14 µm are particularly important for radiative heat transfer in the ambient environment, because of the overlap with the atmospheric transmission window. For instance, a high midinfrared emissivity can facilitate surface cooling, whereas a low midinfrared emissivity can minimize heat loss to surroundings. Here we find that the midinfrared emissivity of butterfly wings from warmer climates such asArchaeoprepona demophoon(Oaxaca, Mexico) andHeliconius sara(Pichincha, Ecuador) is up to 2 times higher than that of butterfly wings from cooler climates such asCelastrina echo(Colorado) andLimenitis arthemis(Florida), using Fourier-transform infrared (FTIR) spectroscopy and infrared thermography. Our optical computations using a unit cell approach reproduce the spectroscopy data and explain how periodic microstructures play a critical role in the midinfrared. The emissivity spectrum governs the temperature of butterfly wings, and we demonstrate thatC. echowings heat up to 8 °C more thanA. demophoonwings under the same sunlight in the clear sky of Irvine, CA. Furthermore, our thermal computations show that butterfly wings in their respective habitats can maintain a moderate temperature range through a balance of solar absorption and infrared emission. These findings suggest that the surface microstructures of butterfly wings potentially contribute to thermoregulation and provide an insight into butterflies' survival.