A thermochromic material VO₂-based metamaterial device for efficient temperature-adaptive radiative cooling

Abstract

Radiative cooling has attracted significant interest for its ability to passively dissipate heat into outer space without energy consumption. Despite its potential, challenges such as limited cooling power and complex fabrication processes persist. This study presents an efficient selective radiative cooling emitter enabled by a vanadium dioxide (VO₂) metamaterial. The device efficiently activates radiation cooling for heat dissipation at high temperatures, while deactivating cooling at low temperatures to avoid excessive cooling. Within the atmospheric window band, the average emissivity of the radiative cooling device increases significantly from 0.03 in low-temperature mode to 0.87 in high-temperature mode, while maintaining a nearly constant emissivity in the solar irradiation band. When the ambient temperature matches that of the radiative cooling metamaterial device, its cooling power reaches 277 W m⁻². Additionally, the design exhibits angular stability across varying incident angles and demonstrates scalability through systematic parameter optimization. The proposed temperature-adaptive radiative cooling metamaterial device holds promise for applications in adaptive optics systems, as well as in buildings and vehicles, offering significant potential for energy conservation and environmental protection.

---

1. Introduction

In recent years, with the rapid development of the economy, energy consumption has also been steadily increasing. Global greenhouse gas emissions are still soaring, and our world is striving to achieve the 1.5 °C target in the Paris Agreement. Reducing energy consumption and environmental protection are key factors in promoting sustainable development in society. The demand for green and sustainable energy-saving technologies has widely promoted the development of refrigeration technology.¹ Radiation cooling is a cutting-edge technology that has attracted widespread attention due to its unique working principle.^2–4 Compared with other refrigeration technologies, radiation cooling can effectively reduce the temperature of objects without external power or refrigerant, eliminating the limitations of traditional refrigeration methods and achieving more flexible and efficient energy utilization.^5–7 It is achieved by reflecting most of the sunlight (wavelengths in the range of 0.3 to 2.5 μm) from an object facing the sky, and emitting strong longwave infrared radiation into the cold universe through an atmospheric transparent window (wavelengths in the range of 8–13 μm).^8,9 In this way, objects can be passively cooled below ambient temperature with zero energy input and greenhouse gas emissions. This characteristic has been achieved in various materials, such as coloured paint films,^10,11 multilayer films,^12,13 biomimetic structures,^14,15 patterned surface photonic structures,^16,17etc. However, the emissivity of these schemes remains static, and the cooling power of the entire system remains unchanged. Consequently, when the temperature of the object falls below the desired level, continuous heat dissipation and cooling can result in unnecessary supercooling, which is why such systems are typically limited to daytime radiative cooling.^18,19 Therefore, it is crucial to design a radiative cooling device capable of achieving temperature adaptation.

A promising solution is to use thermochromic phase change materials to automatically switch between radiation cooling and heat retention modes, effectively solving the well-known problem of supercooling passive radiation cooling.^20,21 Among them, the thermochromic phase change material vanadium dioxide (VO₂) has an insulating state that changes to a metallic state at a temperature of 68 °C, thus having adjustable absorption and emissivity.²² The optical properties of VO₂ exhibit distinct characteristics in the infrared wavelength range, with the insulating state being a low loss dielectric and the metallic state being a plasma metal with a high damping constant.^23,24 And the phase transition temperature of VO₂ can be reduced to near room temperature through doping with elements such as tungsten or defect engineering,^25,26 which provides a promising design for dynamic radiative cooling. In 2017, Wu et al. proposed a switchable thermal emission method using vanadium dioxide coating on a silicon cone array.²⁷ Ono et al. proposed an adaptive radiative cooling photonic structure by a combination of VO₂ based multi-layer coolers and top spectral selection filters.²⁸ Subsequently, Zhang²⁹ and Liu³⁰ also proposed similar switchable radiative cooling systems. Tang et al. designed a temperature-adaptive, mechanically flexible VO₂-based coating, providing an interesting solution to prevent overcooling caused by radiation cooling in winter.³¹ Yang et al. developed a VO₂-based metasurface radiative cooling device using mask filling technology, offering an effective approach for dynamic thermal regulation with adaptive temperature control.³² Although passive radiative cooling technology has the potential to reduce indoor temperature regulation energy consumption, its performance has not yet reached the level where it can completely replace active air conditioning systems. Furthermore, compared to previous studies on adaptive radiative cooling based on VO₂, there remains considerable room for optimization in achieving greater absorption contrast and broader absorption rates.^33,34

In this paper, we present a temperature-adaptive radiative cooling device, which consists of a periodically patterned VO₂ metamaterial atop a silver/silicon substrate. The device exhibits switchable atmospheric window emissivity, transitioning sharply from an average emissivity of 0.87 in the metallic phase to 0.03 in the dielectric phase. Through systematic analysis of the electric field distributions, we have elucidated the physical mechanism behind absorption enhancement. Meanwhile, the variations of emissivity with incident angle and geometric parameters have been investigated. By synergistically leveraging solar reflectance and atmospheric radiation, the device achieves a net cooling power of 277 W m⁻² in its metallic phase. These results position our thermally adaptive emitter as a promising candidate for energy-efficient building thermal management systems, combining dynamic optical regulation with high radiative efficiency.

2. Theory

2.1. Design concept and cooling structure

Temperature-adaptive radiative cooling refers to the capability of a material or system to autonomously activate or deactivate radiative cooling in response to ambient temperature fluctuations. When the environment heats up, the device must maximize emissivity in the atmospheric window (8–13 μm) to effectively radiate heat into space, while simultaneously minimizing the absorption of solar radiation by suppressing emissivity in the solar radiation range (0.3–2.5 μm).^35,36 When the system temperature falls below a critical temperature, the device enters an “off” state, exhibiting the minimum emissivity across the entire wavelength range to prevent overcooling, as shown in Fig. 1(a).

Fig. 1 Adaptive radiative cooling mechanism. (a) The ideal spectral characteristics of the adaptive radiation cooling device in both on (red) and off (blue line) cooling modes. (b) Ideal working diagram for the temperature adaptive radiation cooling device.

To achieve this functionality, we modulate the optical properties by introducing the thermochromic material VO₂, enabling dynamic regulation of radiative cooling performance. Thermochromic materials can sensitively capture subtle fluctuations in environmental temperature and reversibly transform their phase state or internal structure through unique physical mechanisms, enabling them to effectively handle various cooling demands in complex and dynamic environments.^37,38 By leveraging the material characteristics and structural design, a balance can be achieved between solar radiation absorption and infrared radiation heat dissipation of the object itself. This approach enables efficient energy utilization and contributes to creating a more comfortable and energy-efficient environment for both living and working.³⁹ When the ambient temperature rises and exceeds a specific ideal temperature threshold, the “radiative cooling mode” of the temperature-adaptive material is activated, resulting in a sudden increase in thermal emissivity. This enables spontaneous heat dissipation through radiation, thereby achieving efficient spontaneous radiative cooling effect. On the contrary, once the temperature drops below the ideal temperature, it quickly switches to the “keep warm mode”, and the thermal emissivity decreases to minimize heat loss and keep warm, as shown in Fig. 1(b).

Fig. 2 shows the temperature-adaptive metamaterial radiative cooling device proposed in this paper, along with a schematic diagram of its unit cell structure. The metamaterial device consists of three materials: a silver reflective layer with a thickness of H₁ = 100 nm and Si with a thickness of H₂ = 760 nm, and a VO₂ ring embedded in the top layer of the Si. The VO₂ ring has a thickness of H₃ = 60 nm. The outer and inner radii of the VO₂ ring are R₁ = 1870 nm and R₂ = 630 nm, respectively. The unit cell structure of the radiative cooling device has a period of p_x = p_y = 5 μm in both the x and y directions. In numerical calculations, the dielectric constants of Si and silver are referenced from Palik.⁴⁰

Fig. 2 (a) Schematic diagram of the three-dimensional structure array of the temperature adaptive metamaterial radiation cooling device. (b) Three-dimensional schematic diagram of the unit cell.

The complex dielectric function of VO₂ can be determined by the Lorentz Drude dispersion model of multiple oscillators:^28,41

where ω is the variable frequency, ε_∞ is the high frequency dielectric constant, ε_s is the static dielectric function at zero frequency, and Γ₀ is the broadening of each oscillator, also known as the damping factor. The damping effect is due to the absorption process of transitions between two states. ω_t is the resonant frequency of the oscillator, f_j, ω_oj, and γ_j are the oscillator strengths, resonance (peak) energy, and damping constant in the j-th Lorentz oscillator, respectively. Γ_d is the collision frequency. In the insulating phase, the Lorentz model represented by the first three terms of the equation fits the complex dielectric function of VO₂. In the metal phase of vanadium dioxide, due to the strong absorption of VO₂, the last term is added to the dielectric function, which is the Drude model dielectric function. The dielectric constants of VO₂ in metallic and insulating states are shown in Fig. 3. In the metallic state, the dielectric constant of VO₂ varies with wavelength, resulting in distinct response characteristics across different spectral regions. In the dielectric state, the imaginary part of the dielectric constant in the visible and near-infrared bands is close to zero, indicating low absorption.^42,43

Fig. 3 Optical properties of VO₂ in the metallic (red line) and insulating (blue line) states. (a) Real part and (b) imaginary part of the dielectric constant of VO₂.

2.2. Principle of radiative cooling

The radiation cooling device is opaque within its operating range due to the presence of a silver substrate as a reflector. Therefore, its emissivity ε(λ) and absorptivity a(λ) are calculated as ε(λ) = a(λ) = 1 − r(λ), where r(λ) represents the reflectivity of the radiation cooling device. The solar absorption rate A is the average absorption rate obtained by weighting the distribution of solar irradiance using spectral reflectance data according to the following formula:⁴⁴where I_AM1.5 (λ) is the standard solar spectral radiation power of AM1.5. The infrared emissivity of the atmospheric window band ε is defined as the weighted average emissivity calculated using spectral reflectance data between 8 μm and 13 μm, calculated by the following formula:where E_b is the spectral emission power of the blackbody, according to Planck's law:where k₀ and h are the Boltzmann constant and Planck constant, respectively, with k₀ = 1.381 × 10–23 J K⁻¹, h = 6.626 × 10–34 J s, T is temperature, and c₀ is the speed of light in a vacuum.

To evaluate the cooling performance of a heat emitter, it is essential to determine its net radiative cooling power (P_net). This is typically influenced by four factors in a daytime environment: the infrared radiation, solar irradiance, atmospheric thermal radiation, and nonradiative radiation of the radiation cooler. The definition of net radiative cooling power P_net is:¹³

P_net = P_rad − P_atm − P_sun − P_{cond + conv}, (5)

where P_rad is the radiation power on the surface of the radiative cooler, as follows:and P_atm is the energy absorbed from atmospheric thermal radiation,where T is the temperature of the radiation cooling device, and T_amb is the ambient temperature. The ambient temperature is the average temperature of the atmosphere. P_sun is absorbed solar energy,P_cond+conv is the power absorbed by conduction and convection,where h_c is the coefficient of conduction and convection, and the difference between the effective cooling efficiency T and T_amb is quantified to evaluate the cooling capacity.

3. Results and discussion

Fig. 4 illustrates the emissivity spectra of the designed temperature-adaptive radiative cooling device across the solar spectrum and atmospheric transmission windows. It can be observed from Fig. 4 that within the atmospheric window band, the emissivity is relatively high when VO₂ is in the metallic state, while the emissivity is relatively low when VO₂ is in the dielectric state. The phase-change characteristic of VO₂ enables temperature-dependent switching between radiative cooling and heating modes. When the ambient temperature exceeds the transition threshold, VO₂ adopts a metallic state, activating the cooling mode. According to formula (2)–(4), the solar absorption rate A_C is 0.44 and the emissivity within the atmospheric transmission window ε_c is 0.87. In contrast, at lower temperatures, VO₂ reverts to its insulating state, initiating heating mode with values of A_h = 0.43 and ε_h = 0.03. The emissivity tunability (Δε = ε_c − ε_h = 0.84) demonstrates that the designed metamaterial can dynamically modulate its thermal emission via temperature-induced phase switching, fulfilling the goals of our temperature-adaptive radiative cooling device.

Fig. 4 Emissivity spectra of a temperature-adaptive radiative cooling device in the solar irradiation and atmospheric window bands. The red and blue lines represent the emissivity spectra of the device in low and high temperature modes, respectively.

To evaluate the net cooling power of the designed radiation cooling device, one can observe from formula (4)–(8) that h_c, T_amb and T have an influence on the net cooling power of the entire device. Fig. 5 shows the variation of radiative cooling power with different values of h_c and ΔT (where ΔT = T_amb − T) when vanadium dioxide is in its metallic state, with T set as 341 K. It can be clearly seen that as the ΔT gradually decreases, the cooling power gradually increases. Furthermore, when the temperature of the radiation cooling device is higher than the ambient temperature (ΔT < 0), the cooling power increases with the enhancement of the coefficient of conduction convection. Conversely, and when the device temperature is below ambient temperature (ΔT > 0), the radiative cooling power decreases because the temperature gradient favors heat gain from the environment, and increased h_c accelerates this undesired heat transfer. At thermal equilibrium, that is T_amb = T, the device achieves a steady-state cooling power of 277 W m⁻², which remains unaffected by h_c. These results indicate that the proposed device has excellent cooling performance compared to previously reported devices.^28,34Table 1 presents a comparative analysis between our proposed temperature-adaptive radiative cooling device and previously reported designs, focusing on structural design, thermal emission across heating and cooling modes, and emissivity tunability. Notably, our design demonstrates superior radiative regulation compared to existing approaches, achieving a more advanced thermal control emitter.

Fig. 5 The effect of temperature difference ΔT on net cooling power of the radiation cooling device with different h_c in high temperature mode.

Table 1 Comparison with reported VO₂-based radiative cooling devices

Ref.	Structure design	ε h	ε c	Δε
28	(Filter)/VO2/MgF2/W	0.054	0.63	0.58
33	VO2/Ge/VO2/Ag	0.10	0.78	0.68
45	(Filter)/VO2/Si/Ag	0.18	0.78	0.60
46	BaF2/VO2/Si/Al	0.27	0.95	0.68
47	Si/VO2/BaF2/Au	0.12	0.64	0.52
This work	VO2/Si/Ag	0.03	0.87	0.84

---

To thoroughly investigate the absorption mechanism of the radiative cooling device within the atmospheric window under high-temperature mode, further analysis is performed on the electric field intensity distribution in both the x–z plane and the x–y surface of the structure at wavelengths of 8 μm, 10.6 μm, and 13 μm, as depicted in Fig. 6. From Fig. 6(a) and (d), it can be observed that the electric field excitation at shorter wavelengths is mainly localized between the unit cells. This suggests that intercellular coupling significantly contributes to the absorption process at this wavelength. From Fig. 6(b) and (e), it is shown that the electric field at the absorption peak is predominantly concentrated on the outer side of the VO₂ ring, indicative of edge-dominated plasmonic resonance. In Fig. 6(c) and (f), at longer wavelengths, the electric field shifts to both sides of the VO₂ ring. Notably, as the wavelength increases, the excitation electric field transitions from the outer ring towards the inner ring, indicating a wavelength-dependent shift in resonance localization. In addition, Fig. 6(a)–(c) illustrates the formation of a Fabry–Pérot-like cavity resonance resulting from the interaction between the VO₂ and Ag layers within the dielectric medium. The resonant cavity supports multiple reflections and standing wave formations, further amplifying absorption within the desired spectral range. Therefore, the high absorption observed within the atmospheric window can be primarily attributed to the local surface plasmon resonance generated in the metallic ring-shaped VO₂, as well as the Fabry–Pérot-like cavity resonance.

Fig. 6 Electric field distribution of the radiative cooling device in the x–z (a)–(c) plane and x–y (d)–(f) plane at 8 μm (a) and (d), 10.6 μm (b) and (e), and 13 μm (c) and (d) in high temperature mode.

Fig. 7 analyzes the effect of incident angle on the cooling performance and absorption characteristics of the radiation cooling device. Fig. 7(a) presents the alterations in the absorption spectrum and average emissivity of the radiation cooling device in the atmospheric transmission window when the incident angle changes from 0° to 40°. It can be discerned that as the incident angle increases, the average emissivity of the radiative cooling device in the atmospheric window escalates gradually, and the absorption spectrum experiences a blue shift. Fig. 7(b) elucidates the impact of incident angle on the cooling power of the designed radiation cooling device. It can be observed that the cooling power remains relatively stable when the incident angle varies. When the incident angle is 10°, the radiation cooling power reaches a maximum of 284 W m⁻². When the incident angle is 40°, the radiation cooling power drops to a minimum of 272 W m⁻². Although it can be observed from the inset that the average emissivity of the radiation cooling device within the atmospheric window reaches its peak when the incident angle is 40°, its radiation cooling power is at the minimum. This is primarily ascribed to the influence of the absorption characteristics within the solar radiation band. The designed metamaterial radiative cooling device exhibits minimal variation in the cooling power as the incident angle changes, indicating its strong angular insensitivity. This characteristic makes it well-suited for practical applications where incident light can come from various angles.

Fig. 7 (a) The influence of incident angle variation on the emission spectra in the atmospheric window. The inset represents alterations in the average emissivity of the radiation cooling device. (b) The influence of cooling power with the incident angle.

Fig. 8 elucidates the influence of geometric parameters on radiative cooling device's spectral response and net cooling power. From Fig. 8(a), it can be observed that as H₂ increases, the absorption rate of short wavelengths gradually decreases, while the absorption rate of long wavelengths gradually increases, with the average emissivity rate reaching its highest at H₂ = 760 nm. The corresponding cooling power likewise first increases with H₂ and then declines, mirroring the emissivity trend, as shown in Fig. 8(d). Fig. 8(b) demonstrates that the absorption spectrum and average emissivity of the radiative cooling device within the atmospheric window undergo changes with the variation of H₃. The device achieves its maximum average emissivity when H₃ = 60 nm. From Fig. 8(e), it can be observed that the cooling power initially increases with the thickness H₃, reaching its peak at H₃ = 60 nm before decreasing due to suppressed Fabry–Pérot resonance efficiency in thicker layers. The VO₂ ring width (W = R₁ − R₂) further modulates performance. Fig. 8(c) shows that the emittance decreases as the VO₂ ring width W increases in the short wavelength range, while in the long wavelength range, the emittance increases with an increase in W, and the average emissivity attains its maximum when W = 1.24 μm. The geometric tuning balances the localized plasmonic resonance and cavity-mode broadening. Fig. 8(f) depicts the variation of the cooling power of the designed radiation cooling device with respect to the width W of the VO₂ ring. It can be noted that as the width increases, the cooling power initially increases and then decreases, reaching its peak at W = 1.24 μm. Therefore, based on these results, the optimal geometric parameters synergistically maximize emissivity within the atmospheric window while minimizing solar absorption, ensuring robust cooling performance across thermal and solar spectra.

Fig. 8 (a)–(c) The influence of H₂, H₃ and W on the emission spectrum within the atmospheric window. The insets illustrate the variation in average emissivity. (d)–(f) The effect of cooling power with H₂, H₃, and W.

Conclusions

In conclusion, we demonstrate a dynamically tunable radiative cooling emitter based on vanadium dioxide metamaterials, achieving switchable atmospheric window emissivity from 0.3 to 0.87 in response to temperature variations. This self-regulating functionality enables efficient radiative cooling at high temperatures for heat dissipation while automatically deactivating cooling at low temperatures to prevent overcooling. At 341 K, the cooling power reaches 277 W m⁻², accounting for atmospheric and solar absorption. Electric field analysis reveals the enhanced absorption mechanism underlying high emissivity in the metallic phase. Additionally, the effects of incident angle and geometric parameters on emissivity and radiative power are investigated, demonstrating excellent robustness. This temperature-adaptive metamaterial platform offers promising applications in passive building cooling systems, spacecraft thermal control, and other energy-efficient thermal management solutions.

Author contributions

Zicheng Lin: conceptualization, validation, visualization, methodology, writing – review & editing, and writing – original draft. Bin Tang: validation, formal analysis, writing – review & editing, and writing – original draft, funding acquisition, supervision, project administration.

Data availability

All data generated or analyzed during this study are included in the present article.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Natural Science Foundation of Jiangsu Province (BK20201446) and the State Key Laboratory of Photonics and Communications, Shanghai Jiao Tong University (2025QZKF024).

References

1. J. Song, W. Zhang, Z. Sun, M. Pan, F. Tian, X. Li, M. Ye and X. Deng, Nat. Commun., 2022, 13, 4805.
2. B. Zhao, M. Hu, X. Ao, N. Chen and G. Pei, Appl. Energy, 2019, 236, 489–513.
3. L. Zhu, A. Raman, K. X. Wang, M. A. Anoma and S. Fan, Optica, 2014, 1, 32–38.
4. J. Sui, T. Yao, J. Zou, S. Liao and H.-F. Zhang, Int. J. Heat Mass Trans., 2025, 241, 126783.
5. I. Sarbu and C. Sebarchievici, Energy Build., 2013, 67, 286–297.
6. X. Lu, P. Xu, H. Wang, T. Yang and J. Hou, Renewable Sustainable Energy Rev., 2016, 65, 1079–1097.
7. Y. Wang, H. Ji, B. Liu, P. Tang, Y. Chen, J. Huang, Y. Ou and J. Tao, J. Mater. Chem. A, 2024, 12, 9962–9978.
8. M. Lee, G. Kim, Y. Jung, K. R. Pyun, J. Lee, B.-W. Kim and S. H. Ko, Light: Sci. Appl., 2023, 12, 134.
9. C. Wang, H. Chen and F. Wang, Prog. Mater. Sci., 2024, 144, 101276.
10. X. Li, J. Peoples, Z. Huang, Z. Zhao, J. Qiu and X. Ruan, Cell Reports Phys. Sci., 2020, 1, 100221.
11. K. L. Uemoto, N. M. Sato and V. M. John, Energy Build., 2010, 42, 17–22.
12. D. Chae, M. Kim, P.-H. Jung, S. Son, J. Seo, Y. Liu, B. J. Lee and H. Lee, ACS Appl. Mater. Interfaces, 2020, 12, 8073–8081.
13. A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli and S. Fan, Nature, 2014, 515, 540–544.
14. H. Zhang, K. C. Ly, X. Liu, Z. Chen, M. Yan, Z. Wu, X. Wang, Y. Zheng, H. Zhou and T. Fan, Proc. Natl. Acad. Sci. U. S. A., 2020, 117, 14657–14666.
15. N. N. Shi, C.-C. Tsai, F. Camino, G. D. Bernard, N. Yu and R. Wehner, Science, 2015, 349, 298–301.
16. Y. Jiang, J. Wang, Y. Zhou, J. Li, Z. Chen, P. Yao, H. Ge and B. Zhu, Nanophotonics, 2023, 12, 2213–2220.
17. W. Ma, W. Chen, D. Li, Y. Liu, J. Yin, C. Tu, Y. Xia, G. Shen, P. Zhou and L. Deng, Nanophotonics, 2023, 12, 3589–3601.
18. T. Li, Y. Zhai, S. He, W. Gan, Z. Wei, M. Heidarinejad, D. Dalgo, R. Mi, X. Zhao and J. Song, Science, 2019, 364, 760–763.
19. J. Liu, Z. Zhou, J. Zhang, W. Feng and J. Zuo, Mater. Today Phys., 2019, 11, 100161.
20. Z. Xu, Q. Li, K. Du, S. Long, Y. Yang, X. Cao, H. Luo, H. Zhu, P. Ghosh and W. Shen, Laser Photon. Rev., 2020, 14, 1900162.
21. K. Zhang, Q. Hu, B. Wu, K. Yu, Y. Liu and X. Wu, Opt. Express, 2024, 32, 35243–35255.
22. Y. Ren and B. Tang, J. Light Technol., 2021, 39, 5864–5868.
23. J. Gu, H. Wei, F. Ren, H. Guan, S. Liang, C. Geng, L. Li, J. Zhao, S. Dou and Y. Li, ACS Appl. Mater. Interfaces, 2022, 14, 2683–2690.
24. A. Seeboth, D. Lotzsch, R. Ruhmann and O. Muehling, Chem. Rev., 2014, 114, 3037–3068.
25. M. K. Dietrich, F. Kuhl, A. Polity and P. J. Klar, Appl. Phys. Lett., 2017, 110, 141907.
26. M. Li, X. Wu, L. Li, Y. Wang, D. Li, J. Pan, S. Li, L. Sun and G. Li, J. Mater. Chem. A, 2014, 2, 4520–4523.
27. S.-H. Wu, M. Chen, M. T. Barako, V. Jankovic, P. W. Hon, L. A. Sweatlock and M. L. Povinelli, Optica, 2017, 4, 1390–1396.
28. M. Ono, K. Chen, W. Li and S. Fan, Opt. Express, 2018, 26, A777–A787.
29. W.-W. Zhang, H. Qi, A.-T. Sun, Y.-T. Ren and J.-W. Shi, Opt. Express, 2020, 28, 20609–20623.
30. Y. Liu and Y. Zheng, Nanophotonics, 2024, 13, 701–710.
31. K. Tang, K. Dong, J. Li, M. P. Gordon, F. G. Reichertz, H. Kim, Y. Rho, Q. Wang, C.-Y. Lin and C. P. Grigoropoulos, Science, 2021, 374, 1504–1509.
32. J. Yang, Q. Li, S. Liu, D. Fang, J. Zhang, H. Jin and J. Li, Adv. Photon., 2024, 6, 046006.
33. S. Liang, F. Xu, W. Li, W. Yang, S. Cheng, H. Yang, J. Chen, Z. Yi and P. Jiang, Appl. Therm. Eng., 2023, 232, 121074.
34. B. Wang, L. Li, H. Liu, T. Wang, K. Zhang, X. Wu and K. Yu, Solar Energy Mater. Solar Cells, 2025, 280, 113291.
35. X. Xu, J. Gu, H. Zhao, X. Zhang, S. Dou, Y. Li, J. Zhao, Y. Zhan and X. Li, ACS Appl. Mater. Interfaces, 2022, 14, 14313–14320.
36. M. Yang, H. Zhong, T. Li, B. Wu, Z. Wang and D. Sun, ACS Nano, 2023, 17, 1693–1700.
37. M. Kamalisarvestani, R. Saidur, S. Mekhilef and F. Javadi, Renewable Sustainable Energy Rev., 2013, 26, 353–364.
38. A. Seeboth, R. Ruhmann and O. Mühling, Materials, 2010, 3, 5143–5168.
39. S. Wang, T. Jiang, Y. Meng, R. Yang, G. Tan and Y. Long, Science, 2021, 374, 1501–1504.
40. E. D. Palik, Handbook of optical constants of solids, Academic press, 1998.
41. H. W. Verleur, A. BarkerJr and C. Berglund, Phys. Rev., 1968, 172, 788.
42. H. U. Yang, J. D. Archangel, M. L. Sundheimer, E. Tucker, G. D. Boreman and M. B. Raschke, Phys. Rev. B, 2015, 91, 235137.
43. L. Wu, S. Chen and C. Lin, Opt. Express, 2024, 32, 41213–41229.
44. M. Chen, D. Pang, J. Mandal, X. Chen, H. Yan, Y. He, N. Yu and Y. Yang, Nano Lett., 2021, 21, 1412–1418.
45. M. Kim, D. Lee, Y. Yang and J. Rho, Opto-Electron. Adv., 2021, 4, 200006.
46. Y. Sun, G. Chen, Q. Chen, H. Fu, B. Min, Z. Tao, T. Yue, J. Zhao and J. Qiu, J. Quant. Spectrosc. Radiat. Transfer, 2025, 333, 109325.
47. H. Kim, K. Cheung, R. C. Auyeung, D. E. Wilson, K. M. Charipar, A. Piqué and N. A. Charipar, Sci. Rep., 2019, 9, 11329.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5tc01132a

---