Nonreciprocal thermal metamaterials: Methods and applications

Zhengjiao Xu; Chuanbao Liu; Xueqian Wang; Yongliang Li; Yang Bai

doi:10.1007/s12613-023-2811-6

Volume 31 Issue 7

Jul. 2024

Turn off MathJax

Article Contents

Article Navigation > International Journal of Minerals, Metallurgy and Materials > 2024 > 31(7): 1678-1693

Zhengjiao Xu, Chuanbao Liu, Xueqian Wang, Yongliang Li, and Yang Bai, Nonreciprocal thermal metamaterials: Methods and applications, Int. J. Miner. Metall. Mater., 31(2024), No. 7, pp. 1678-1693. https://doi.org/10.1007/s12613-023-2811-6

Cite this article as:

Zhengjiao Xu, Chuanbao Liu, Xueqian Wang, Yongliang Li, and Yang Bai, Nonreciprocal thermal metamaterials: Methods and applications, Int. J. Miner. Metall. Mater., 31(2024), No. 7, pp. 1678-1693. https://doi.org/10.1007/s12613-023-2811-6

Citation:

PDF( 3270 KB)

Invited Review

Nonreciprocal thermal metamaterials: Methods and applications

+ Author Affiliations

Corresponding authors:
Chuanbao Liu E-mail: cbliu@ustb.edu.cn

Yang Bai E-mail: baiy@mater.ustb.edu.cn
Received: 14 August 2023; Revised: 26 November 2023; Accepted: 14 December 2023; Available online: 15 December 2023

Abstract

Abstract

Nonreciprocity of thermal metamaterials has significant application prospects in isolation protection, unidirectional transmission, and energy harvesting. However, due to the inherent isotropic diffusion law of heat flow, it is extremely difficult to achieve nonreciprocity of heat transfer. This review presents the recent developments in thermal nonreciprocity and explores the fundamental theories, which underpin the design of nonreciprocal thermal metamaterials, i.e., the Onsager reciprocity theorem. Next, three methods for achieving nonreciprocal metamaterials in the thermal field are elucidated, namely, nonlinearity, spatiotemporal modulation, and angular momentum bias, and the applications of nonreciprocal thermal metamaterials are outlined. We also discuss nonreciprocal thermal radiation. Moreover, the potential applications of nonreciprocity to other Laplacian physical fields are discussed. Finally, the prospects for advancing nonreciprocal thermal metamaterials are highlighted, including developments in device design and manufacturing techniques and machine learning-assisted material design.
- thermal metamaterials;
- nonreciprocity;
- nonlinearity;
- spatiotemporal modulation

FullText(HTML)

Supplements(0)

References(119)

References

[1]	C.Z. Fan, Y. Gao, and J.P. Huang, Shaped graded materials with an apparent negative thermal conductivity, Appl. Phys. Lett., 92(2008), No. 25, art. No. 251907. doi: 10.1063/1.2951600
[2]	T. Chen, C.N. Weng, and J.S. Chen, Cloak for curvilinearly anisotropic media in conduction, Appl. Phys. Lett., 93(2008), No. 11, art. No. 114103. doi: 10.1063/1.2988181
[3]	U. Leonhardt, Optical conformal mapping, Science, 312(2006), No. 5781, p. 1777. doi: 10.1126/science.1126493
[4]	J.B. Pendry, D. Schurig, and D.R. Smith, Controlling electromagnetic fields, Science, 312(2006), No. 5781, p. 1780. doi: 10.1126/science.1125907
[5]	S.A. Cummer, B.I. Popa, D. Schurig, D.R. Smith, and J. Pendry, Full-wave simulations of electromagnetic cloaking structures, Phys. Rev. E, 74(2006), No. 3, art. No. 036621. doi: 10.1103/PhysRevE.74.036621
[6]	D. Schurig, J.J. Mock, B.J. Justice, et al., Metamaterial electromagnetic cloak at microwave frequencies, Science, 314(2006), No. 5801, p. 977. doi: 10.1126/science.1133628
[7]	W.S. Cai, U.K. Chettiar, A.V. Kildishev, and V.M. Shalaev, Optical cloaking with metamaterials, Nat. Photonics, 1(2007), p. 224. doi: 10.1038/nphoton.2007.28
[8]	G.X. Zheng, H. Mühlenbernd, M. Kenney, G.X. Li, T. Zentgraf, and S. Zhang, Metasurface holograms reaching 80% efficiency, Nat. Nanotechnol., 10(2015), p. 308. doi: 10.1038/nnano.2015.2
[9]	W.T. Chen, A.Y. Zhu, V. Sanjeev, et al., A broadband achromatic metalens for focusing and imaging in the visible, Nat. Nanotechnol., 13(2018), p. 220. doi: 10.1038/s41565-017-0034-6
[10]	S.M. Wang, P.C. Wu, V.C. Su, et al., A broadband achromatic metalens in the visible, Nat. Nanotechnol., 13(2018), p. 227. doi: 10.1038/s41565-017-0052-4
[11]	R.A. Shelby, D.R. Smith, and S. Schultz, Experimental verification of a negative index of refraction, Science, 292(2001), No. 5514, p. 77. doi: 10.1126/science.1058847
[12]	S.H. Lee, C.M. Park, Y.M. Seo, and C.K. Kim, Reversed Doppler effect in double negative metamaterials, Phys. Rev. B, 81(2010), No. 24, art. No. 241102. doi: 10.1103/PhysRevB.81.241102
[13]	A. Alù and N. Engheta, Achieving transparency with plasmonic and metamaterial coatings, Phy. Rev. E, 72(2005), art. No. 016623. doi: 10.1103/PhysRevE.72.016623
[14]	S. Yang, L.J. Xu, G.L. Dai, and J.P. Huang, Omnithermal metamaterials switchable between transparency and cloaking, J. Appl. Phys., 128(2020), No. 9, art. No. 095102. doi: 10.1063/5.0013270
[15]	T. Qu, J. Wang, and J.P. Huang, Manipulating thermoelectric fields with bilayer schemes beyond Laplacian metamaterials, EPL Europhys. Lett., 135(2021), No. 5, art. No. 54004. doi: 10.1209/0295-5075/ac1648
[16]	S. Narayana and Y. Sato, Heat flux manipulation with engineered thermal materials, Phys. Rev. Lett., 108(2012), No. 21, art. No. 214303. doi: 10.1103/PhysRevLett.108.214303
[17]	S. Guenneau, C. Amra, and D. Veynante, Transformation thermodynamics: Cloaking and concentrating heat flux, Opt. Express, 20(2012), No. 7, p. 8207. doi: 10.1364/OE.20.008207
[18]	R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, Experiments on transformation thermodynamics: Molding the flow of heat, Phys. Rev. Lett., 110(2013), No. 19, art. No. 195901. doi: 10.1103/PhysRevLett.110.195901
[19]	S. Narayana, S. Savo, and Y. Sato, Transient heat flux shielding using thermal metamaterials, Appl. Phys. Lett., 102(2013), No. 20, art. No. 201904. doi: 10.1063/1.4807744
[20]	H.Y. Xu, X.H. Shi, F. Gao, H.D. Sun, and B.L. Zhang, Ultrathin three-dimensional thermal cloak, Phys. Rev. Lett., 112(2014), No. 5, art. No. 054301. doi: 10.1103/PhysRevLett.112.054301
[21]	T.C. Han, X. Bai, D.L. Gao, J.T.L. Thong, B.W. Li, and C.W. Qiu, Experimental demonstration of a bilayer thermal cloak, Phys. Rev. Lett., 112(2014), No. 5, art. No. 054302. doi: 10.1103/PhysRevLett.112.054302
[22]	D.M. Nguyen, H.Y. Xu, Y.M. Zhang, and B.L. Zhang, Active thermal cloak, Appl. Phys. Lett., 107(2015), No. 12, art. No. 121901. doi: 10.1063/1.4930989
[23]	T.C. Han, J.J. Zhao, T. Yuan, D.Y. Lei, B.W. Li, and C.W. Qiu, Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials, Energy Environ. Sci., 6(2013), No. 12, p. 3537. doi: 10.1039/c3ee41512k
[24]	C. Fei and Y.L. Dang, Experimental realization of extreme heat flux concentration with easy-to-make thermal metamaterials, Sci. Rep., 5(2015), art. No. 11552. doi: 10.1038/srep11552
[25]	W. Liu, C. Lan, M. Ji, et al., A flower-shaped thermal energy harvester made by metamaterials, Global Challenges, 1(2017), No. 6, art. No. 1700017. doi: 10.1002/gch2.201700017
[26]	S. Guenneau and C. Amra, Anisotropic conductivity rotates heat fluxes in transient regimes, Opt. Express, 21(2013), No. 5, p. 6578. doi: 10.1364/OE.21.006578
[27]	F.B. Yang, B.Y. Tian, L.J. Xu, and J.P. Huang, Experimental demonstration of thermal chameleonlike rotators with transformation-invariant metamaterials, Phys. Rev. Appl., 14(2020), No. 5, art. No. 054024. doi: 10.1103/PhysRevApplied.14.054024
[28]	T.C. Han, X. Bai, J.T.L. Thong, B.W. Li, and C.W. Qiu, Full control and manipulation of heat signatures: Cloaking, camouflage and thermal metamaterials, Adv. Mater., 26(2014), No. 11, p. 1731. doi: 10.1002/adma.201304448
[29]	T.Z. Yang, Y.S. Su, W.K. Xu, and X.D. Yang, Transient thermal camouflage and heat signature control, Appl. Phys. Lett., 109(2016), No. 12, art. No. 121905. doi: 10.1063/1.4963095
[30]	S. Hong, S. Shin, and R.K. Chen, An adaptive and wearable thermal camouflage device, Adv. Funct. Mater., 30(2020), No. 11, art. No. 1909788. doi: 10.1002/adfm.201909788
[31]	R. Hu, W. Xi, Y.D. Liu, et al., Thermal camouflaging metamaterials, Mater. Today, 45(2021), p. 120. doi: 10.1016/j.mattod.2020.11.013
[32]	R. Hu, S.Y. Huang, M. Wang, L.L. Zhou, X.Y. Peng, and X.B. Luo, Binary thermal encoding by energy shielding and harvesting units, Phys. Rev. Appl., 10(2018), No. 5, art. No. 054032. doi: 10.1103/PhysRevApplied.10.054032
[33]	M. Lei, C.R. Jiang, F.B. Yang, J. Wang, and J.P. Huang, Programmable all-thermal encoding with metamaterials, Int. J. Heat Mass Transf., 207(2023), art. No. 124033. doi: 10.1016/j.ijheatmasstransfer.2023.124033
[34]	M. Kasprzak, M. Sledzinska, K. Zaleski, et al., High-temperature silicon thermal diode and switch, Nano Energy, 78(2020), art. No. 105261. doi: 10.1016/j.nanoen.2020.105261
[35]	Z. Wang, J. Chen, and J. Ren, Geometric heat pump and no-go restrictions of nonreciprocity in modulated thermal diffusion, Phys. Rev. E, 106(2022), No. 3, art. No. L032102. doi: 10.1103/PhysRevE.106.L032102
[36]	Z.J. Coppens and J.G. Valentine, Spatial and temporal modulation of thermal emission, Adv. Mater., 29(2017), No. 39, art. No. 1701275. doi: 10.1002/adma.201701275
[37]	A. Ghanekar, J.H. Wang, S.H. Fan, and M.L. Povinelli, Violation of Kirchhoff’s law of thermal radiation with space–time modulated grating, ACS Photonics, 9(2022), No. 4, p. 1157. doi: 10.1021/acsphotonics.1c01350
[38]	A. Ghanekar, J.H. Wang, C. Guo, S.H. Fan, and M.L. Povinelli, Nonreciprocal thermal emission using spatiotemporal modulation of graphene, ACS Photonics, 10(2022), No. 1, p. 170.
[39]	V.S. Asadchy, M.S. Mirmoosa, A. Díaz-Rubio, S.H. Fan, and S.A. Tretyakov, Tutorial on electromagnetic nonreciprocity and its origins, Proc. IEEE, 108(2020), No. 10, p. 1684. doi: 10.1109/JPROC.2020.3012381
[40]	L.L. Zhou, S.Y. Huang, M. Wang, R. Hu, and X.B. Luo, While rotating while cloaking, Phys. Lett. A, 383(2019), No. 8, p. 759. doi: 10.1016/j.physleta.2018.11.041
[41]	L.J. Xu and J.P. Huang, Negative thermal transport in conduction and advection, Chin. Phys. Lett., 37(2020), No. 8, art. No. 080502. doi: 10.1088/0256-307X/37/8/080502
[42]	X.Y. Huang, C.C. Lu, C. Liang, H.G. Tao, and Y.C. Liu, Loss-induced nonreciprocity, Light. Sci. Appl., 10(2021), No. 1, art. No. 30. doi: 10.1038/s41377-021-00464-2
[43]	X.Y. Huang and Y.C. Liu, Perfect nonreciprocity by loss engineering, Phys. Rev. A, 107(2023), No. 2, art. No. 023703. doi: 10.1103/PhysRevA.107.023703
[44]	Y.S. Su, Y. Li, M.H. Qi, S. Guenneau, H.G. Li, and J. Xiong, Asymmetric heat transfer with linear conductive metamaterials, Phys. Rev. Appl., 20(2023), No. 3, art. No. 034013. doi: 10.1103/PhysRevApplied.20.034013
[45]	W. Muschik, Fundamentals of Nonequilibrium Thermodynamics, , Springer, Vienna, 1993.
[46]	W.J. Mansur, C.A.B. Vasconcellos, N.J.M. Zambrozuski, and O.C. Rotunno Filho, Numerical solution for the linear transient heat conduction equation using an explicit Green’s approach, Int. J. Heat Mass Transf., 52(2009), No. 3-4, p. 694. doi: 10.1016/j.ijheatmasstransfer.2008.07.036
[47]	T.M. Chen, A hybrid Green’s function method for the hyperbolic heat conduction problems, Int. J. Heat Mass Transf., 52(2009), No. 19-20, p. 4273. doi: 10.1016/j.ijheatmasstransfer.2009.04.026
[48]	M. Leindl, E.R. Oberaigner, and T. Antretter, Solution of a time-dependent heat conduction problem by an integral-equation approach, Comput. Mater. Sci., 52(2012), No. 1, p. 178. doi: 10.1016/j.commatsci.2011.07.033
[49]	A. Mandelis, Diffusion-wave Fields : Mathematical Methods and Green Functions, Springer Science & Business Media, Berlin, 2013.
[50]	Y. Li, J.X. Li, M.H. Qi, C.W. Qiu, and H.S. Chen, Diffusive nonreciprocity and thermal diode, Phys. Rev. B, 103(2021), No. 1, art. No. 014307. doi: 10.1103/PhysRevB.103.014307
[51]	G. Wehmeyer, T. Yabuki, C. Monachon, J.Q. Wu, and C. Dames, Thermal diodes, regulators, and switches: Physical mechanisms and potential applications, Appl. Phys. Rev., 4(2017), No. 4, art. No. 041304. doi: 10.1063/1.5001072
[52]	C.W. Chang, D. Okawa, A. Majumdar, and A. Zettl, Solid-state thermal rectifier, Science, 314(2006), No. 5802, p. 1121. doi: 10.1126/science.1132898
[53]	D.B. Go and M. Sen, On the condition for thermal rectification using bulk materials, J. Heat Transf., 132(2010), No. 12, art. No. 1.
[54]	Y. Li, X. Shen, Z. Wu, et al., Temperature-dependent transformation thermotics: From switchable thermal cloaks to macroscopic thermal diodes, Phys. Rev. Lett., 115(2015), No. 19, art. No. 195503. doi: 10.1103/PhysRevLett.115.195503
[55]	X. Shen, Y. Li, C. Jiang, and J. Huang, Temperature trapping: Energy-free maintenance of constant temperatures as ambient temperature gradients change, Phys. Rev. Lett., 117(2016), No. 5, art. No. 055501. doi: 10.1103/PhysRevLett.117.055501
[56]	J. Wang, J. Shang, and J.P. Huang, Negative energy consumption of thermostats at ambient temperature: Electricity generation with zero energy maintenance, Phys. Rev. Appl., 11(2019), No. 2, art. No. 024053. doi: 10.1103/PhysRevApplied.11.024053
[57]	S.D. Lubner, J. Choi, G. Wehmeyer, et al., Reusable bi-directional 3ω sensor to measure thermal conductivity of 100-μm thick biological tissues, Rev. Sci. Instrum., 86(2015), No. 1, art. No. 014905. doi: 10.1063/1.4905680
[58]	R.T. Zheng, J.W. Gao, J.J. Wang, and G. Chen, Reversible temperature regulation of electrical and thermal conductivity using liquid–solid phase transitions, Nat. Commun., 2(2011), art. No. 289. doi: 10.1038/ncomms1288
[59]	J.X. Li, Y. Li, P.C. Cao, et al., Reciprocity of thermal diffusion in time-modulated systems, Nat. Commun., 13(2022), art. No. 167. doi: 10.1038/s41467-021-27903-3
[60]	M.A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27(1956), No. 3, p. 240. doi: 10.1063/1.1722351
[61]	P.A. Huidobro, M.G. Silveirinha, E. Galiffi, and J.B. Pendry, Homogenization theory of space-time metamaterials, Phys. Rev. Appl., 16(2021), No. 1, art. No. 014044. doi: 10.1103/PhysRevApplied.16.014044
[62]	L.J. Xu, J.P. Huang, and X.P. Ouyang, Tunable thermal wave nonreciprocity by spatiotemporal modulation, Phys. Rev. E, 103(2021), No. 3, art. No. 032128. doi: 10.1103/PhysRevE.103.032128
[63]	M. Camacho, B. Edwards, and N. Engheta, Achieving asymmetry and trapping in diffusion with spatiotemporal metamaterials, Nat. Commun., 11(2020), art. No. 3733. doi: 10.1038/s41467-020-17550-5
[64]	J. Li, Y. Li, P.C. Cao, et al., A continuously tunable solid-like convective thermal metadevice on the reciprocal line, Adv. Mater., 32(2020), No. 42, art. No. e2003823. doi: 10.1002/adma.202003823
[65]	J. Li, Y. Li, W. Wang, L. Li, and C.W. Qiu, Effective medium theory for thermal scattering off rotating structures, Opt. Express, 28(2020), No. 18, p. 25894. doi: 10.1364/OE.399799
[66]	D. Torrent, O. Poncelet, and J.C. Batsale, Nonreciprocal thermal material by spatiotemporal modulation, Phys. Rev. Lett., 120(2018), No. 12, art. No. 125501. doi: 10.1103/PhysRevLett.120.125501
[67]	A.N. No. ris, A.L. Shuvalov, and A.A. Kutsenko, Analytical formulation of three-dimensional dynamic homogenization for periodic elastic systems, Proc. R. Soc. A, 468(2012), No. 2142, p. 1629. doi: 10.1098/rspa.2011.0698
[68]	J. Ordonez-Miranda, Y.Y. Guo, J.J. Alvarado-Gil, S. Volz, and M. Nomura, Thermal-wave diode, Phys. Rev. Appl., 16(2021), No. 4, art. No. L041002. doi: 10.1103/PhysRevApplied.16.L041002
[69]	L.J. Xu, G.Q. Xu, J.X. Li, Y. Li, J.P. Huang, and C.W. Qiu, Thermal Willis coupling in spatiotemporal diffusive metamaterials, Phys. Rev. Lett., 129(2022), No. 15, art. No. 155901. doi: 10.1103/PhysRevLett.129.155901
[70]	L.J. Xu, G.Q. Xu, J.P. Huang, and C.W. Qiu, Diffusive fizeau drag in spatiotemporal thermal metamaterials, Phys. Rev. Lett., 128(2022), No. 14, art. No. 145901. doi: 10.1103/PhysRevLett.128.145901
[71]	S.D. Sun, S.F. Liang, W.C. Xu, G.F. Xu, and S. Wu, Photoresponsive polymers with multi-azobenzene groups, Polym. Chem., 10(2019), No. 32, p. 4389. doi: 10.1039/C9PY00793H
[72]	R. Fleury, D.L. Sounas, C.F. Sieck, M.R. Haberman, and A. Alù, Sound isolation and giant linear nonreciprocity in a compact acoustic circulator, Science, 343(2014), No. 6170, p. 516. doi: 10.1126/science.1246957
[73]	L.J. Xu, J.P. Huang, and X.P. Ouyang, Nonreciprocity and isolation induced by an angular momentum bias in convection-diffusion systems, Appl. Phys. Lett., 118(2021), No. 22, art. No. 221902. doi: 10.1063/5.0049774
[74]	Y. Li, Y.G. Peng, L. Han, et al., Anti-parity-time symmetry in diffusive systems, Science, 364(2019), No. 6436, p. 170. doi: 10.1126/science.aaw6259
[75]	L.J. Xu and J.P. Huang, Robust one-way edge state in convection-diffusion systems, EPL Europhys. Lett., 134(2021), No. 6, art. No. 60001. doi: 10.1209/0295-5075/134/60001
[76]	H. Hu, S. Han, Y. Yang, et al., Observation of topological edge states in thermal diffusion, Adv. Mater., 34(2022), No. 31, art. No. e2202257. doi: 10.1002/adma.202202257
[77]	Y. Hatsugai, Edge states in the integer quantum Hall effect and the Riemann surface of the Bloch function, Phys. Rev. B: Condens. Matter., 48(1993), No. 16, p. 11851. doi: 10.1103/PhysRevB.48.11851
[78]	L.X. Zhu and S.H. Fan, Near-complete violation of detailed balance in thermal radiation, Phys. Rev. B, 90(2014), No. 22, art. No. 220301. doi: 10.1103/PhysRevB.90.220301
[79]	Z. Chen, L.X. Zhu, W. Li, and S.H. Fan, Simultaneously and synergistically harvest energy from the Sun and outer space, Joule, 3(2019), No. 1, p. 101. doi: 10.1016/j.joule.2018.10.009
[80]	L.X. Zhu, A.P. Raman, and S.H. Fan, Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody, Proc. Natl. Acad. Sci. USA, 112(2015), No. 40, p. 12282. doi: 10.1073/pnas.1509453112
[81]	Z.N. Zhang and L.X. Zhu, Nonreciprocal thermal photonics for energy conversion and radiative heat transfer, Phys. Rev. Appl., 18(2022), No. 2, art. No. 027001. doi: 10.1103/PhysRevApplied.18.027001
[82]	J. Wu, F. Wu, T.C. Zhao, and X.H. Wu, Tunable nonreciprocal thermal emitter based on metal grating and graphene, Int. J. Therm. Sci., 172(2022), art. No. 107316. doi: 10.1016/j.ijthermalsci.2021.107316
[83]	J. Wu and Y.M. Qing, The enhancement of nonreciprocal radiation for light near to normal incidence with double-layer grating, Adv. Compos. Hybrid Mater., 6(2023), No. 3, art. No. 87. doi: 10.1007/s42114-023-00671-y
[84]	J. Wu and Y.M. Qing, Strong nonreciprocal radiation for extreme small incident angle, Int. Commun. Heat Mass Transf., 144(2023), art. No. 106794. doi: 10.1016/j.icheatmasstransfer.2023.106794
[85]	J. Wu and Y.M. Qing, Near-perfect nonreciprocal radiation for extremely small incident angle based on cascaded grating structure, Int. J. Therm. Sci., 190(2023), art. No. 108340. doi: 10.1016/j.ijthermalsci.2023.108340
[86]	B. Zhao, C. Guo, C.A.C. Garcia, P. Narang, and S. Fan, Axion-field-enabled nonreciprocal thermal radiation in Weyl semimetals, Nano Lett., 20(2020), No. 3, p. 1923. doi: 10.1021/acs.nanolett.9b05179
[87]	Y. Tsurimaki, X. Qian, S. Pajovic, F. Han, M.D. Li, and G. Chen, Large nonreciprocal absorption and emission of radiation in type-I Weyl semimetals with time reversal symmetry breaking, Phys. Rev. B, 101(2020), No. 16, art. No. 165426. doi: 10.1103/PhysRevB.101.165426
[88]	X.H. Wu, H.Y. Yu, F. Wu, and B.Y. Wu, Enhanced nonreciprocal radiation in Weyl semimetals by attenuated total reflection, AIP Adv., 11(2021), No. 7, art. No. 075106. doi: 10.1063/5.0055418
[89]	J. Wu, Z.M. Wang, H. Zhai, Z.X. Shi, X.H. Wu, and F. Wu, Near-complete violation of Kirchhoff’s law of thermal radiation in ultrathin magnetic Weyl semimetal films, Opt. Mater. Express, 11(2021), No. 12, art. No. 4058. doi: 10.1364/OME.444308
[90]	J. Wu and Y.M. Qing, Nonreciprocal thermal emitter for near perpendicular incident light with cascade grating involving weyl semimetal, Mater. Today Phys., 32(2023), art. No. 101025. doi: 10.1016/j.mtphys.2023.101025
[91]	J. Wu, Y.S. Sun, B.Y. Wu, Z.M. Wang, and X.H. Wu, Extremely wide-angle nonreciprocal thermal emitters based on Weyl semimetals with dielectric grating structure, Case Stud. Therm. Eng., 40(2022), art. No. 102566. doi: 10.1016/j.csite.2022.102566
[92]	J. Wu and Y.M. Qing, Tunable near-perfect nonreciprocal radiation with a Weyl semimetal and graphene, Phys. Chem. Chem. Phys., 25(2023), No. 13, p. 9586. doi: 10.1039/D2CP05945B
[93]	M.Q. Liu, C. Zhao, Y.X. Zeng, Y. Chen, C.Y. Zhao, and C.W. Qiu, Evolution and nonreciprocity of loss-induced topological phase singularity pairs, Phys. Rev. Lett., 127(2021), No. 26, art. No. 266101. doi: 10.1103/PhysRevLett.127.266101
[94]	J. Wu and Y.M. Qing, Strong nonreciprocal radiation with topological photonic crystal heterostructure, Appl. Phys. Lett., 121(2022), No. 11, art. No. 112101. doi: 10.1063/5.0107022
[95]	J. Wu, Z.M. Wang, B.Y. Wu, Z.X. Shi, and X.H. Wu, The giant enhancement of nonreciprocal radiation in Thue-morse aperiodic structures, Opt. Laser Technol., 152(2022), art. No. 108138. doi: 10.1016/j.optlastec.2022.108138
[96]	J. Wu, F. Wu, T.C. Zhao, M. Antezza, and X.H. Wu, Dual-band nonreciprocal thermal radiation by coupling optical Tamm states in magnetophotonic multilayers, Int. J. Therm. Sci., 175(2022), art. No. 107457. doi: 10.1016/j.ijthermalsci.2022.107457
[97]	J. Wu and Y.M. Qing, Strong multi-band nonreciprocal radiation with Fibonacci multilayer involving Weyl semimetal, Results Phys., 51(2023), art. No. 106642. doi: 10.1016/j.rinp.2023.106642
[98]	J. Wu and Y.M. Qing, Multichannel nonreciprocal thermal radiation with Weyl semimetal and photonic crystal heterostructure, Case Stud. Therm. Eng., 48(2023), art. No. 103161. doi: 10.1016/j.csite.2023.103161
[99]	J. Wu and Y.M. Qing, A multi-band nonreciprocal thermal emitter involving a Weyl semimetal with a Thue–Morse multilayer, Phys. Chem. Chem. Phys., 25(2023), No. 16, p. 11477. doi: 10.1039/D3CP00492A
[100]	J. Wu, B.Y. Wu, Z.M. Wang, and X.H. Wu, The enhanced nonreciprocal radiation with topological interface states, Opt. Laser Technol., 158(2023), art. No. 108907. doi: 10.1016/j.optlastec.2022.108907
[101]	K.J. Shayegan, B. Zhao, Y. Kim, S. Fan, and H.A. Atwater, Nonreciprocal infrared absorption via resonant magneto-optical coupling to InAs, Sci. Adv., 8(2022), No. 18, art. No. eabm4308. doi: 10.1126/sciadv.abm4308
[102]	M.Q. Liu, S. Xia, W.J. Wan, et al., Broadband mid-infrared non-reciprocal absorption using magnetized gradient epsilon-near-zero thin films, Nat. Mater., 22(2023), p. 1196. doi: 10.1038/s41563-023-01635-9
[103]	K.J. Shayegan, S. Biswas, B. Zhao, S.H. Fan, and H.A. Atwater, Direct observation of the violation of Kirchhoff’s law of thermal radiation, Nat. Photonics, 17(2023), p. 891. doi: 10.1038/s41566-023-01261-6
[104]	Y. Hadad, J.C. Soric, and A. Alu, Breaking temporal symmetries for emission and absorption, Proc. Natl. Acad. Sci. USA, 113(2016), No. 13, p. 3471. doi: 10.1073/pnas.1517363113
[105]	S. Buddhiraju, W. Li, and S.H. Fan, Photonic refrigeration from time-modulated thermal emission, Phys. Rev. Lett., 124(2020), No. 7, art. No. 077402. doi: 10.1103/PhysRevLett.124.077402
[106]	L.J. Fernández-Alcázar, H.N. Li, M. Nafari, and T. Kottos, Implementation of optimal thermal radiation pumps using adiabatically modulated photonic cavities, ACS Photonics, 8(2021), No. 10, p. 2973. doi: 10.1021/acsphotonics.1c00896
[107]	H.N. Li, L.J. Fernández-Alcázar, F. Ellis, B. Shapiro, and T. Kottos, Adiabatic thermal radiation pumps for thermal photonics, Phys. Rev. Lett., 123(2019), No. 16, art. No. 165901. doi: 10.1103/PhysRevLett.123.165901
[108]	C. Khandekar and A.W. Rodriguez, Near-field thermal upconversion and energy transfer through a Kerr medium, Opt. Express, 25(2017), No. 19, p. 23164. doi: 10.1364/OE.25.023164
[109]	C. Khandekar, R. Messina, and A.W. Rodriguez, Near-field refrigeration and tunable heat exchange through four-wave mixing, AIP Adv., 8(2018), No. 5, art. No. 055029. doi: 10.1063/1.5018734
[110]	J. Li, Z. Zhang, G. Xu, et al., Tunable rectification of diffusion-wave fields by spatiotemporal metamaterials, Phys. Rev. Lett., 129(2022), No. 25, art. No. 256601. doi: 10.1103/PhysRevLett.129.256601
[111]	L.W. Zeng and R.X. Song, Controlling chloride ions diffusion in concrete, Sci. Rep., 3(2013), art. No. 3359. doi: 10.1038/srep03359
[112]	Y. Li, C.B. Liu, Y. Bai, L.J. Qiao, and J. Zhou, Ultrathin hydrogen diffusion cloak, Adv. Theory Simul., 1(2018), No. 1, art. No. 1700004. doi: 10.1002/adts.201700004
[113]	Y. Li, C.B. Liu, P. Li, et al., Scattering cancellation by a monolayer cloak in oxide dispersion-strengthened alloys, Adv. Funct. Mater., 30(2020), No. 36, art. No. 2003270. doi: 10.1002/adfm.202003270
[114]	Y. Li, C.Y. Yu, C.B. Liu, et al., Mass diffusion metamaterials with “plug and switch” modules for ion cloaking, concentrating, and selection: Design and experiments, Adv. Sci., 9(2022), No. 30, art. No. 2201032. doi: 10.1002/advs.202201032
[115]	J.M. Restrepo-Flórez and M. Maldovan, Mass separation by metamaterials, Sci. Rep., 6(2016), art. No. 21971. doi: 10.1038/srep21971
[116]	X. Zhou, G.Q. Xu, and H.Y. Zhang, Binary masses manipulation with composite bilayer metamaterial, Compos. Struct., 267(2021), art. No. 113866. doi: 10.1016/j.compstruct.2021.113866
[117]	Z. Zhang, L. Xu, and J. Huang, Controlling chemical waves by transforming transient mass transfer, Adv. Theor. Simul., 5(2022), No. 3, art. No. 2100375. doi: 10.1002/adts.202100375
[118]	B. Liu, L.J. Xu, and J.P. Huang, Thermal transparency with periodic particle distribution: A machine learning approach, J. Appl. Phys., 129(2021), No. 6, art. No. 065101. doi: 10.1063/5.0039002
[119]	S.A.M. Loos, S. Arabha, A. Rajabpour, A. Hassanali, and É. Roldán, Nonreciprocal forces enable cold-to-hot heat transfer between nanoparticles, Sci. Rep., 13(2023), No. 1, art. No. 4517. doi: 10.1038/s41598-023-31583-y