“…Since the advent of transformation optics ( Pendry et al., 2006 ) and neutral inclusion ( Zhou and Hu, 2006 ; He and Wu, 2013 ), metamaterials have been in the promising field, which have been successfully demonstrated in various communities, such as optics ( Pendry et al., 2006 ), electromagnetic waves ( Schurig et al., 2006 ; Chen and Chan, 2007 ; Rahm et al., 2008 ; Han and Zhang, 2020 ; Berry and Rumpf, 2020 ; Fakheri et al., 2020 ; Asrafali et al., 2021 ), acoustics ( Zhang et al., 2011 ; Popa et al., 2011 ), elastic mechanics ( Brun et al., 2009 ; Farhat et al., 2009 ), direct current (DC) electric fields ( Yang et al., 2012 ; Jiang et al., 2012 ; Han et al., 2014a ; 2019 ; Feng and Ni, 2022a , 2022b ), and thermotics ( Fan et al., 2008 ; Narayana and Sato, 2012 ; Guenneau et al., 2012 ; Narayana et al., 2013 ; Han et al., 2014b , 2018 ; Li et al., 2015 , 2018 , 2019 , 2020 , 2021 , 2022 ; Yang et al., 2017 , 2021 ; Xu et al., 2020a ; Feng and Ni, 2022a , 2022b ). These metamaterials exhibit excellent performances in their certain conditions.…”