[1] R. Bistritzer, A. H. MacDonald. Moiré bands in twisted double-layer graphene. Proc. Natl. Acad. Sci. USA, 108, 12233-12237(2011).
[2] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, P. Jarillo-Herrero. Unconventional superconductivity in magic-angle graphene superlattices. Nature, 556, 43-50(2018).
[3] Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, P. Jarillo-Herrero. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature, 556, 80-84(2018).
[4] G. W. Burg, J. Zhu, T. Taniguchi, K. Watanabe, A. H. MacDonald, E. Tutuc. Correlated insulating states in twisted double bilayer graphene. Phys. Rev. Lett., 123, 197702(2019).
[5] S. Carr, D. Massatt, S. Fang, P. Cazeaux, M. Luskin, E. Kaxiras. Twistronics: manipulating the electronic properties of two-dimensional layered structures through their twist angle. Phys. Rev. B, 95, 075420(2017).
[6] J. W. Fleischer, M. Segev, N. K. Efremidis, D. N. Christodoulides. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature, 422, 147-150(2003).
[7] P. Wang, Y. Zheng, X. Chen, C. Huang, Y. V. Kartashov, L. Torner, V. V. Konotop, F. Ye. Localization and delocalization of light in photonic moiré lattices. Nature, 577, 42-46(2020).
[8] Q. Fu, P. Wang, C. Huang, Y. V. Kartashov, L. Torner, V. V. Konotop, F. Ye. Optical soliton formation controlled by angle twisting in photonic moiré lattices. Nat. Photonics, 14, 663-668(2020).
[9] C. Huang, F. Ye, X. Chen, Y. V. Kartashov, V. V. Konotop, L. Torner. Localization-delocalization wavepacket transition in Pythagorean aperiodic potentials. Sci. Rep., 6, 32546(2016).
[10] X.-R. Mao, Z.-K. Shao, H.-Y. Luan, S.-L. Wang, R.-M. Ma. Magic-angle lasers in nanostructured moiré superlattice. Nat. Nanotechnol., 16, 1099-1105(2021).
[11] Y. V. Kartashov, F. Ye, V. V. Konotop, L. Torner. Multifrequency solitons in commensurate-incommensurate photonic moiré lattices. Phys. Rev. Lett., 127, 163902(2021).
[12] A. González-Tudela, J. I. Cirac. Cold atoms in twisted-bilayer optical potentials. Phys. Rev. A, 100, 053604(2019).
[13] T. Salamon, A. Celi, R. W. Chhajlany, I. Frérot, M. Lewenstein, L. Tarruell, D. Rakshit. Simulating twistronics without a twist. Phys. Rev. Lett., 125, 030504(2020).
[14] X.-W. Luo, C. Zhang. Spin-twisted optical lattices: tunable flat bands and Larkin-Ovchinnikov superfluids. Phys. Rev. Lett., 126, 103201(2021).
[15] Z. Chen, X. Liu, J. Zeng. Electromagnetically induced moiré optical lattices in a coherent atomic gas. Front. Phys., 17, 42508(2022).
[16] Y. S. Kivshar, G. P. Agrawal. Optical Solitons: From Fibers to Photonic Crystals(2003).
[17] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade. Photonic Crystals: Molding the Flow of Light(2011).
[18] I. L. Garanovich, S. Longhi, A. A. Sukhorukova, Y. S. Kivshar. Light propagation and localization in modulated photonic lattices and waveguides. Phys. Rep., 518, 1-79(2012).
[19] O. Morsch, M. Oberthaler. Dynamics of Bose-Einstein condensates in optical lattices. Rev. Mod. Phys., 78, 179-215(2006).
[20] Y. V. Kartashov, B. A. Malomed, L. Torner. Solitons in nonlinear lattices. Rev. Mod. Phys., 83, 247-305(2011).
[21] Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, L. Torner. Frontiers in multidimensional self-trapping of nonlinear fields and matter. Nat. Rev. Phys., 1, 185-197(2019).
[22] I. H. Deutsch, R. J. C. Spreeuw, S. L. Rolston, W. D. Phillips. Photonic band gaps in optical lattices. Phys. Rev. A, 52, 1394-1410(1995).
[23] W. Chen, D. L. Mills. Gap solitons and the nonlinear optical response of superlattices. Phys. Rev. Lett., 58, 160-163(1987).
[24] S. John, N. Aközbek. Nonlinear optical solitary waves in a photonic band gap. Phys. Rev. Lett., 71, 1168-1171(1993).
[25] A. Kozhekin, G. Kurizki. Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances. Phys. Rev. Lett., 74, 5020-5023(1995).
[26] A. E. Kozhekin, G. Kurizki, B. Malomed. Standing and moving gap solitons in resonantly absorbing gratings. Phys. Rev. Lett., 81, 3647-3650(1998).
[27] Y. Zhang, B. Wu. Composition relation between gap solitons and Bloch waves in nonlinear periodic systems. Phys. Rev. Lett., 102, 093905(2009).
[28] E. A. Ostrovskaya, Y. S. Kivshar. Matter-wave gap solitons in atomic band-gap structures. Phys. Rev. Lett., 90, 160407(2003).
[29] L. Zeng, J. Zeng. Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices. Adv. Photon., 1, 046004(2019).
[30] J. Shi, J. Zeng. Self-trapped spatially localized states in combined linear-nonlinear periodic potentials. Front. Phys., 15, 12602(2020).
[31] J. Li, J. Zeng. Dark matter-wave gap solitons in dense ultracold atoms trapped by a one-dimensional optical lattice. Phys. Rev. A, 103, 013320(2021).
[32] J. Chen, J. Zeng. Dark matter-wave gap solitons of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities. Chaos Solitons Fractals, 150, 111149(2021).
[33] B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, J. E. Sipe. Bragg grating solitons. Phys. Rev. Lett., 76, 1627-1630(1996).
[34] D. Mandelik, R. Morandotti, J. S. Aitchison, Y. Silberberg. Gap solitons in waveguide arrays. Phys. Rev. Lett., 92, 093904(2004).
[35] B. Eiermann, T. Anker, M. Albiez, M. Taglieber, P. Treutlein, K. P. Marzlin, M. K. Oberthaler. Bright Bose-Einstein gap solitons of atoms with repulsive interaction. Phys. Rev. Lett., 92, 230401(2004).
[36] C. M. Bender, S. Boettcher. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett., 80, 5243-5246(1998).
[37] C. M. Bender. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys., 70, 947-1018(2007).
[38] L. Feng, R. El-Ganainy, L. Ge. Non-Hermitian photonics based on parity-time symmetry. Nat. Photonics, 11, 752-762(2017).
[39] H. Zhao, L. Feng. Parity-time symmetric photonics. Natl. Sci. Rev., 5, 183-199(2018).
[40] S. K. Özdemir, S. Rotter, F. Nori, L. Yang. Parity-time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019).
[41] S. K. Gupta, Y. Zou, X.-Y. Zhu, M.-H. Lu, L.-J. Zhang, X.-P. Liu, Y.-F. Chen. Parity-time symmetry in non-Hermitian complex optical media. Adv. Mater., 32, 1903639(2020).
[42] C. Hang, G. X. Huang, V. V. Konotop. PT symmetry with a system of three-level atoms. Phys. Rev. Lett., 110, 083604(2013).
[43] Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. Zhang, M. Xiao. Observation of parity-time symmetry in optically induced atomic lattices. Phys. Rev. Lett., 117, 123601(2016).
[44] Z. H. Musslimani, K. G. Makris, R. El-Ganainy, D. N. Christodoulides. Optical solitons in PT periodic potentials. Phys. Rev. Lett., 100, 030402(2008).
[45] J. Zeng, Y. Lan. Two-dimensional solitons in PT linear lattice potentials. Phys. Rev. E, 85, 047601(2012).
[46] V. V. Konotop, J. Yang, D. A. Zezyulin. Nonlinear waves in PT-symmetric systems. Rev. Mod. Phys., 88, 035002(2016).
[47] S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, Y. S. Kivshar. Nonlinear switching and solitons in PT-symmetric photonic systems. Laser Photon. Rev., 10, 177-213(2016).
[48] J. Li, Y. Zhang, J. Zeng. Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices. iScience., 25, 104026(2022).
[49] Y. V. Kartashov, C. Hang, G. Huang, L. Torner. Three-dimensional topological solitons in PT-symmetric optical lattices. Optica, 3, 1048-1055(2016).
[50] B. I. Mantsyzov, R. N. Kuzmin. Coherent interaction of light with a discrete periodic resonant medium. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, 91, 65-77(1986).
[51] D. E. Pelinovsky. Localization in Periodic Potential: From Schrödinger Operators to the Gross-Pitaevskii Equation(2011).
[52] Z. J. Wong, Y. L. Xu, J. Kim, K. O’Brien, Y. Wang, L. Feng, X. Zhang. Lasing and anti-lasing in a single cavity. Nat. Photonics, 10, 796-801(2016).
[53] S. Longhi. Optical realization of relativistic non-Hermitian quantum mechanics. Phys. Rev. Lett., 105, 013903(2010).
[54] J. Yang. Nonlinear Waves in Integrable and Nonintegrable Systems(2010).
