Wilczek, F. Origins of mass. Cent. Eur. J. Phys. 10, 1021–1037 (2012).
Anderson, P. W. Plasmons, gauge invariance, and mass. Phys. Rev. 130, 439–442 (1963).
Higgs, P. W. Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508–509 (1964).
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).
Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015 (1988).
Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).
Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Aad, G. et al. Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716, 1–29 (2012).
Clay Mathematics Institute. Yang-Mills and the mass gap. Clay Mathematics Institute https://www.claymath.org/millennium/yang-mills-the-maths-gap/ (2023).
Bansil, A., Lin, H. & Das, T. Colloquium: Topological band theory. Rev. Mod. Phys. 88, 021004 (2016).
Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).
Zaletel, M. P. et al. Colloquium: Quantum and classical discrete time crystals. Rev. Mod. Phys. 95, 031001 (2023).
Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian Hamiltonians having \({\mathcal{P}}{\mathcal{T}}\) symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).
Mostafazadeh, A. Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. J. Math. Phys. 43, 205–214 (2002).
Szameit, A., Rechtsman, M. C., Bahat-Treidel, O. & Segev, M. \({\mathcal{P}}{\mathcal{T}}\)-symmetry in honeycomb photonic lattices. Phys. Rev. A 84, 021806 (2011).
Zhen, B. et al. Spawning rings of exceptional points out of Dirac cones. Nature 525, 354–358 (2015).
Cerjan, A. et al. Experimental realization of a Weyl exceptional ring. Nat. Photon. 13, 623–628 (2019).
Doppler, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).
Özdemir, Ş. K., Rotter, S., Nori, F. & Yang, L. Parity–time symmetry and exceptional points in photonics. Nat. Mater. 18, 783–798 (2019).
Regensburger, A. et al. Parity–time synthetic photonic lattices. Nature 488, 167–171 (2012).
Xue, H., Wang, Q., Zhang, B. & Chong, Y. D. Non-Hermitian Dirac cones. Phys. Rev. Lett. 124, 236403 (2020).
Terh, Y. Y., Banerjee, R., Xue, H. & Chong, Y. D. Scattering dynamics and boundary states of a non-Hermitian Dirac equation. Phys. Rev. B 108, 045419 (2023).
Holstein, B. R. Klein’s paradox. Am. J. Phys. 66, 507–512 (1998).
Dombey, N. & Calogeracos, A. Seventy years of the Klein paradox. Phys. Rep. 315, 41–58 (1999).
Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2, 620–625 (2006).
Jiang, X. et al. Direct observation of Klein tunneling in phononic crystals. Science 370, 1447–1450 (2020).
Bacot, V., Labousse, M., Eddi, A., Fink, M. & Fort, E. Time reversal and holography with spacetime transformations. Nat. Phys. 12, 972–977 (2016).
Zhou, Y. et al. Broadband frequency translation through time refraction in an epsilon-near-zero material. Nat. Commun. 11, 2180 (2020).
Lustig, E. et al. in Proc. 2021 Conference on Lasers and Electro-Optics (eds Kang, J. et al.) FF2H.1 (Optica Publishing Group, 2021).
Moussa, H. et al. Observation of temporal reflection and broadband frequency translation at photonic time interfaces. Nat. Phys. 19, 863–868 (2023).
Dong, Z. et al. Quantum time reflection and refraction of ultracold atoms. Nat. Photon. 18, 68–73 (2023).
Wimmer, M., Price, H. M., Carusotto, I. & Peschel, U. Experimental measurement of the Berry curvature from anomalous transport. Nat. Phys. 13, 545–550 (2017).
Leykam, D., Rechtsman, M. & Chong, Y. Anomalous topological phases and unpaired Dirac cones in photonic Floquet topological insulators. Phys. Rev. Lett. 117, 013902 (2016).
Özdemir, Ş. K. Fermi arcs connect topological degeneracies. Science 359, 995–996 (2018).
Zeuner, J. M. et al. Observation of a topological transition in the bulk of a non-Hermitian system. Phys. Rev. Lett. 115, 040402 (2015).
Wimmer, M. et al. Optical diametric drive acceleration through action–reaction symmetry breaking. Nat. Phys. 9, 780–784 (2013).
Peleg, O. et al. Conical diffraction and gap solitons in honeycomb photonic lattices. Phys. Rev. Lett. 98, 103901 (2007).
Miri, M.-A., Regensburger, A., Peschel, U. & Christodoulides, D. N. Optical mesh lattices with \({\mathcal{P}}{\mathcal{T}}\) symmetry. Phys. Rev. A 86, 023807 (2012).
Ye, H. et al. Reconfigurable refraction manipulation at synthetic temporal interfaces with scalar and vector gauge potentials. Proc. Natl Acad. Sci. USA 120, e2300860120 (2023).
Lee, K. et al. Linear frequency conversion via sudden merging of meta-atoms in time-variant metasurfaces. Nat. Photon. 12, 765–773 (2018).
Bukov, M., D’Alessio, L. & Polkovnikov, A. Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering. Adv. Phys. 64, 139–226 (2015).
Weidemann, S., Kremer, M., Longhi, S. & Szameit, A. Topological triple phase transition in non-Hermitian Floquet quasicrystals. Nature 601, 354–359 (2022).
Jackiw, R. & Rebbi, C. Solitons with fermion number ½. Phys. Rev. D 13, 3398–3409 (1976).
Angelakis, D. G., Das, P. & Noh, C. Probing the topological properties of the Jackiw-Rebbi model with light. Sci. Rep. 4, 6110 (2014).
Takata, K. & Notomi, M. Photonic topological insulating phase induced solely by gain and loss. Phys. Rev. Lett. 121, 213902 (2018).
