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Unveiling Higher-Order Topology via Polarized Topological Charges
Published 9 May 2024 in cond-mat.mes-hall, cond-mat.other, cond-mat.quant-gas, and quant-ph | (2405.05505v3)
Abstract: Higher-order topological phases (HOTPs) host exotic topological states that go beyond the traditional bulk-boundary correspondence. Up to now, there is still a lack of experimentally measurable momentum-space topological characterization for the HOTPs, which is not conducive to revealing the essential properties of these topological states and also restricts their detection in quantum simulation systems. Here, we propose a concept of polarized topological charges to characterize chiral-symmetric HOTPs in momentum space, which further facilitates a feasible experimental scheme to detect the HOTPs in ${87}$Rb cold atomic system. Remarkably, our characterization theory not only shows that the second-order (third-order) topological phases are determined by a quarter (negative eighth) of the total polarized topological charges, but also reveals that the higher-order topological phase transitions are identified by the creation or annihilation of polarized topological charges. Particularly, these polarized topological charges can be measured by pseudospin structures of the systems. Due to theoretical simplicity and observational intuitiveness, this work shall advance the broad studies of the HOTPs in both theory and experiment.
- W. A. Benalcazar, B. A. Bernevig, and T. L. Hughes, Quantized electric multipole insulators, Science 357, 61 (2017a).
- Z. Song, Z. Fang, and C. Fang, (d-2)-dimensional edge states of rotation symmetry protected topological states, Phys. Rev. Lett. 119, 246402 (2017).
- E. Khalaf, Higher-order topological insulators and superconductors protected by inversion symmetry, Phys. Rev. B 97, 205136 (2018).
- M. Ezawa, Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices, Phys. Rev. Lett. 120, 026801 (2018).
- S. A. A. Ghorashi, T. L. Hughes, and E. Rossi, Vortex and surface phase transitions in superconducting higher-order topological insulators, Phys. Rev. Lett. 125, 037001 (2020a).
- M. Ezawa, Edge-corner correspondence: Boundary-obstructed topological phases with chiral symmetry, Phys. Rev. B 102, 121405(R) (2020).
- K. Asaga and T. Fukui, Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field, Phys. Rev. B 102, 155102 (2020).
- J. Claes and T. L. Hughes, Wannier band transitions in disordered π𝜋\piitalic_π-flux ladders, Phys. Rev. B 102, 100203(R) (2020).
- L. Li, W. Zhu, and J. Gong, Direct dynamical characterization of higher-order topological phases with nested band inversion surfaces, Sci. Bull. 66, 1502 (2021a).
- L. Trifunovic and P. W. Brouwer, Higher-order bulk-boundary correspondence for topological crystalline phases, Phys. Rev. X 9, 011012 (2019).
- R. Queiroz and A. Stern, Splitting the hinge mode of higher-order topological insulators, Phys. Rev. Lett. 123, 036802 (2019).
- D. Călugăru, V. Juričić, and B. Roy, Higher-order topological phases: A general principle of construction, Phys. Rev. B 99, 041301(R) (2019).
- R.-X. Zhang, F. Wu, and S. DasSarma, Möbius insulator and higher-order topology in MnBi2nTe3n+1subscriptMnBi2𝑛subscriptTe3𝑛1\text{MnBi}_{2n}\text{Te}_{3n+1}MnBi start_POSTSUBSCRIPT 2 italic_n end_POSTSUBSCRIPT Te start_POSTSUBSCRIPT 3 italic_n + 1 end_POSTSUBSCRIPT, Phys. Rev. Lett. 124, 136407 (2020b).
- M. Lin and T. L. Hughes, Topological quadrupolar semimetals, Phys. Rev. B 98, 241103 (2018).
- S. A. A. Ghorashi, T. Li, and T. L. Hughes, Higher-order Weyl semimetals, Phys. Rev. Lett. 125, 266804 (2020b).
- Z. Yan, F. Song, and Z. Wang, Majorana corner modes in a high-temperature platform, Phys. Rev. Lett. 121, 096803 (2018).
- Z. Yan, Higher-order topological odd-parity superconductors, Phys. Rev. Lett. 123, 177001 (2019).
- X. Zhu, Second-order topological superconductors with mixed pairing, Phys. Rev. Lett. 122, 236401 (2019).
- Y. Volpez, D. Loss, and J. Klinovaja, Second-order topological superconductivity in π𝜋\piitalic_π-junction Rashba layers, Phys. Rev. Lett. 122, 126402 (2019).
- Y. Tan, Z.-H. Huang, and X.-J. Liu, Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes, Phys. Rev. B 105, L041105 (2022).
- Y. Peng and G. Refael, Floquet second-order topological insulators from nonsymmorphic space-time symmetries, Phys. Rev. Lett. 123, 016806 (2019).
- B. Huang and W. V. Liu, Floquet higher-order topological insulators with anomalous dynamical polarization, Phys. Rev. Lett. 124, 216601 (2020).
- X.-W. Luo and C. Zhang, Higher-order topological corner states induced by gain and loss, Phys. Rev. Lett. 123, 073601 (2019).
- C. H. Lee, L. Li, and J. Gong, Hybrid higher-order skin-topological modes in nonreciprocal systems, Phys. Rev. Lett. 123, 016805 (2019).
- A. A. Stepanenko, M. D. Lyubarov, and M. A. Gorlach, Higher-order topological phase of interacting photon pairs, Phys. Rev. Lett. 128, 213903 (2022).
- A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997).
- A. Kitaev, Periodic table for topological insulators and superconductors, AIP Conf. Proc. 1134, 22 (2009).
- W. A. Benalcazar and A. Cerjan, Chiral-Symmetric Higher-Order Topological Phases of Matter, Phys. Rev. Lett. 128, 127601 (2022).
- L. Lin and C. Lee, Probing chiral-symmetric higher-order topological insulators with multipole winding number, arXiv:2401.03699 (2024).
- M. Z. Hasan and C. L. Kane, Colloquium: topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
- X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
- I. Bloch, J. Dalibard, and S. Nascimbene, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
- Z. Lei, Y. Deng, and L. Li, Topological classification of higher-order topological phases with nested band inversion surfaces, Phys. Rev. B 106, 245105 (2022).
- T. Morimoto and A. Furusaki, Topological classification with additional symmetries from Clifford algebras, Phys. Rev. B 88, 125129 (2013).
- C.-K. Chiu, H. Yao, and S. Ryu, Classification of topological insulators and superconductors in the presence of reflection symmetry, Phys. Rev. B 88, 075142 (2013).
- L. Zhang, L. Zhang, and X.-J. Liu, Dynamical detection of topological charges, Phys. Rev. A 99, 053606 (2019b).
- R. Okugawa, S. Hayashi, and T. Nakanishi, Second-order topological phases protected by chiral symmetry, Phys. Rev. B 100, 235302 (2019).
- L. Zhang, L. Zhang, and X.-J. Liu, Unified theory to characterize Floquet topological phases by quench dynamics, Phys. Rev. Lett. 125, 183001 (2020c).
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