Bulk-boundary correspondence in point-gap topological phases (2205.15635v4)
Abstract: A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the $K$-theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states.
- M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 102, 065703 (2009).
- Y. C. Hu and T. L. Hughes, Phys. Rev. B 84, 153101 (2011).
- H. Schomerus, Opt. Lett. 38, 1912 (2013).
- T. E. Lee, Phys. Rev. Lett. 116, 133903 (2016).
- Y. Xiong, J. Phys. Commun. 2, 035043 (2018).
- V. Kozii and L. Fu, arXiv:1708.05841 .
- K. Takata and M. Notomi, Phys. Rev. Lett. 121, 213902 (2018).
- S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018).
- J. Carlström and E. J. Bergholtz, Phys. Rev. A 98, 042114 (2018).
- C. H. Lee and R. Thomale, Phys. Rev. B 99, 201103 (2019).
- L. Jin and Z. Song, Phys. Rev. B 99, 081103 (2019).
- R. Okugawa and T. Yokoyama, Phys. Rev. B 99, 041202 (2019).
- F. K. Kunst and V. Dwivedi, Phys. Rev. B 99, 245116 (2019).
- S. Longhi, Phys. Rev. Lett. 122, 237601 (2019).
- H. Zhou and J. Y. Lee, Phys. Rev. B 99, 235112 (2019).
- K. Yokomizo and S. Murakami, Phys. Rev. Lett. 123, 066404 (2019).
- P. A. McClarty and J. G. Rau, Phys. Rev. B 100, 100405 (2019).
- N. Okuma and M. Sato, Phys. Rev. Lett. 123, 097701 (2019).
- E. J. Bergholtz and J. C. Budich, Phys. Rev. Res. 1, 012003 (2019).
- W. Brzezicki and T. Hyart, Phys. Rev. B 100, 161105 (2019).
- H. Schomerus, Phys. Rev. Res. 2, 013058 (2020).
- K.-I. Imura and Y. Takane, Phys. Rev. B 100, 165430 (2019).
- X.-X. Zhang and M. Franz, Phys. Rev. Lett. 124, 046401 (2020).
- S. Longhi, Phys. Rev. Lett. 124, 066602 (2020).
- K. Yokomizo and S. Murakami, Phys. Rev. Res. 2, 043045 (2020).
- F. Terrier and F. K. Kunst, Phys. Rev. Res. 2, 023364 (2020).
- T. Bessho and M. Sato, Phys. Rev. Lett. 127, 196404 (2021).
- J. Claes and T. L. Hughes, Phys. Rev. B 103, L140201 (2021).
- H.-G. Zirnstein and B. Rosenow, Phys. Rev. B 103, 195157 (2021).
- N. Okuma and M. Sato, Phys. Rev. B 103, 085428 (2021).
- Y. Yi and Z. Yang, Phys. Rev. Lett. 125, 186802 (2020).
- K. Shiozaki and S. Ono, Phys. Rev. B 104, 035424 (2021).
- A. K. Ghosh and T. Nag, Phys. Rev. B 106, L140303 (2022).
- Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
- Skin modes are obtained using GBZ and thus bulk modes Yao and Wang (2018), while surface states are not obtained using GBZ and thus not bulk modes.
- J. Song and E. Prodan, Phys. Rev. B 89, 224203 (2014).
- E. Prodan and H. Schulz-Baldes, J. Funct. Anal. 271, 1150 (2016).
- H. Katsura and T. Koma, J. Math. Phys. 59, 031903 (2018).
- A. Y. Kitaev, Ann. Phys. (N.Y.) 321, 2 (2006).
- Note that the isotropic structure of ∓e±ikyminus-or-plussuperscript𝑒plus-or-minus𝑖subscript𝑘𝑦\mp e^{\pm ik_{y}}∓ italic_e start_POSTSUPERSCRIPT ± italic_i italic_k start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT end_POSTSUPERSCRIPT in the complex energy plane causes highly degenerated in-gap skin modes at E=0𝐸0E=0italic_E = 0.
- H. Katsura and T. Koma, J. Math. Phys. 57, 021903 (2016).