Boundary Physics and Bulk-Boundary Correspondence in Topological Phases of Matter pp 191-198 | Cite as

Summary and Outlook

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• Authors and affiliations

• Abhijeet Alase

Chapter

First Online: 21 November 2019

Part of the Springer Theses book series (Springer Theses)

Abstract

The key findings of the previous chapters are summarized, along with possible directions of future research.

Keywords

Topological insulators Topological superconductors Symmetry-protected topological phases Bulk-boundary correspondence Bloch’s theorem Boundary conditions Wiener–Hopf factorization 

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References

1. 1.
   D. Vanderbilt, R. Resta, Quantum electrostatics of insulators: polarization, Wannier functions, and electric fields. Contemp. Concepts Condens. Matter Sci. 2, 139–163 (2006). https://doi.org/10.1016/S1572-0934(06)02005-1 CrossRefGoogle Scholar
2. 2.
   L. Gor’kov, Surface and superconductivity, in Recent Progress in Many-body Theories, ed. by J.A. Carlson, G. Ortiz (2006), pp. 3–7Google Scholar
3. 3.
   L. Isaev, G. Ortiz, I. Vekhter, Tunable unconventional Kondo effect on topological insulator surfaces. Phys. Rev. B 92, 205423 (2015).  https://doi.org/10.1103/PhysRevB.92.205423 ADSCrossRefGoogle Scholar
4. 4.
   K. Binder, D. Landau, Critical phenomena at surfaces. Phys. A Stat. Mech. Appl. 163, 17–30 (1990). https://doi.org/10.1016/0378-4371(90)90311-F CrossRefGoogle Scholar
5. 5.
   W.A. Benalcazar, B.A. Bernevig, T.L. Hughes, Quantized electric multipole insulators. Science 357, 61–66 (2017).  https://doi.org/10.1126/science.aah6442 ADSMathSciNetCrossRefGoogle Scholar
6. 6.
   K. Hashimoto, X. Wu, T. Kimura, Edge states at an intersection of edges of a topological material. Phys. Rev. B 95, 165443 (2017).  https://doi.org/10.1103/PhysRevB.95.165443 ADSCrossRefGoogle Scholar
7. 7.
   F.K. Kunst, G. van Miert, E.J. Bergholtz, Lattice models with exactly solvable topological hinge and corner states. Phys. Rev. B 97, 241405 (2018).  https://doi.org/10.1103/PhysRevB.97.241405 ADSCrossRefGoogle Scholar
8. 8.
   S. Hegde, V. Shivamoggi, S. Vishveshwara, D. Sen, Quench dynamics and parity blocking in Majorana wires. New J. Phys. 17, 053036 (2015). https://doi.org/10.1088/1367-2630/17/5/053036 ADSCrossRefGoogle Scholar
9. 9.
   T. Kitagawa, E. Berg, M. Rudner, E. Demler, Topological characterization of periodically driven quantum systems. Phys. Rev. B 82, 235114 (2010).  https://doi.org/10.1103/PhysRevB.82.235114 ADSCrossRefGoogle Scholar
10. 10.
    A. Poudel, G. Ortiz, L. Viola, Dynamical generation of Floquet Majorana flat bands in s-wave superconductors. Europhys. Lett. 110, 17004 (2015). https://doi.org/10.1209/0295-5075/110/17004 ADSCrossRefGoogle Scholar
11. 11.
    T. Prosen, Third quantization: a general method to solve master equations for quadratic open Fermi systems. New J. Phys. 10, 043026 (2008). https://doi.org/10.1088/1367-2630/10/4/043026 ADSMathSciNetCrossRefGoogle Scholar
12. 12.
    S. Diehl, E. Rico, M.A. Baranov, P. Zoller, Topology by dissipation in atomic quantum wires. Nat. Phys. 7, 971 (2011).  https://doi.org/10.1038/nphys2106 CrossRefGoogle Scholar
13. 13.
    I. Mandal, Exceptional points for chiral Majorana fermions in arbitrary dimensions. Europhys. Lett. 110, 67005 (2015). https://doi.org/10.1209/0295-5075/110/67005 ADSCrossRefGoogle Scholar
14. 14.
    A. Tayebi, T.N. Hoatson, J. Wang, V. Zelevinsky, Environment-protected solid-state-based distributed charge qubit. Phys. Rev. B 94, 235150 (2016).  https://doi.org/10.1103/PhysRevB.94.235150 ADSCrossRefGoogle Scholar
15. 15.
    D. Leykam, S. Flach, Y.D. Chong, Flat bands in lattices with non-Hermitian coupling. Phys. Rev. B 96, 064305 (2017).  https://doi.org/10.1103/PhysRevB.96.064305 ADSCrossRefGoogle Scholar
16. 16.
    M. Gluza, C. Krumnow, M. Friesdorf, C. Gogolin, J. Eisert, Equilibration via gaussification in fermionic lattice systems. Phys. Rev. Lett. 117, 190602 (2016).  https://doi.org/10.1103/PhysRevLett.117.190602 ADSCrossRefGoogle Scholar
17. 17.
    I. Rotter, A non-Hermitian Hamilton operator and the physics of open quantum systems. J. Phys. A Math. Theor. 42, 153001 (2009). https://doi.org/10.1088/1751-8113/42/15/153001 ADSMathSciNetCrossRefGoogle Scholar
18. 18.
    G. Giorgadze, G. Khimshiashvili, Factorization of loops in loop groups. Bull. Georgian Natl. Acad. Sci. 5, 35 (2011)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

• Abhijeet Alase
  • 1

1. 1.Institute for Quantum Science and TechnologyUniversity of CalgaryCalgaryCanada