Topological insulators and C*-algebras: Theory and numerical practice

Annals of Physics

Volumn 326, Issue 7, 2011, Pages 1699-1759

  Hastings, Matthew B ^a,b   Loring, Terry A ^a,c  

^a DUKE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

K theory; Topological insulators

Indexed keywords

EID: 79957662433     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2010.12.013     Document Type: Article

References (40)

1. Hastings M.B., Loring T.A. J. Math. Phys. 2010, 51:015214.
2. Silvestrelli P.L., Marzari N., Vanderbilt D., Parrinello M. Solid State Commun. 1998, 107:7.
3. Evenbly G., Vidal G. Phys. Rev. B 2010, 81:235102.
4. Aguado M., Vidal G. Phys. Rev. Lett. 2008, 100:070404.
5. Bernevig B.A., Hughes T.L., Zhang S.C. Science 2006, 314:1757.
6. König M., et al. Science 2007, 318:766.
7. Fu L., Kane C.L. Phys. Rev. B 2007, 76:045302.
8. Hsieh D., et al. Nature 2008, 452:970.
9. Roy R. Phys. Rev. B 2009, 79:195322.
10. A.P. Schnyder et al., Phys. Rev. B 78 (2008) 195125.
11. A. Kitaev, available from: arxiv:0901.2686.
12. T.A. Loring, M.B. Hastings, Disordered Topological Insulators via C* Algebras, available from: arxiv:1005.4883.
13. Hastings M.B. JSTAT 2008, L01001.
14. Essin A.M., Moore J.E. Phys. Rev. B 2009, 76:165307.
15. M. Dadarlat, Private Communication.
16. Lin H. Fields Inst. Commun. 1995, 13:193.
17. Hastings M.B. Commun. Math. Phys. 2009, 291:321. See. arxiv:0808.2474v3.
18. Loring T.A. Math. Scand. 1998, 82(2):305.
19. Shulman T. Bull. Lond. Math. Soc. 2008, 40(6):1002.
20. Exel R., Loring T.A. J. Funct. Anal. 1991, 95:364.
21. Voiculescu D. Acta Sci. Math. 1983, 45:429.
22. Moore J.E., Balents L. Phys. Rev. B 2007, 75:121306. For example, see, where it was found that (in the translationally invariant case in three dimensions) there were additional invariants arising from lower dimensions.
23. B. Blackadar, Operator Algebras, Encyclopaedia of Mathematical Sciences, vol. 122, Springer-Verlag, 2006.
24. M. Rørdam, An introduction to K-theory for C*-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, 2000.
25. Kasparov G.G. Math. USSR-Izvestiya 1981, 16:513.
26. A. Kitaev, A. Ludwig, Private Communication.
27. Zhang H., et al. Nature Phys. 2009, 5:438.
28. Wood R. Topology 1966, 4(4):371.
29. Schröder H. K-Theory for Real C*-Algebras and Applications 1993, Chapman & Hall/CRC.
30. Connes A., Higson N. Sér. I Math. 1990, 313:101.
31. M.B. Hastings, S. Michalakis, arxiv:0911.4706.
32. König M., et al. J. Phys. Soc. Jpn. 2008, 77:031007.
33. Bellisssard J., van Elst A., Shultz-Baldes H. J. Math. Phys. 1994, 35:537.
34. E. Prodan, arxiv:1010.0595.
35. Hastings M.B. Phys. Rev. B 2004, 69:104431.
36. Higham N.J. Functions of Matrices: Theory and Computation 2008, Society for Industrial Mathematics.
37. Golub G.H. Appl. Mater. 1968, 13(1):44.
38. Zirnbauer M.R. J. Math. Phys. 1996, 37:4986.
39. Guo H.-M. Phys. Rev. B 2010, 82:115122.
40. Guo H.-M., Rosenberg G., Refael G., Franz M. Phys. Rev. Lett. 2010, 105:216601.