Notes on topological insulators

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R. M. Kaufmann, D. Li & B. Wehefritz-Kaufmann Khalkhali, in chronological order, for further useful discussions at the different stages of the project. RK thankfully acknowledges support from the Simons founda- tion under collaboration grant # 317149 and BK thankfully acknowledges support from the NSF under the grants PHY-0969689 and PHY-1255409. References [1] A. Altland and M. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal- superconducting hybrid structures, Phys. Rev. B 55 (1997) 1142–1161. [2] L. Alvarez-Gaum ́e, S. Pietra and G. Moore, Anomalies and odd dimensions, Ann. Phys. 163(2) (1985) 288–317. [3] N. W. Ashcroft and N. Mermin, Solid State Physics (Sunders College Publishing, 1976). [4] M. Atiyah, K-theory and reality, Quart. J. Math. 17(2) (1966) 367–386. [5] M. Atiyah, R. Bott and A. Shapiro, Clifford modules, Topology 3 (1964) 3–38. [6] M. Atiyah, V. Patodi and I. M. Singer, Spectral asymmetry and Riemannian geom- etry III, Math. Proc. Camb. Phil. Soc. 79 (1976) 71–99. [7] M. Atiyah and I. M. Singer, The index of elliptic operators: I, Ann. Math. 87(3) (1968) 484–530. [8] M. Atiyah and I. M. Singer, Index theory for skew-adjoint Fredholm operators, Inst. Hautes Etudes Sci. Publ. Math. 37 (1969) 5–26. [9] M. Atiyah and I. M. Singer, The index of elliptic operators: V, Ann. Math. 93(1) (1971) 139–149. [10] J. Avila, H. Schulz-Baldes and C. Villegas-Blas, Topological invariants of edge states for periodic two-dimensional models, Math. Phys., Anal. Geom. 16 (2013) 137–170. [11] J. Avron, D. Osadchy and R. Seiler, A topological look at the quantum Hall effect, Physics Today 56(8) (2003) 38. [12] J. Avron, L. Sadun, J. Segert and B. Simon, Topological invariants in Fermi systems with time-reversal invariance, Phys. Rev. Lett. 61 (1988) 1329–1332. [13] J. Avron, R. Seiler and B. Simon, Homotopy and quantization in condensed matter physics, Phys. Rev. Lett. 51 (1983) 51–53. [14] J. Avron, R. Seiler and B. Simon, The quantum Hall effect and the relative index for projections, Phys. Rev. Lett. 65 (1990) 2185–2188. [15] P. Baum and R. G. Douglas, K-homology and index theory, in Operator Algebras and Applications, Proc. Sympos. Pure and Appl. Math., Vol. 38 (AMS. Providence RI, 1982), pp. 117–173. [16] J. Bellissard, A. van Elst and H. Schulz-Baldes, The noncommutative geometry of the quantum Hall effect, J. Math. Phys. 35 (1994) 5373–5451. [17] B. Bernevig, T. Hughes and S. C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314 (2006) 1757–1761. [18] M. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. A 392 (1984) 45–57. [19] J. M. Bismut and D. Freed, The analysis of elliptic families II: Dirac operators, eta invariants and the holonomy theorem, Comm. Math. Phys. 107 (1986) 103–163. [20] C. Bourne, A. Carey and A. Rennie, The bulk-edge correspondence for the quantum Hall effect in Kasparov theory, Lett. Math. Phys. 105 (2015) 1253–1273. [21] S. Cappell, R. Lee and E. Miller, On the Maslov index, Comm. Pure Appl. Math. 47 (1994) 121–186. 1630003-54 Rev. Math. Phys. 2016.28. Downloaded from www.worldscientific.com by PURDUE UNIVERSITY on 08/11/17. For personal use only.

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