Topological polarization in graphene-like systems

Journal of Physics A: Mathematical and Theoretical

Volumn 46, Issue 38, 2013, Pages

  De Nittis, Giuseppe ^a   Lein, Max ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84883881493     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/46/38/385001     Document Type: Article

References (51)

1. Altland A and Zirnbauer M R 1997 Non-standard symmetry classes in mesoscopic normal-superconducting hybrid structures Phys. Rev. B 55 1142-61 (Pubitemid 127486420)
2. Athmouni N, Mǎntoiu M and Purice R 2010 On the continuity of spectra for families of magnetic pseudodifferential operators J. Math. Phys. 51 083517
3. Bellissard J 1986 K-theory of C*-Algebras in Solid State Physics (Lecture Notes in Physics vol 257) (Berlin: Springer) pp 99-156
4. Bellissard J 1988 C*-Algebras in Solid State Physics: 2D Electrons in a Uniform Magnetic Field (London Mathematical Society Lecture Note Series vol 136) (Cambridge: Cambridge University Press) pp 49-76
5. Bellissard J, van Elst A and Schulz-Baldes H 1994 The noncommutative geometry of the quantum Hall effect J. Math. Phys. 35 5373-451 (Pubitemid 24823398)
6. Berry M V 1984 Quantal phase factors accompanying adiabatic changes Proc. R. Soc. Lond. A 392 45-57
7. Birkhoff G D 1931 Proof of the ergodic theorem Proc. Natl Acad. Sci. USA 17 656-60
8. Bott R and Tu L W 1982 Differential Forms in Algebraic Topology (Berlin: Springer)
9. Bratteli O, Elliott G A and Jørgensen P E T 1984 Decomposition of unbounded derivations into invariant and approximately inner parts J. Reine Angew. Math. 1984 166-93
10. Castro Neto A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 The electronic properties of graphene Rev. Mod. Phys. 81 109-62
11. Connes A 1994 Noncommutative Geometry (San Diego, CA: Academic)
12. De Nittis G and Lein M 2011 Exponentially localized Wannier functions in periodic zero flux magnetic fields J. Math. Phys. 52 112103
13. De Nittis G and Panati G 2012 The topological Bloch-Floquet transform and some applications Spectral Analysis of Quantum Hamiltonians (Operator Theory: Advances and Applications vol 224) ed R Benguria, E Friedman and M Mǎntoiu (Basel: Birkhäuser) pp 67-106
14. Følner E 1955 On groups with full Banach mean value Math. Scand. 3 243-54
15. Gracia-Bondía J M, Várilly J C and Figueroa H 2001 Elements of Noncommutative Geometry (Basel: Birkhäuser)
16. Hasegawa Y, Konno R, Nakano H and Kohmoto M 2006 Zero modes of tight-binding electrons on the honeycomb lattice Phys. Rev. B 74 033413 (Pubitemid 44141412)
17. Hatcher A 2002 Algebraic Topology (Cambridge: Cambridge University Press)
18. Hatcher A 2009 Vector Bundles and K-Theory (www.math.cornell.edu/ ∼hatcher/VBKT/VB.pdf)
19. Hörmander L 1990 An Introduction to Complex Analysis in Several Variables (Amsterdam: North-Holland)
20. Husemöller D 1994 Fibre Bundles (Berlin: Springer)
21. Kane C L and Mele E J 2005 Topological order and the quantum spin Hall effect Phys. Rev. Lett. 95 146802 (Pubitemid 41777602)
22. Karoubi M 1987 Homologie cyclique et K-théorie (Astérisque vol 149) (Paris: Société mathématique de France)
23. Kato T 1995 Perturbation Theory for Linear Operators (Berlin: Springer)
24. Kim K S, Zhao Y, Jang H, Lee S Y, Kim J M, Kim K S, Ahn J H, Kim P, Choi J Y and Hong B H 2009 Large-scale pattern growth of graphene films for stretchable transparent electrodes Nature 457 706-10
25. King-Smith R D and Vanderbilt D 1993 Theory of polarization in crystalline solids Phys. Rev. B 47 1651-4
26. Kohmoto M 1985 Topological invariant and the quantization of the Hall conductance Ann. Phys. 160 343-54
27. Kunz H and Souillard B 1980 Sur le spectre des opérateurs aux différences finis aléatoires Commun. Math. Phys. 78 201-46
28. Lee C, Wei X, Kysar J W and Hone J 2008 Measurement of the elastic properties and intrinsic strength of monolayer graphene Science 321 385-8 (Pubitemid 352029970)
29. Lee H C 1948 On Clifford algebras and their representations Ann. Math. 49 760-73
30. Liu F, Ming P and Li J 2007 Ab initio calculation of ideal strength and phonon instability of graphene under tension Phys. Rev. B 76 064120
31. Martin R M 1974 Comment on calculations of electric polarization in crystals Phys. Rev. B 9 1998-9
32. Milnor J W and Stasheff J D 1974 Characteristic Classes (Princeton, NJ: Princeton University Press)
33. Nenciu G 1983 Existence of the exponentially localised Wannier functions Commun. Math. Phys. 91 81-85
34. Ong M T and Reed E J 2012 Engineered piezoelectricity in graphene ACS Nano 6 1387-94
35. Onoda S, Murakami S and Nagaosa N 2004 Topological nature of polarization and charge pumping in ferroelectrics Phys. Rev. Lett. 93 167602
36. Panati G 2007 Triviality of Bloch and Bloch-Dirac bundles Ann. Henri Poincare 8 995-1011
37. Panati G, Sparber C and Teufel S 2009 Geometric currents in piezoelectricity Arch. Ration. Mech. Anal. 191 387-422
38. Pastur L A 1980 Spectral properties of disordered systems in the one-body approximation Commun. Math. Phys. 75 179-96
39. Pereira V M, Castro Neto A H and Peres N M R 2009 Tight-binding approach to uniaxial strain in graphene Phys. Rev. B 80 045401
40. Reed M and Simon B 1978 Methods of Mathematical Physics IV: Analysis of Operators (New York: Academic)
41. Resta R 1992 Theory of the electric polarization in crystals Ferroelectrics 136 51-55
42. Ribeiro R M, Pereira V M, Peres N M R, Briddon P R and Castro Neto A H 2009 Strained graphene: tight-binding and density functional calculations New J. Phys. 11 115002
43. Rice M J and Mele E J 1982 Elementary excitations of a linearly conjugated diatomic polymer Phys. Rev. Lett. 49 1455-9
44. Schnyder A P, Ryu S, Furusaki A and Ludwig A W W 2008 Classification of topological insulators and superconductors in three spatial dimensions Phys. Rev. B 78 195125
45. Schulz-Baldes H and Teufel S 2013 Orbital polarization and magnetization for independent particles in disordered media Commun. Math. Phys. 319 649-81
46. Swan R 1962 Vector bundles and projective modules Trans. Am. Math. Soc. 105 264-77
47. Thouless D J, Kohmoto M, Nightingale M P and Den Nijs M 1982 Quantized Hall conductance in a two-dimensional periodic potential Phys. Rev. Lett. 49 405-8
48. Treves F 1967 Topological Vector Spaces, Distributions and Kernels (New York: Academic)
49. Veselić I 2008 Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators (Lecture Notes in Mathematics vol 1917) (Berlin: Springer)
50. Williams D P 2007 Crossed Products of C*-Algebras (Mathematical Surveys and Monographs vol 134) (Providence, RI: American Mathematical Society)
51. Xiao D, Chang M C and Niu Q 2010 Berry phase effects on electronic properties Rev. Mod. Phys. 82 1959-2007