P. A. Dirac, Quantised Singularities in the Electromagnetic Field, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.133, issue.821, pp.60-72, 1931.
DOI : 10.1098/rspa.1931.0130

G. Toulouse and M. Kléman, Principles of a classification of defects in ordered media, Journal de Physique Lettres, vol.37, issue.6, p.149, 1976.
DOI : 10.1051/jphyslet:01976003706014900

URL : https://hal.archives-ouvertes.fr/jpa-00231261

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. Den-nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Physical Review Letters, vol.49, issue.6, pp.405-408, 1982.
DOI : 10.1103/PhysRevLett.49.405

J. E. Avron and R. Seiler, Quantization of the Hall Conductance for General, Multiparticle Schr??dinger Hamiltonians, Physical Review Letters, vol.54, issue.4, p.259, 1985.
DOI : 10.1103/PhysRevLett.54.259

Q. Niu, D. J. Thouless, and Y. Wu, Quantized Hall conductance as a topological invariant, Physical Review B, vol.31, issue.6, p.3372, 1985.
DOI : 10.1103/PhysRevB.31.3372

X. Wen, TOPOLOGICAL ORDERS IN RIGID STATES, International Journal of Modern Physics B, vol.04, issue.02, p.239, 1990.
DOI : 10.1142/S0217979290000139

F. D. Haldane, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly", Physical Review Letters, vol.61, issue.18, pp.2015-2018, 1988.
DOI : 10.1103/PhysRevLett.61.2015

M. V. Berry, Quantal Phase Factors Accompanying Adiabatic Changes, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.392, issue.1802, pp.45-57, 1984.
DOI : 10.1098/rspa.1984.0023

B. Simon, Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase, Physical Review Letters, vol.51, issue.24, pp.2167-2170, 1983.
DOI : 10.1103/PhysRevLett.51.2167

C. L. Kane and E. J. Mele, Topological Order and the Quantum Spin Hall Effect, Physical Review Letters, vol.95, issue.14, p.146802, 2005.
DOI : 10.1103/PhysRevLett.95.146802

M. Z. Hasan and C. L. Kane, : Topological insulators, Reviews of Modern Physics, vol.82, issue.4, pp.3045-3067, 2010.
DOI : 10.1103/RevModPhys.82.3045

X. Qi and S. Zhang, Topological insulators and superconductors, Reviews of Modern Physics, vol.83, issue.4, p.1057, 2011.
DOI : 10.1103/RevModPhys.83.1057

B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors, p.2013
DOI : 10.1515/9781400846733

E. I. Blount, Formalisms of Band Theory, Solid State Physics, pp.305-373, 1962.
DOI : 10.1016/S0081-1947(08)60459-2

Y. Aharonov and D. Bohm, Significance of Electromagnetic Potentials in the Quantum Theory, Physical Review, vol.115, issue.3, p.485, 1959.
DOI : 10.1103/PhysRev.115.485

R. A. Webb, S. Washburn, C. P. Umbach, and R. P. Laibowitz, Aharonov-Bohm Oscillations in Normal-Metal Rings, Physical Review Letters, vol.54, issue.25, p.2696, 1985.
DOI : 10.1103/PhysRevLett.54.2696

T. Kato, On the Adiabatic Theorem of Quantum Mechanics, Journal of the Physical Society of Japan, vol.5, issue.6, p.435, 1950.
DOI : 10.1143/JPSJ.5.435

Y. Aharonov and J. Anandan, Phase change during a cyclic quantum evolution, Physical Review Letters, vol.58, issue.16, p.1593, 1987.
DOI : 10.1103/PhysRevLett.58.1593

J. Anandan and Y. Aharonov, Geometry of quantum evolution, Physical Review Letters, vol.65, issue.14, p.1697, 1990.
DOI : 10.1103/PhysRevLett.65.1697

M. Nakahara, Geometry, Topology and Physics, 2003.
DOI : 10.1887/0750306068

D. Xiao, M. Chang, and Q. Niu, Berry phase effects on electronic properties, Reviews of Modern Physics, vol.82, issue.3, pp.1959-2007, 2010.
DOI : 10.1103/RevModPhys.82.1959

M. Fruchart, D. Carpentier, and K. Gawedzki, Parallel transport and band theory in crystals, EPL (Europhysics Letters), vol.106, issue.6
DOI : 10.1209/0295-5075/106/60002

URL : https://hal.archives-ouvertes.fr/ensl-00958214

C. Bena and G. Montambaux, Remarks on the tight-binding model of graphene, New Journal of Physics, vol.11, issue.9, 2009.
DOI : 10.1088/1367-2630/11/9/095003

URL : https://hal.archives-ouvertes.fr/cea-00442938

M. Fruchart and D. Carpentier, An introduction to topological insulators, Comptes Rendus Physique, vol.14, issue.9-10, p.779, 2013.
DOI : 10.1016/j.crhy.2013.09.013

URL : https://hal.archives-ouvertes.fr/ensl-00868307

F. Piéchon and Y. Suzumura, Inversion symmetry and wave-functionnodal-lines of dirac electrons in organic conductor ?-(BEDT-TTF) 2 I 3

J. N. Fuchs, F. Piéchon, M. O. Goerbig, and G. Montambaux, Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models, The European Physical Journal B, vol.96, issue.3, pp.351-362, 2010.
DOI : 10.1140/epjb/e2010-00259-2

D. Sticlet, F. Piéchon, J. Fuchs, P. Kalugin, and P. Simon, Geometrical engineering of a two-band Chern insulator in two dimensions with arbitrary topological index, Physical Review B, vol.85, issue.16, p.165456, 2012.
DOI : 10.1103/PhysRevB.85.165456

J. J. Sakurai, Modern Quantum Mechanics, 1993.

L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Physical Review B, vol.76, issue.4, p.45302, 2007.
DOI : 10.1103/PhysRevB.76.045302

URL : http://arxiv.org/abs/cond-mat/0611341

G. M. Graf and M. Porta, Bulk-Edge Correspondence for Two-Dimensional Topological Insulators, Communications in Mathematical Physics, vol.6, issue.3, p.851, 2013.
DOI : 10.1007/s00220-013-1819-6

L. Fu, C. L. Kane, and E. J. Mele, Topological Insulators in Three Dimensions, Physical Review Letters, vol.98, issue.10, p.106803, 2007.
DOI : 10.1103/PhysRevLett.98.106803

L. Fu and C. L. Kane, adiabatic spin pump, Physical Review B, vol.74, issue.19, p.195312, 2006.
DOI : 10.1103/PhysRevB.74.195312

R. Roy, Z 2 classification of quantum spin Hall systems: An approach using time-reversal invariance, Phys. Rev. B, vol.79, 2009.

J. E. Moore and L. Balents, Topological invariants of time-reversal-invariant band structures, Physical Review B, vol.75, issue.12, p.121306, 2007.
DOI : 10.1103/PhysRevB.75.121306

A. A. Soluyanov and D. Vanderbilt, topological insulators, Physical Review B, vol.83, issue.3, p.35108, 2011.
DOI : 10.1103/PhysRevB.83.035108

X. Qi, T. L. Hughes, and S. Zhang, Topological field theory of time-reversal invariant insulators, Physical Review B, vol.78, issue.19, 2008.
DOI : 10.1103/PhysRevB.78.195424

Z. Wang, X. Qi, and S. Zhang, Equivalent topological invariants of topological insulators, New Journal of Physics, vol.12, issue.6, p.65007, 2010.
DOI : 10.1088/1367-2630/12/6/065007

B. A. Bernevig, T. L. Hughes, and S. Zhang, Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells, Science, vol.314, issue.5806, pp.1757-1761, 2006.
DOI : 10.1126/science.1133734

C. Liu, T. L. Hughes, X. L. Qi, K. Wang, and S. C. Zhang, Quantum Spin Hall Effect in Inverted Type-II Semiconductors, Physical Review Letters, vol.100, issue.23, p.236601, 2008.
DOI : 10.1103/PhysRevLett.100.236601

R. Jackiw and C. Rebbi, Solitons with fermion number ??, Physical Review D, vol.13, issue.12, pp.3398-3409, 1976.
DOI : 10.1103/PhysRevD.13.3398

S. Murakami, Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase, New Journal of Physics, vol.10, issue.2, p.356, 2007.
DOI : 10.1088/1367-2630/10/2/029802

A. M. Turner and A. Vishwanath, Beyond Band Insulators: Topology of Semi-metals and Interacting Phases. chap

S. M. Young, S. Zaheer, J. C. Teo, C. L. Kane, E. J. Mele et al., Dirac Semimetal in Three Dimensions, Physical Review Letters, vol.108, issue.14, p.140405, 2012.
DOI : 10.1103/PhysRevLett.108.140405

E. Grigory and . Volovik, The Universe in a Helium Droplet, 2003.

G. Montambaux, F. Piéchon, J. Fuchs, and M. O. Goerbig, Merging of Dirac points in a two-dimensional crystal, Physical Review B, vol.80, issue.15, p.153412, 2009.
DOI : 10.1103/PhysRevB.80.153412

L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature, vol.19, issue.7389, p.302, 2012.
DOI : 10.1038/nature10871

URL : https://hal.archives-ouvertes.fr/hal-00820435