K. Von-klitzing, The quantized Hall effect, Reviews of Modern Physics, vol.54, issue.3, p.519, 1986.
DOI : 10.1007/BF01507943

F. Haldane, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly", Physical Review Letters, vol.285, issue.18, p.2015, 1988.
DOI : 10.1016/0550-3213(87)90343-9

D. J. Thouless, M. Kohmoto, M. Nightingale, and M. Den-nijs, Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Physical Review Letters, vol.88, issue.6, p.405, 1982.
DOI : 10.1002/pssb.2220880243

M. Z. Hasan and C. Kane, : Topological insulators, Reviews of Modern Physics, vol.70, issue.4, pp.3045-67, 2010.
DOI : 10.1103/PhysRevB.65.245420

X. Qi and S. Zhang, Topological insulators and superconductors, Reviews of Modern Physics, vol.70, issue.4, p.1057, 2011.
DOI : 10.1103/PhysRevB.82.113305

M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen et al., Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond, Advances in Physics, vol.70, issue.2, pp.243-379, 2007.
DOI : 10.1103/PhysRevLett.72.797

URL : http://arxiv.org/abs/cond-mat/0606771

I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Reviews of Modern Physics, vol.91, issue.196, p.885, 2008.
DOI : 10.1103/PhysRevLett.91.250401

URL : https://hal.archives-ouvertes.fr/hal-00195515

X. J. Liu, X. Liu, C. Wu, and J. Sinova, Quantum anomalous Hall effect with cold atoms trapped in a square lattice, Physical Review A, vol.81, issue.3, p.33622, 2010.
DOI : 10.1103/PhysRevLett.98.260402

T. Stanescu, V. Galitski, and S. Sarma, Topological states in two-dimensional optical lattices, Physical Review A, vol.11, issue.1, p.13608, 2010.
DOI : 10.1103/PhysRevA.78.023616

URL : http://arxiv.org/pdf/0912.3559

J. Dalibard, F. Gerbier, and J. , : Artificial gauge potentials for neutral atoms, Reviews of Modern Physics, vol.2, issue.4, pp.1523-1566, 2011.
DOI : 10.1103/PhysRevLett.64.256

D. Jaksch and P. Zoller, Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms, New Journal of Physics, vol.5, p.56, 2003.
DOI : 10.1088/1367-2630/5/1/356

F. Gerbier and J. Dalibard, Gauge fields for ultracold atoms in optical superlattices, New Journal of Physics, vol.12, issue.3, p.33007, 2010.
DOI : 10.1088/1367-2630/12/3/033007

URL : https://hal.archives-ouvertes.fr/hal-00425517

L. Lim, M. Smith, C. Hemmerich, and A. , Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice, Physical Review Letters, vol.100, issue.13, p.130402, 2008.
DOI : 10.1103/PhysRevA.63.053601

M. Aidelsburger, M. Atala, S. Nascimbène, S. Trotzky, Y. A. Chen et al., Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice, Physical Review Letters, vol.107, issue.25, p.255301, 2011.
DOI : 10.1103/PhysRevA.76.023613

URL : https://hal.archives-ouvertes.fr/hal-00659354

E. Alba, X. Fernandez-gonzalvo, J. Mur-petit, J. K. Pachos, and J. J. Garcia-ripoll, Seeing Topological Order in Time-of-Flight Measurements, Physical Review Letters, vol.107, issue.23, p.235301, 2011.
DOI : 10.1103/PhysRevB.83.245115

J. Ruostekoski, G. Dunne, and J. Javanainen, Particle Number Fractionalization of an Atomic Fermi-Dirac Gas in an Optical Lattice, Physical Review Letters, vol.87, issue.18, p.180401, 2002.
DOI : 10.1103/PhysRevLett.87.120407

X. L. Qi, Y. Wu, and S. Zhang, Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors, Physical Review B, vol.160, issue.8, p.85308, 2006.
DOI : 10.1103/PhysRevB.52.R5539

P. Wallace, The Band Theory of Graphite, Physical Review, vol.16, issue.9, pp.622-656, 1947.
DOI : 10.1063/1.1710273

A. H. Neto, F. Guinea, N. Peres, K. Novoselov, and A. Geim, The electronic properties of graphene, Reviews of Modern Physics, vol.48, issue.1, pp.109-62, 2009.
DOI : 10.1103/PhysRevLett.80.3113

C. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene, Physical Review Letters, vol.95, issue.22, p.226801, 2005.
DOI : 10.1103/PhysRevLett.93.197402

URL : http://arxiv.org/abs/cond-mat/0411737

J. Luttinger, The Effect of a Magnetic Field on Electrons in a Periodic Potential, Physical Review, vol.74, issue.4, pp.814-821, 1951.
DOI : 10.1103/PhysRev.74.433

D. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Physical Review B, vol.69, issue.6, pp.2239-2288, 1976.
DOI : 10.1002/pssb.2220690137

M. Nakahara, Topology and Physics (Graduate Student Series in Physics), Geometry, 2003.

D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Reviews of Modern Physics, vol.2, issue.3, p.1959, 2010.
DOI : 10.1038/nmat2003

URL : http://arxiv.org/pdf/0907.2021

T. T. Wu and C. Yang, Concept of nonintegrable phase factors and global formulation of gauge fields, Physical Review D, vol.35, issue.12, p.3845, 1975.
DOI : 10.1103/PhysRevLett.35.760

Y. Hatsugai, Chern number and edge states in the integer quantum Hall effect, Physical Review Letters, vol.316, issue.22, p.3697, 1993.
DOI : 10.1007/978-3-642-96585-2

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-kurn, D. Pritchard et al., Bragg Spectroscopy of a Bose-Einstein Condensate, Physical Review Letters, vol.81, issue.23, p.4569, 1999.
DOI : 10.1103/PhysRevLett.81.2194

J. Steinhauer, R. Ozeri, N. Katz, and N. Davidson, Excitation Spectrum of a Bose-Einstein Condensate, Physical Review Letters, vol.77, issue.12, p.120407, 2002.
DOI : 10.1103/PhysRevLett.77.5315

N. Goldman, J. Beugnon, and F. Gerbier, Detecting Chiral Edge States in the Hofstadter Optical Lattice, Physical Review Letters, vol.108, issue.25, p.255303, 2012.
DOI : 10.1038/nature09378

M. Hafezi, A. S. Sørensen, E. Demler, and M. Lukin, Fractional quantum Hall effect in optical lattices, Physical Review A, vol.76, issue.2, p.23613, 2007.
DOI : 10.1103/PhysRevLett.76.4508

URL : http://arxiv.org/abs/0706.0757

R. O. Umucalilar, H. Zhai, and M. Oktel, Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator, Physical Review Letters, vol.14, issue.7, p.70402, 2008.
DOI : 10.1103/PhysRevLett.94.080403

A. Bermudez, N. Goldman, A. Kubasiak, M. Lewenstein, and M. Martin-delgado, Topological phase transitions in the non-Abelian honeycomb lattice, New Journal of Physics, vol.12, issue.3, p.33041, 2010.
DOI : 10.1088/1367-2630/12/3/033041

H. Price and C. N. , Mapping the Berry curvature from semiclassical dynamics in optical lattices, Physical Review A, vol.85, issue.3, p.33620, 2012.
DOI : 10.1103/PhysRevLett.100.080404

S. Girvin, arXiv:cond-mat/9907002v1 [cond-mat, 1999.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C. X. Liu et al., The Quantum Spin Hall Effect: Theory and Experiment, Journal of the Physical Society of Japan, vol.77, issue.3, p.31007, 2008.
DOI : 10.1143/JPSJ.77.031007

E. Prada, P. San-jose, L. Brey, and H. A. Fertig, Band topology and the quantum spin Hall effect in bilayer graphene, Solid State Communications, vol.151, issue.16, pp.1075-83, 2011.
DOI : 10.1016/j.ssc.2011.05.016

Y. Hatsugai, Characterization of Topological Insulators: Chern Numbers for Ground State Multiplet, Journal of the Physical Society of Japan, vol.74, issue.5, p.1374, 2005.
DOI : 10.1143/JPSJ.74.1374

N. Goldman, W. Beugeling, M. Smith, and C. , Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field, EPL (Europhysics Letters), vol.97, issue.2, p.23003, 2012.
DOI : 10.1209/0295-5075/97/23003

W. Beugeling, N. Goldman, M. Smith, and C. , Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling, Physical Review B, vol.86, issue.7, p.75118, 2012.
DOI : 10.1103/PhysRevB.69.115108

N. Goldman, D. Urban, and D. Bercioux, Topological phases for fermionic cold atoms on the Lieb lattice, Physical Review A, vol.83, issue.6, p.63601, 2011.
DOI : 10.1103/PhysRevLett.98.210403

H. Guo and F. M. , Topological insulator on the kagome lattice, Physical Review B, vol.80, issue.11, p.113102, 2009.
DOI : 10.1103/PhysRevLett.103.046811

URL : http://arxiv.org/pdf/0905.3385

Z. Lan and N. Goldman, and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice, Physical Review B, vol.85, issue.15, p.155451, 2012.
DOI : 10.1016/j.aop.2005.10.005

B. A. Bernevig and S. Zhang, Quantum Spin Hall Effect, Physical Review Letters, vol.56, issue.10, p.106802, 2006.
DOI : 10.1103/PhysRevLett.95.136602

C. Wu, B. A. Bernevig, and S. Zhang, Helical Liquid and the Edge of Quantum Spin Hall Systems, Physical Review Letters, vol.41, issue.10, p.106401, 2006.
DOI : 10.1103/PhysRevB.1.4464

N. Goldman, I. Satija, P. Nikolic, A. Bermudez, M. Martin-delgado et al., Realistic Time-Reversal Invariant Topological Insulators with Neutral Atoms, Physical Review Letters, vol.105, issue.25, p.255302, 2010.
DOI : 10.1103/PhysRevLett.100.070402

URL : http://arxiv.org/pdf/1011.3909

B. Béri and C. N. , Topological Insulators in Ultracold Atomic Gases, Physical Review Letters, vol.107, issue.14, p.145301, 2011.
DOI : 10.1103/PhysRevLett.105.256803

L. Mazza, A. Bermudez, N. Goldman, M. Rizzi, M. A. Martin-delgado et al., An optical-lattice-based quantum simulator for relativistic field theories and topological insulators, New Journal of Physics, vol.14, issue.1, p.15007, 2012.
DOI : 10.1088/1367-2630/14/1/015007

URL : http://arxiv.org/abs/1105.0932

M. Buchhold, D. Cocks, and W. Hofstetter, Effects of smooth boundaries on topological edge modes in optical lattices, Physical Review A, vol.85, issue.6, p.63614, 2012.
DOI : 10.1103/PhysRevLett.88.120407

D. Cocks, P. P. Orth, R. S. Buchhold, M. Hur, K. L. Hofstetter et al., Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions, Physical Review Letters, vol.85, issue.20, p.205303, 2012.
DOI : 10.1103/PhysRevA.85.061605

URL : http://arxiv.org/abs/1204.4171

S. Raghu, X. L. Qi, C. Honerkamp, and S. Zhang, Topological Mott Insulators, Physical Review Letters, vol.100, issue.15, p.156401, 2008.
DOI : 10.1103/PhysRevLett.93.153001

URL : http://arxiv.org/abs/0710.0030

K. Sun, W. V. Liu, A. Hemmerich, and D. Sarma, Topological semimetal in a fermionic optical lattice, Nature Physics, vol.8, issue.1, p.67, 2011.
DOI : 10.1103/PhysRevB.82.115125

A. Dauphin, M. Müller, and M. Martin-delgado, Rydberg-atom quantum simulation and Chern-number characterization of a topological Mott insulator, Physical Review A, vol.11, issue.5, p.53618, 2012.
DOI : 10.1088/1367-2630/14/3/033044