E. N. Adams, Motion of an Electron in a Perturbed Periodic Potential, Physical Review, vol.86, issue.3, pp.427-428, 1952.
DOI : 10.1103/PhysRev.86.427

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes et al., Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices, Physical Review Letters, vol.111, issue.18, 2013.
DOI : 10.1103/PhysRevLett.111.185301

A. S. Alexandrov and H. Capellmann, Orbital diamagnetism of two-dimensional electrons, Physical Review Letters, vol.66, issue.3, pp.365-368, 1991.
DOI : 10.1103/PhysRevLett.66.365

H. Aoki, M. Ando, and H. Matsumura, Hofstadter butterflies for flat bands, R17296?R17299. DOI : 10.1103/PhysRevB.54.R17296, 1996.
DOI : 10.1103/PhysRevB.54.R17296

URL : http://arxiv.org/abs/cond-mat/9607223

J. E. Avron, R. Seiler, and B. Simon, Homotopy and Quantization in Condensed Matter Physics, Homotopy and Quantization in Condensed Matter Physics, pp.51-53, 1983.
DOI : 10.1103/PhysRevLett.51.51

M. Y. Azbel, « Energy spectrum of a conduction electron in a magnetic field, Journal of Experimental and Theoretical Physics, vol.19, p.634, 1964.

S. Banerjee and W. E. Pickett, Phenomenology of a semi-Dirac semi-Weyl semimetal, Physical Review B, vol.86, issue.7, 2012.
DOI : 10.1103/PhysRevB.86.075124

C. Bena and G. Montambaux, Remarks on the tight-binding model of graphene, New Journal of Physics, vol.11, issue.9, p.95003, 2009.
DOI : 10.1088/1367-2630/11/9/095003

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

D. Bercioux, D. F. Urban, H. Grabert, and W. Häusler, « Massless Dirac-Weyl fermions in a T 3 optical lattice, Physical Review A, vol.80, 2009.

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

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

URL : http://cds.cern.ch/record/1529190/files/069115175X_TOC.pdf

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

M. V. Berry and A. K. Geim, Of flying frogs and levitrons, European Journal of Physics, vol.18, issue.4, p.307, 1997.
DOI : 10.1088/0143-0807/18/4/012

E. I. Blount, Bloch Electrons in a Magnetic Field, Physical Review, vol.126, issue.5, pp.1636-1653, 1962.
DOI : 10.1103/PhysRev.126.1636

E. I. Blount-seitz, F. Et-turnbull, and D. , Solid-State Physics. T. 13, 1961.

T. B. Boykin, R. C. Bowen, and G. Klimeck, Electromagnetic coupling and gauge invariance in the empirical tight-binding method, Physical Review B, vol.63, issue.24, 2001.
DOI : 10.1103/PhysRevB.63.245314

P. Briet, H. D. Cornean, and B. Savoie, A Rigorous Proof of the Landau-Peierls Formula and much more, Annales Henri Poincar??, vol.136, issue.3, 2012.
DOI : 10.1007/s00023-011-0128-x

URL : https://hal.archives-ouvertes.fr/hal-00540577

A. H. Castro, F. Neto, N. M. Guinea, K. S. Peres, A. K. Novoselov et al., The electronic properties of graphene, Reviews of Modern Physics, vol.81, issue.1, pp.109-162, 2009.
DOI : 10.1103/RevModPhys.81.109

M. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands, Physical Review B, vol.53, issue.11, pp.7010-7023, 1996.
DOI : 10.1103/PhysRevB.53.7010

K. Chen and P. A. Lee, Unified formalism for calculating polarization, magnetization, and more in a periodic insulator, Physical Review B, vol.84, issue.20, 2011.
DOI : 10.1103/PhysRevB.84.205137

W. J. De-haas and P. M. Van-alphen, « The Dependence of the Susceptibility of Diamagnetic Metals upon the Fields, Commun. Kamerlingh Onnes Lab. Univ. Leiden, vol.212, p.170, 1930.

C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari et al., Hofstadter???s butterfly and the fractal quantum Hall effect in moir?? superlattices, Nature, vol.11, issue.7451, pp.598-602, 1038.
DOI : 10.1038/nature12186

P. Dietl, « Le graphène et le réseau nid d'abeille généralisé sous champ magnétique ». Rapport de stage, 2007.

P. Dietl, F. Piéchon, and G. Montambaux, « New Magnetic Field Dependence of Landau Levels in a Graphene-like Structure, Physical Review Letters, vol.100, 2008.

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

C. Duval, Z. Horváth, P. A. Horváthy, L. Martina, and P. C. Stichel, BERRY PHASE CORRECTION TO ELECTRON DENSITY IN SOLIDS AND "EXOTIC" DYNAMICS, Modern Physics Letters B, vol.20, issue.07, pp.373-378, 2006.
DOI : 10.1142/S0217984906010573

URL : https://hal.archives-ouvertes.fr/hal-00133300

C. Duval, Z. Horváth, P. A. Horváthy, L. Martina, P. C. Stichel et al., Comment on ???Berry Phase Correction to Electron Density of States in Solids???, Physical Review Letters, vol.96, issue.9, 2006.
DOI : 10.1103/PhysRevLett.96.099701

J. E. Hebborn and E. H. Et-sondheimer, The diamagnetism of conduction electrons in metals, Journal of Physics and Chemistry of Solids, vol.13, issue.1-2, pp.105-123, 1960.
DOI : 10.1016/0022-3697(60)90131-1

H. Essén, Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas, EPL (Europhysics Letters), vol.94, issue.4, p.47003, 2011.
DOI : 10.1209/0295-5075/94/47003

H. Essén and M. C. Fiolhais, Meissner effect, diamagnetism, and classical physics???a review, American Journal of Physics, vol.80, issue.2, pp.164-169, 2012.
DOI : 10.1119/1.3662027

M. Fruchart, D. Carpentier, and K. Gawedzki, Parallel transport and band theory in crystals, EPL (Europhysics Letters), vol.106, issue.6, pp.295-5075, 2014.
DOI : 10.1209/0295-5075/106/60002

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

J. 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, 1140.
DOI : 10.1140/epjb/e2010-00259-2

H. Fukuyama, A formula for the orbital magnetic susceptibility of Bloch electrons in weak fields, Physics Letters A, vol.32, issue.2, pp.111-112, 1970.
DOI : 10.1016/0375-9601(70)90117-9

H. Fukuyama, Anomalous Orbital Magnetism and Hall Effect of Massless Fermions in Two Dimension, Journal of the Physical Society of Japan, vol.76, issue.4, 2007.
DOI : 10.1143/JPSJ.76.043711

H. Fukuyama, Hall Effect and Orbital Magnetism of Binary Alloys, Progress of Theoretical Physics, vol.44, issue.4, pp.879-898, 1970.
DOI : 10.1143/PTP.44.879

H. Fukuyama, Theory of Orbital Magnetism of Bloch Electrons: Coulomb Interactions, Progress of Theoretical Physics, vol.45, issue.3, pp.704-729, 1971.
DOI : 10.1143/PTP.45.704

H. Fukuyama, Y. Fuseya, M. Ogata, A. Kobayashi, and Y. Suzumura, Dirac electrons in solids, Proceedings of the International Workshop on Electronic Crystals (ECRYS-2011), pp.1943-1947, 2012.
DOI : 10.1016/j.physb.2012.01.071

H. Fukuyama and R. Kubo, Interband Effect on Magnetic Susceptibility. I. A Simple Two-Band Model, Journal of the Physical Society of Japan, vol.27, issue.3, pp.604-614, 1969.
DOI : 10.1143/JPSJ.27.604

H. Fukuyama and R. Kubo, Interband Effects on Magnetic Susceptibility. II. Diamagnetism of Bismuth, Journal of the Physical Society of Japan, vol.28, issue.3, pp.570-581, 1970.
DOI : 10.1143/JPSJ.28.570

Y. Fuseya, M. Ogata, and H. Fukuyama, Transport Properties and Diamagnetism of Dirac Electrons in Bismuth, Journal of the Physical Society of Japan, vol.84, issue.1, 2015.
DOI : 10.7566/JPSJ.84.012001

R. De, G. , J. Fuchs, M. O. Goerbig, F. Piéchon et al., « Manipulation of Dirac points in graphene-like crystals, Proceedings of the International Workshop on Electronic Crystals (ECRYS-2011), pp.1948-1952, 2012.

N. Ganguli and K. S. Krishnan, The Magnetic and Other Properties of the Free Electrons in Graphite, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.177, issue.969, pp.168-182, 1941.
DOI : 10.1098/rspa.1941.0002

Y. Gao, S. A. Yang, and Q. Niu, Field Induced Positional Shift of Bloch Electrons and Its Dynamical Implications, Physical Review Letters, vol.112, issue.16, 2014.
DOI : 10.1103/PhysRevLett.112.166601

Y. Gao, S. A. Yang, and Q. Niu, Geometrical effects in orbital magnetic susceptibility, Physical Review B, vol.91, issue.21, 2015.
DOI : 10.1103/PhysRevB.91.214405

M. O. Goerbig, Electronic properties of graphene in a strong magnetic field, Reviews of Modern Physics, vol.83, issue.4, pp.1193-1243, 2011.
DOI : 10.1103/RevModPhys.83.1193

A. Goetz and A. B. Focke, The Crystaldiamagnetism of Bismuth Crystals, Physical Review, vol.45, issue.3, pp.170-199, 1934.
DOI : 10.1103/PhysRev.45.170

N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices, Nature Physics, vol.4, issue.7, pp.639-645, 2016.
DOI : 10.1038/nphys3803

M. Goldstein and R. Berkovits, Orbital magnetic susceptibility of disordered mesoscopic systems, Physical Review B, vol.69, issue.3, 2004.
DOI : 10.1103/PhysRevB.69.035323

G. Gómez-santos and T. Stauber, Measurable Lattice Effects on the Charge and Magnetic Response in Graphene, Physical Review Letters, vol.106, issue.4, 2011.
DOI : 10.1103/PhysRevLett.106.045504

P. Gosselin, F. Ménas, A. Bérard, and H. Mohrbach, Semiclassical dynamics of electrons in magnetic Bloch bands: A Hamiltonian approach, Europhysics Letters (EPL), vol.76, issue.4, pp.2006-10321, 2006.
DOI : 10.1209/epl/i2006-10321-4

URL : https://hal.archives-ouvertes.fr/hal-00017432

K. Gottfried and T. Yan, Quantum mechanics : fundamentals, 2013.
DOI : 10.1007/978-0-387-21623-2

A. Gutiérrez-rubio, T. Stauber, G. Gómez-santos, R. Asgari, and F. Guinea, « Orbital magnetic susceptibility of graphene and MoS 2, Phys. Rev. B, vol.93, 2016.

F. D. Haldane, Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property, Physical Review Letters, vol.93, issue.20, 2004.
DOI : 10.1103/PhysRevLett.93.206602

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

Y. Hasegawa, P. Lederer, T. M. Rice, and P. B. Wiegmann, Theory of electronic diamagnetism in two-dimensional lattices, Theory of electronic diamagnetism in two-dimensional lattices, pp.907-910, 1989.
DOI : 10.1103/PhysRevLett.63.907

J. E. Hebborn, J. M. Luttinger, E. H. Sondheimer, and P. J. Stiles, The orbital diamagnetic susceptibility of Bloch electrons, Journal of Physics and Chemistry of Solids, vol.25, issue.7, pp.741-749, 1964.
DOI : 10.1016/0022-3697(64)90186-6

J. E. Hebborn and E. H. Sondheimer, Diamagnetism of Conduction Electrons in Metals, Diamagnetism of Conduction Electrons in Metals, pp.150-152, 1959.
DOI : 10.1103/PhysRevLett.2.150

J. E. Hebborn and E. H. Sondheimer, The diamagnetism of conduction electrons in metals, Journal of Physics and Chemistry of Solids, vol.13, issue.1-2, pp.105-123, 1960.
DOI : 10.1016/0022-3697(60)90131-1

H. Lillian, B. Gordon, and E. Michael, « The development of the quantummechanical electron theory of metals : 19281933 », In : Review of Modern Physics, vol.59, pp.287-327, 1987.

D. R. Hofstadter, « Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields », In : Physical Review B, vol.14, 1976.

J. Ibañez-azpiroz, A. Eiguren, A. Bergara, G. Pettini, and M. Modugno, Breakdown of the Peierls substitution for the Haldane model with ultracold atoms, Physical Review A, vol.90, issue.3, 2014.
DOI : 10.1103/PhysRevA.90.033609

C. L. Kane and E. J. Mele, « Quantum Spin Hall Effect in Graphene, Physical Review Letters, vol.95, 2005.

R. Karplus and J. M. Luttinger, Hall Effect in Ferromagnetics, Physical Review, vol.95, issue.5, pp.1154-1160, 1954.
DOI : 10.1103/PhysRev.95.1154

W. Kohn, Theory of Bloch Electrons in a Magnetic Field: The Effective Hamiltonian, Physical Review, vol.115, issue.6, 1959.
DOI : 10.1103/PhysRev.115.1460

M. Koshino, Chiral orbital current and anomalous magnetic moment in gapped graphene, Physical Review B, vol.84, issue.12, 2011.
DOI : 10.1103/PhysRevB.84.125427

M. Koshino and T. Ando, Anomalous orbital magnetism in Dirac-electron systems: Role of pseudospin paramagnetism, Physical Review B, vol.81, issue.19, 2010.
DOI : 10.1103/PhysRevB.81.195431

M. Koshino and T. Ando, Orbital diamagnetism in multilayer graphenes: Systematic study with the effective mass approximation, Physical Review B, vol.76, issue.8, 2007.
DOI : 10.1103/PhysRevB.76.085425

M. Koshino, Y. Arimura, and T. Ando, Magnetic Field Screening and Mirroring in Graphene, Physical Review Letters, vol.102, issue.17, 2009.
DOI : 10.1103/PhysRevLett.102.177203

M. Koshino and E. Mccann, « Trigonal warping and Berry's phase N ? in ABC-stacked multilayer graphene, Physical Review B, vol.80, 2009.

A. S. Kotosonov, « Diamagnetism of quasi-two-dimensional graphites, JETP Letters, vol.43, pp.37-39, 1986.

L. Landau and E. Lifchitz, Théorie des champs, Éditions Mir, 1970.

Z. Li, L. Chen, S. Meng, L. Guo, J. Huang et al., Field and temperature dependence of intrinsic diamagnetism in graphene: Theory and experiment, Physical Review B, vol.91, issue.9, 2015.
DOI : 10.1103/PhysRevB.91.094429

T. Louvet, P. Delplace, A. A. Fedorenko, and D. Carpentier, On the origin of minimal conductivity at a band crossing, Physical Review B, vol.92, issue.15, 2015.
DOI : 10.1103/PhysRevB.92.155116

J. M. Luttinger, The Effect of a Magnetic Field on Electrons in a Periodic Potential, Physical Review, vol.84, issue.4, pp.814-817, 1951.
DOI : 10.1103/PhysRev.84.814

J. M. Luttinger and W. Kohn, Motion of Electrons and Holes in Perturbed Periodic Fields, Physical Review, vol.97, issue.4, pp.869-883, 1955.
DOI : 10.1103/PhysRev.97.869

T. L. Makarova, Magnetic properties of carbon structures, Semiconductors, vol.38, issue.6, pp.615-638, 2004.
DOI : 10.1134/1.1766362

H. Matsuura and M. Ogata, Theory of Orbital Susceptibility in the Tight-Binding Model: Corrections to the Peierls Phase, Journal of the Physical Society of Japan, vol.85, issue.7, 2016.
DOI : 10.7566/JPSJ.85.074709

F. Mauri and S. G. Louie, Magnetic Susceptibility of Insulators from First Principles, Physical Review Letters, vol.76, issue.22, pp.4246-4249, 1996.
DOI : 10.1103/PhysRevLett.76.4246

E. Mccann and M. Koshino, The electronic properties of bilayer graphene, Reports on Progress in Physics, vol.76, issue.5, 2013.
DOI : 10.1088/0034-4885/76/5/056503

J. W. Mcclure, Diamagnetism of Graphite, Diamagnetism of Graphite, pp.666-671, 1956.
DOI : 10.1103/PhysRev.104.666

A. Mielke, Ferromagnetism in the Hubbard model on line graphs and further considerations, Journal of Physics A: Mathematical and General, vol.24, issue.14, 1991.
DOI : 10.1088/0305-4470/24/14/018

P. K. Misra and L. Kleinman, Theory of the Magnetic Susceptibility of Bloch Electrons, Theory of the Magnetic Susceptibility of Bloch Electrons, pp.4581-4597, 1972.
DOI : 10.1103/PhysRevB.5.4581

P. K. Misra and L. M. Roth, Theory of Diamagnetic Susceptibility of Metals, Physical Review, vol.177, issue.3, 1969.
DOI : 10.1103/PhysRev.177.1089

M. Modugno, J. Iban-ez-azpiroz, and G. Pettini, Tight-binding models for ultracold atoms in optical lattices: general formulation and applications, Science China Physics, Mechanics & Astronomy, vol.15, issue.6, 2016.
DOI : 10.1007/s11433-015-0514-5

G. Montambaux, An equivalence between monolayer and bilayer honeycomb lattices, The European Physical Journal B, vol.86, issue.11, pp.2012-30570, 2012.
DOI : 10.1140/epjb/e2012-30570-7

URL : http://arxiv.org/abs/1205.4459

G. Montambaux, Comment on ??????Theory of electronic diamagnetism in two-dimensional lattices??????, Physical Review Letters, vol.63, issue.15, pp.1657-1657, 1989.
DOI : 10.1103/PhysRevLett.63.1657

G. Montambaux, F. Piéchon, J. Fuchs, and M. O. Goerbig, A universal Hamiltonian for motion and merging of Dirac points in a two-dimensional crystal, The European Physical Journal B, vol.80, issue.4, pp.509-520, 2009.
DOI : 10.1140/epjb/e2009-00383-0

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, 2009.
DOI : 10.1103/PhysRevB.80.153412

M. Morigi, « Coupled bands effects in dice-like lattices under magnetic field

P. J. Morrison, Hamiltonian description of the ideal fluid, Reviews of Modern Physics, vol.70, issue.2, pp.467-521, 1998.
DOI : 10.1103/RevModPhys.70.467

R. R. Nair, M. Sepioni, I. Tsai, O. Lehtinen, J. Keinonen et al., Spin-half paramagnetism in graphene induced by point defects, Nature Physics, vol.8, issue.3, pp.199-202, 1038.
DOI : 10.1103/PhysRevB.84.024114

T. Neupert, C. Chamon, and C. Mudry, Measuring the quantum geometry of Bloch bands with current noise, Physical Review B, vol.87, issue.24, 2013.
DOI : 10.1103/PhysRevB.87.245103

H. K. Nguyen and S. Chakravarty, -density-wave order in the cuprates, Physical Review B, vol.65, issue.18, 2002.
DOI : 10.1103/PhysRevB.65.180519

URL : https://hal.archives-ouvertes.fr/hal-00801132

V. N. Nicopoulos, S. A. Trugman, and . Comment-on, Comment on ??????Theory of electronic diamagnetism in two-dimensional lattices??????, Physical Review Letters, vol.64, issue.2, pp.237-237, 1990.
DOI : 10.1103/PhysRevLett.64.237

E. G. Nikolaev, A. S. Kotosonov, E. A. Shalashugina, A. M. Troyanovskii, and V. I. Tsebro, Local diamagnetic susceptibility of quasi-two-dimensional graphite, Journal of Experimental and Theoretical Physics, vol.117, issue.2, pp.338-342, 2013.
DOI : 10.1134/S1063776113100166

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang et al., Electric Field Effect in Atomically Thin Carbon Films, Science, vol.306, issue.5696, pp.666-669, 2004.
DOI : 10.1126/science.1102896

S. L. O-'dell and R. K. Zia, « Classical and semiclassical diamagnetism : A critique of treatment in elementary texts, American Journal of Physics, vol.54, pp.32-35, 1986.

M. Ogata, Orbital Magnetism of Bloch Electrons: II. Application to Single-Band Models and Corrections to Landau???Peierls Susceptibility, Journal of the Physical Society of Japan, vol.85, issue.6, 2016.
DOI : 10.7566/JPSJ.85.064709

M. Ogata, Orbital Magnetism of Bloch Electrons: III. Application to Graphene, Journal of the Physical Society of Japan, vol.85, issue.10, 2016.
DOI : 10.7566/JPSJ.85.104708

M. Ogata and H. Fukuyama, Orbital Magnetism of Bloch Electrons I. General Formula, Journal of the Physical Society of Japan, vol.84, issue.12, 2015.
DOI : 10.7566/JPSJ.84.124708

Y. Ominato and M. Koshino, Orbital magnetic susceptibility of finite-sized graphene, Physical Review B, vol.85, issue.16, 2012.
DOI : 10.1103/PhysRevB.85.165454

Y. Ominato and M. Koshino, Orbital magnetism of graphene flakes, Physical Review B, vol.87, issue.11, 2013.
DOI : 10.1103/PhysRevB.87.115433

B. Pannetier, J. Chaussy, and R. Rammal, Experimental determination of the (H, T) phase diagram of a superconducting network, Journal de Physique Lettres, vol.44, issue.20, pp.853-858019830044020085300, 1983.
DOI : 10.1051/jphyslet:019830044020085300

URL : https://hal.archives-ouvertes.fr/jpa-00232273

M. Vitor, A. H. Pereira, . Castro, N. M. Neto, and . Peres, « Tight-binding approach to uniaxial strain in graphene, Physical Review B, vol.80, 2009.

F. Piéchon, J. Fuchs, A. Raoux, and G. Montambaux, tight-binding models, Journal of Physics, pp.1742-6596, 2015.
DOI : 10.1088/1742-6596/603/1/012001

F. Piéchon, A. Raoux, J. Fuchs, and G. Montambaux, Geometric orbital susceptibility: Quantum metric without Berry curvature, Physical Review B, vol.94, issue.13, 2016.
DOI : 10.1103/PhysRevB.94.134423

A. Principi, M. Polini, G. Vignale, and M. I. Katsnelson, Many-Body Orbital Paramagnetism in Doped Graphene Sheets, Physical Review Letters, vol.104, issue.22, 2010.
DOI : 10.1103/PhysRevLett.104.225503

J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Communications in Mathematical Physics, vol.20, issue.3, pp.289-301, 1980.
DOI : 10.1007/BF02193559

A. Raoux, M. Morigi, J. Fuchs, F. Piéchon, and G. Montambaux, From Dia- to Paramagnetic Orbital Susceptibility of Massless Fermions, Physical Review Letters, vol.112, issue.2, 2014.
DOI : 10.1103/PhysRevLett.112.026402

A. Raoux, F. Piéchon, J. Fuchs, and G. Montambaux, « Orbital magnetism in coupledbands models, Physical Review B, vol.91, 2015.

R. Resta, Manifestations of Berry's phase in molecules and condensed matter, R107. DOI : 10.1088, pp.953-8984, 0201.
DOI : 10.1088/0953-8984/12/9/201

L. M. Roth, Theory of bloch electrons in a magnetic field, Journal of Physics and Chemistry of Solids, vol.23, issue.5, pp.433-446, 1962.
DOI : 10.1016/0022-3697(62)90083-5

S. A. Safran, Stage dependence of magnetic susceptibility of intercalated graphite, Physical Review B, vol.30, issue.1, pp.421-423, 1984.
DOI : 10.1103/PhysRevB.30.421

S. A. Safran and F. J. Disalvo, Theory of magnetic susceptibility of graphite intercalation compounds, Physical Review B, vol.20, issue.12, pp.4889-4895, 1979.
DOI : 10.1103/PhysRevB.20.4889

B. Savoie, A rigorous proof of the Bohr???van Leeuwen theorem in the semiclassical limit, Reviews in Mathematical Physics, vol.27, issue.08, pp.1550019-1550029, 2015.
DOI : 10.1142/S0129055X15500191

URL : https://hal.archives-ouvertes.fr/hal-00958203

G. A. Schober, H. Murakawa, M. S. Bahramy, R. Arita, Y. Kaneko et al., Mechanisms of Enhanced Orbital Dia- and Paramagnetism: Application to the Rashba Semiconductor BiTeI, Physical Review Letters, vol.108, issue.24, 2012.
DOI : 10.1103/PhysRevLett.108.247208

W. Gordon and . Semenoff, « Condensed-Matter Simulation of a Three-Dimensional Anomaly, Physical Review Letters, vol.53, pp.2449-2452, 1984.

S. G. Sharapov, V. P. Gusynin, and H. Beck, Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations, Physical Review B, vol.69, issue.7, 2004.
DOI : 10.1103/PhysRevB.69.075104

D. Shoenberg and M. Z. Uddin, The Magnetic Properties of Bismuth. I. Dependence of Susceptibility on Temperature and Addition of Other Elements, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.156, issue.889, pp.687-701, 1936.
DOI : 10.1098/rspa.1936.0175

L. V. Shubnikov, W. J. De, and H. , « New phenomena in the change in resistance of bismuth crystals in a magnetic field at the temperature of liquid hydrogen, Proceedings of the Royal Netherlands Academy of Arts and Science, vol.33, pp.363-378, 1930.

S. Barry and . Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase », In : Physical Review Letters, vol.51, 1983.

P. Skudlarski and G. Vignale, Electronic diamagnetism in a three-dimensional lattice, Physical Review B, vol.43, issue.7, pp.5764-5768, 1991.
DOI : 10.1103/PhysRevB.43.5764

A. A. Soluyanov and D. Vanderbilt, Smooth gauge for topological insulators, Physical Review B, vol.85, issue.11, 2012.
DOI : 10.1103/PhysRevB.85.115415

URL : http://arxiv.org/abs/1201.5356

T. Stauber and G. Gómez-santos, Dynamical current-current correlation of the hexagonal lattice and graphene, Physical Review B, vol.82, issue.15, 2010.
DOI : 10.1103/PhysRevB.82.155412

D. Sticlet and F. Piéchon, Distant-neighbor hopping in graphene and Haldane models, Physical Review B, vol.87, issue.11, 2013.
DOI : 10.1103/PhysRevB.87.115402

URL : https://hal.archives-ouvertes.fr/hal-00811626

P. Streda, Theory of quantised Hall conductivity in two dimensions, Journal of Physics C: Solid State Physics, vol.15, issue.22, 1982.
DOI : 10.1088/0022-3719/15/22/005

G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Physical Review B, vol.59, issue.23, pp.14915-14925, 1999.
DOI : 10.1103/PhysRevB.59.14915

B. Sutherland, Localization of electronic wave functions due to local topology, Physical Review B, vol.34, issue.8, pp.5208-5211, 1986.
DOI : 10.1103/PhysRevB.34.5208

L. Tarruell, 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, 2012.
DOI : 10.1038/nature10871

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

T. Thonhauser, THEORY OF ORBITAL MAGNETIZATION IN SOLIDS, International Journal of Modern Physics B, vol.25, issue.11, pp.1429-1458, 2011.
DOI : 10.1142/S0217979211058912

T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Orbital Magnetization in Periodic Insulators, Physical Review Letters, vol.95, issue.13, 2005.
DOI : 10.1103/PhysRevLett.95.137205

D. J. Thouless, Quantization of particle transport, Quantization of particle transport, pp.6083-6087, 1983.
DOI : 10.1103/PhysRevB.27.6083

D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. Den, and N. , 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

G. M. Tia, « Le magnétisme orbital dans le graphène sur réseau, 2011.

J. H. Van and . Vleck, « Quantum mechanics ? The key to understanding magnetism », In : Review of Modern Physics, vol.50, pp.181-189, 1978.

J. Vidal, R. Mosseri, and B. Douçot, Aharonov-Bohm Cages in Two-Dimensional Structures, Physical Review Letters, vol.81, issue.26, pp.5888-5891, 1998.
DOI : 10.1103/PhysRevLett.81.5888

G. Vignale, Orbital paramagnetism of electrons in a two-dimensional lattice, Physical Review Letters, vol.67, issue.3, pp.358-361, 1991.
DOI : 10.1103/PhysRevLett.67.358

P. R. Wallace, The Band Theory of Graphite, Physical Review, vol.71, issue.9, pp.622-634, 1947.
DOI : 10.1103/PhysRev.71.622

G. H. Wannier and U. N. Upadhyaya, Zero-Field Susceptibility of Bloch Electrons, A803?A810. DOI : 10.1103/PhysRev.136.A803, 1964.
DOI : 10.1103/PhysRev.136.A803

A. Widom, Thermodynamic derivation of the Hall effect current, Physics Letters A, vol.90, issue.9, pp.474-484, 1982.
DOI : 10.1016/0375-9601(82)90401-7

B. Wunsch, F. Guinea, and F. Sols, Dirac-point engineering and topological phase transitions in honeycomb optical lattices, New Journal of Physics, vol.10, issue.10, 2008.
DOI : 10.1088/1367-2630/10/10/103027

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

D. Xiao, J. Shi, and Q. Niu, Berry Phase Correction to Electron Density of States in Solids, Physical Review Letters, vol.95, issue.13, 2005.
DOI : 10.1103/PhysRevLett.95.137204

Y. Xiao, V. Pelletier, P. M. Chaikin, and D. A. Huse, Landau levels in the case of two degenerate coupled bands:???Kagom?? lattice tight-binding spectrum, Physical Review B, vol.67, issue.10, 2003.
DOI : 10.1103/PhysRevB.67.104505