A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, Emergent phenomena induced by spin???orbit coupling at surfaces and interfaces, Nature, vol.349, issue.60, p.509, 2016.
DOI : 10.1126/science.aab3689

URL : http://arxiv.org/pdf/1611.09521

S. A. Wolf, Spintronics: A Spin-Based Electronics Vision for the Future, Science, vol.294, issue.5546, p.1488, 2001.
DOI : 10.1126/science.1065389

K. Yaji, Y. Ohtsubo, S. Hatta, H. Okuyama, K. Miyamoto et al., Large Rashba spin splitting of a metallic surface-state band on a semiconductor surface, Nature Communications, vol.77, issue.147, p.1, 2010.
DOI : 10.1103/PhysRevB.79.241408

URL : http://www.nature.com/articles/ncomms1016.pdf

X. Ren, H. Kim, S. Yi, Y. Jia, and J. Cho, Spin-orbit coupling effects on the stability of two competing structures in Pb/Si(111) and Pb/Ge(111), Physical Review B, vol.94, issue.7, p.75436, 2016.
DOI : 10.1016/j.susc.2005.12.041

L. V. Bondarenko, Large spin splitting of metallic surface-state bands at adsorbate-modified gold/silicon surfaces, Scientific Reports, vol.77, issue.333, p.1826, 2013.
DOI : 10.1103/PhysRevLett.77.3865

URL : http://www.nature.com/articles/srep01826.pdf

J. M. Carpinelli, H. H. Weitering, E. W. Plummer, and R. Stumpf, Direct observation of a surface charge density wave, Nature, vol.381, issue.6581, p.398, 1996.
DOI : 10.1038/381398a0

J. M. Carpinelli, H. H. Weitering, M. Bartkowiak, R. Stumpf, and E. W. Plummer, Phase of Sn/Ge(111), Physical Review Letters, vol.23, issue.58, p.2859, 1997.
DOI : 10.1016/0022-3697(62)90066-5

G. Profeta, L. Ottaviano, and A. Continenza, surface, Physical Review B, vol.69, issue.24, p.241307, 2004.
DOI : 10.1103/PhysRevB.61.1752

P. Cudazzo, G. Profeta, and A. Continenza, Low temperature phases of Pb/Si(111) and related surfaces, Surface Science, vol.602, issue.3, p.747, 2008.
DOI : 10.1016/j.susc.2007.12.001

]. R. Cortés, A. Tejeda, J. Lobo, C. Didiot, B. Kierren et al., at Low Temperature, Physical Review Letters, vol.96, issue.12, p.126103, 2006.
DOI : 10.1103/PhysRevLett.94.036105

G. Profeta and E. Tosatti, Surfaces, Physical Review Letters, vol.2, issue.8, p.86401, 2007.
DOI : 10.1103/PhysRevB.74.014408

G. Li, P. Höpfner, J. Schäfer, C. Blumenstein, S. Meyer et al., Magnetic order in a frustrated two-dimensional atom lattice at a semiconductor surface, Nature Communications, vol.58, issue.287, p.1620, 2013.
DOI : 10.1103/PhysRevB.58.R7475

URL : http://www.nature.com/articles/ncomms2617.pdf

J. Lee, H. Kim, and J. Cho, Surface, Physical Review Letters, vol.248, issue.10, p.106403, 2013.
DOI : 10.1143/JPSJ.75.051007

URL : https://hal.archives-ouvertes.fr/hal-01562769

A. B. Odobescu, A. A. Maizlakh, N. I. Fedotov, and S. V. Zaitsev-zotov, -Sn surface, Physical Review B, vol.95, issue.19, p.195151, 2017.
DOI : 10.1103/PhysRevLett.108.126802

P. Hansmann, T. Ayral, L. Vaugier, P. Werner, and S. Biermann, and Dynamical Mean-Field Theory, Physical Review Letters, vol.2, issue.2, p.166401, 2013.
DOI : 10.1103/PhysRevLett.82.442

URL : https://hal.archives-ouvertes.fr/cea-01342181

I. Brihuega, O. Custance, M. Ugeda, and J. Gómez-rodrígues, system, Physical Review B, vol.377, issue.379, p.155411, 2007.
DOI : 10.1103/PhysRevLett.95.156101

P. Hansmann, T. Ayral, L. Vaugier, P. Werner, and S. Biermann, on surfaces? Extended Hubbard models for adatom systems from first principles, Journal of Physics: Condensed Matter, vol.25, issue.9, p.94005, 2013.
DOI : 10.1088/0953-8984/25/9/094005

URL : http://arxiv.org/pdf/1310.2062

D. I. Badrtdinov, S. A. Nikolaev, M. I. Katsnelson, and V. V. Mazurenko, Spin-orbit coupling and magnetic interactions in Si(111):{C,Si,Sn,Pb}, Physical Review B, vol.95, issue.22, p.224418, 2016.
DOI : 10.1103/PhysRevB.92.214439

URL : http://arxiv.org/pdf/1609.07648

R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy: Methods and Applications, 1994.
DOI : 10.1017/CBO9780511524356

Y. Kohsaka, How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+??, Nature, vol.101, issue.7208, p.1072, 2008.
DOI : 10.1038/nature07243

URL : http://arxiv.org/pdf/0808.3816

H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Physical Review B, vol.10, issue.12, p.5188, 1976.
DOI : 10.1016/0021-9991(72)90046-0

L. Lin, Adaptively Compressed Exchange Operator, Journal of Chemical Theory and Computation, vol.12, issue.5, p.2242, 2016.
DOI : 10.1021/acs.jctc.6b00092

URL : http://arxiv.org/pdf/1601.07159

D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Physical Review B, vol.23, issue.8, p.85117, 2013.
DOI : 10.1103/PhysRevLett.77.3865

URL : http://arxiv.org/pdf/1306.4707

M. Schlipf and F. Gygi, Optimization algorithm for the generation of ONCV pseudopotentials, Computer Physics Communications, vol.196, p.36, 2015.
DOI : 10.1016/j.cpc.2015.05.011

URL : https://doi.org/10.1016/j.cpc.2015.05.011

C. Brun, T. Cren, and D. Roditchev, Review of 2D superconductivity: the ultimate case of epitaxial monolayers, Superconductor Science and Technology, vol.30, issue.1, p.13003, 2017.
DOI : 10.1088/0953-2048/30/1/013003

URL : https://hal.archives-ouvertes.fr/hal-01399357

S. Modesti, H. Gutzmann, J. Wiebe, and R. Wiesendanger, at 0.3 K, Physical Review B, vol.80, issue.12, p.125326, 2009.
DOI : 10.1103/PhysRevB.58.4584

I. Battisti, V. Fedoseev, K. M. Bastiaans, A. De-la-torre, R. S. Perry et al., Poor electronic screening in lightly doped Mott insulators observed with scanning tunneling microscopy, Physical Review B, vol.95, issue.23, p.235141, 2017.
DOI : 10.1103/PhysRevB.84.100402

URL : https://authors.library.caltech.edu/78599/1/PhysRevB.95.235141.pdf

C. Brun, Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon, Nature Physics, vol.32, issue.6, p.444, 2014.
DOI : 10.1103/PhysRevLett.107.097202

URL : https://hal.archives-ouvertes.fr/hal-01233576

M. Cococcioni and S. De-gironcoli, method, Physical Review B, vol.17, issue.3, p.35105, 2005.
DOI : 10.1029/JB095iB13p21549

C. Chen, Introduction to Scanning Tunneling Microscopy, Oxford Monographs on the Physics and Chemistry of Materials, pp.153-167, 2008.

P. A. Lee and T. Ramakrishnan, Disordered electronic systems, Reviews of Modern Physics, vol.86, issue.110, p.287, 1985.
DOI : 10.1143/JPSJ.43.415

C. Brun, K. H. Muller, I. Hong, F. Patthey, C. Flindt et al., Dynamical Coulomb Blockade Observed in Nanosized Electrical Contacts, Physical Review Letters, vol.108, issue.12, p.126802, 2012.
DOI : 10.1103/PhysRevB.84.195470

URL : https://hal.archives-ouvertes.fr/hal-01233584

L. Simon, C. Bena, F. Vonau, M. Cranney, and D. Aubel, Fourier-transform scanning tunnelling spectroscopy: the possibility to obtain constant-energy maps and band dispersion using a local measurement, Journal of Physics D: Applied Physics, vol.44, issue.46, p.464010, 2011.
DOI : 10.1088/0022-3727/44/46/464010

URL : http://arxiv.org/pdf/1107.3648

]. Y. Kohsaka, T. Machida, K. Iwaya, M. Kanou, T. Hanaguri et al., Spin-orbit scattering visualized in quasiparticle interference, Physical Review B, vol.39, issue.11, p.115307, 2017.
DOI : 10.1103/PhysRevLett.101.206802

URL : http://arxiv.org/pdf/1703.06234

C. Brand, Spin-resolved band structure of a densely packed Pb monolayer on Si(111), Physical Review B, vol.39, issue.3, p.35432, 2017.
DOI : 10.1103/PhysRevB.77.193310

URL : https://infoscience.epfl.ch/record/230633/files/Brand_PbSidense_published.pdf

F. Ming, Realization of a Hole-Doped Mott Insulator on a Triangular Silicon Lattice, Physical Review Letters, vol.119, issue.26, p.266802, 2017.
DOI : 10.1103/PhysRevLett.101.156402

X. Cao, -wave superconductivity in a triangular surface lattice mediated by long-range interaction, Physical Review B, vol.97, issue.15, p.155145, 2018.
DOI : 10.1103/PhysRevB.97.075403