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Strongly Correlated Topological Phases

Abstract : This thesis is dedicated largely to the study of theoretical models describing interacting fermions with a spin-orbit coupling. These models (i) can describe a class of 2D iridate materials on the honeycomb lattice or (ii) could be realized artificially in ultra-cold gases in optical lattices. We have studied, in the first part, the half-filled honeycomb lattice model with on-site Hubbard interaction and anisotropic spin-orbit coupling. We find sev- eral different phases: the topological insulator phase at weak coupling, and two frustrated magnetic phases, the Néel order and spiral order, in the limit of strong correlations. The transition between the weak and strong correlation regimes is a Mott transition, through which electrons are fractionalized into spins and charges. Charges are localized by the in- teractions. The spin sector exhibits strong fluctuations which are modeled by an instanton gas. Then, we have explored a system described by the Kitaev-Heisenberg spin Hamil- tonian at half-filling, which exhibits a zig-zag magnetic order. While doping the system around the quarter filling, the band structure presents novel symmetry centers apart from the inversion symmetry point. The Kitaev-Heisenberg coupling favors the formation of triplet Cooper pairs around these new symmetry centers. The condensation of these pairs around these non-trivial wave vectors is manifested by the spatial modulation of the super- conducting order parameter, by analogy to the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconductivity. The last part of the thesis is dedicated to an implementation of the Haldane and Kane-Mele topological phases in a system composed of two fermionic species on the honeycomb lattice. The driving mechanism is the RKKY interaction induced by the fast fermion species on the slower one.
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Submitted on : Monday, February 8, 2016 - 1:36:38 PM
Last modification on : Sunday, June 26, 2022 - 9:59:30 AM
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  • HAL Id : tel-01270697, version 1


Tianhan Liu. Strongly Correlated Topological Phases. Strongly Correlated Electrons [cond-mat.str-el]. UPMC, Sorbonne Universites CNRS, 2015. English. ⟨tel-01270697⟩



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