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Table of contents
1 Introduction
1.1 Topology in Condensed Matter
1.1.1 Quantum Hall System
1.1.2 Haldane Model and Chern Number
1.1.3 Kane-Mele Model and Z2 Topological Invariant
1.2 Mott Physics
1.2.1 Doped Mott Insulators
1.3 Frustrated Magnetism
1.3.1 Geometrical Frustration
1.3.2 Order by Disorder
1.3.3 Spin Liquid
1.3.4 Kane-Mele-Hubbard Model
1.4 Introduction to Iridate System
1.4.1 Balents’ Diagram
1.4.2 The Honeycomb Iridates
1.5 Doped Honeycomb Iridates
1.6 Summary
2 Iridates on Honeycomb Lattice at Half-filling
2.1 Topological Insulator Phase
2.1.1 Numerical Diagonalization
2.1.2 Edge State Solution via Transfer Matrix
2.2 The Frustrated Magnetism in Strong Coupling limit
2.2.1 Néel Phase for J1 > J2
2.2.2 Non-Colinear Spiral Phase for J1 < J2
2.2.3 Phase Transition at J1 = J2
2.3 Intermediate Interaction Region – Mott Transition
2.3.1 Slave Rotor Representation for the Mott Transition
2.3.2 Gauge Fluctuation Upon Mott Transition
2.3.3 Spin Texture upon Insertion of Flux
2.4 Lattice Gauge Field by Construction of Loop Variables
2.5 Spin Texture under Two Adjacent Monopoles
2.6 Conclusion
3 Doping Iridates on the Honeycomb Lattice – t − J Model
3.1 Introduction
3.2 Duality between Heisenberg and Kitaev-Heisenberg model
3.2.1 Duality at Half-filling
3.2.2 Duality beyond Half-filling
3.3 Exact Diagonalization on one Plaquette – Triplet Pairings
3.3.1 Half-filling
3.3.2 Doped System
3.4 Band Structure of the Spin-Orbit Coupling System
3.5 FFLO Superconductivity
3.5.1 The Spin-Orbit Coupling Limit t = J1 = 0
3.5.2 Near the Spin-Orbit Coupling Limit t, J1 → 0
3.6 Numerical Proofs of the FFLO Superconductivity
3.7 Conclusion
4 Engineering Topological Mott Phases
4.1 RKKY Interaction
4.2 Haldane Mass Induced by the RKKY Interaction
4.3 Mott Transition Induced by the RKKY Interaction
4.4 Conclusion
5 Conclusion
A Annexe
A.1 Loop Variables Construction: Curl and Divergence on a Lattice
