We investigate possible topological superconductivity in the Kondo-Kitaev model on the honeycomb lattice, where the Kitaev spin liquid is coupled to conduction electrons via the Kondo coupling. We use the self-consistent Abrikosov-fermion mean-field theory to map out the phase diagram. Upon increasing the Kondo coupling, a first order transition occurs from the decoupled phase of spin liquid and conduction electrons to a ferromagnetic topological superconductor of Class D with a single chiral Majorana edge mode. This is followed by a second order transition into a paramagnetic topological superconductor of Class DIII with a single helical Majorana edge mode. These findings offer a novel route to topological superconductivity in the Kondo lattice system. We discuss the connection between topological nature of the Kitaev spin liquid and topological superconductors obtained in this model. arXiv:1804.10212v1 [cond-mat.str-el]

We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.Topological systems have attracted a considerable attention these last decades [1, 2] as they show robust gapless edge modes which are relevant for quantum information purposes [3]. The Haldane model [4] on the honeycomb lattice, which has been realized in ultra-cold atoms [5,6], graphene [7], quantum materials [8], and photonic topological systems [9-13] now appears as a paradigmatic model in the topological classification of Bloch energy bands. For spinless fermions, the bulk state is insulating at half-filling and characterized by a topological invariant, the first Chern number, while the edges of the system reveal a one-dimensional gapless chiral mode by analogy with the quantum Hall effect [14][15][16][17][18][19]. Topological proximity effects induced by a topological band insulator [20][21][22] have also started to gain interest as a generalization of the proximity effect induced from a superconductor onto a metallic system [23,24]. In this Letter, we study the proximity effect when tunnel coupling a Haldane model with a layer of graphene [25][26][27]. We assume spinless particles in both layers and the tunnel process couples the same sublattice in the two layers. Particle-hole processes at the interface open a gap as a result of pseudospin effects, inducing an inverse topological order in the graphene system when both layers are half-filled.The Haldane model and graphene layers are described through the same pseudospin-1/2 representation in momentum space, as a result of the two sublattices of the honeycomb lattice [28], allowing us to describe the proximity effect in the same torus representation of the first Brillouin zone and fiber bundle approach on the Bloch sphere. We address different geometries and protocols to describe the bulk-edge correspondence and the Berry curvatures [29] of Bloch bands which could be equivalently probed for fermions and bosons at the one-particle level. We draw an analogy with the Kane-Mele model [30][31][32] and with ...

We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition's first-order nature in the interacting Haldane model on the honeycomb geometry from a mean-field variational approach supported by density matrix renormalization group results and Ginzburg-Landau arguments. From the Bloch sphere, we make predictions for circular dichroism of light related to the quantum Hall conductivity on the lattice and in the presence of interactions. This analysis shows that the topological number can be measured from the light response at the Dirac points. Electron-electron interactions can also produce a substantial number of particle-hole pairs above the band gap, which leads us to propose a stochastic Chern number as an interacting measure of the topology. The stochastic Chern number can describe disordered situations with a fluctuating staggered potential, and we build an analogy between interaction-induced particlehole pairs and temperature effects. Our stochastic approach is physically intuitive, easy to implement, and leads the way to further studies of interaction effects.