**Julian Legendre (CPHT, École Polytechnique)**

Two topological models on the kagome lattice: tuning the quantum anomalous Hall phase with ferromagnetism and a Z2 topological insulator with spin-orbit coupling

(Egalement par zoom

https://us06web.zoom.us/j/82521180172?pwd=eG1LMmhGRGg2ak0rM2ozdkFrQy83dz09

Meeting ID: 825 2118 0172

Passcode: 298577)

Topological phases, contrarily to many other phases of matter, cannot be understood in terms of local order parameters. Depending on the symmetries and the dimension of the system under consideration, an appropriate topological invariant describes the topological phase. For instance, the (first) Chern number characterizes the quantum anomalous Hall (QAH) phase associated to the Haldane model. With "two copies" of the Haldane model, we can restore time-reversal symmetry; the system is then characterized by a Z2 topological invariant. In this talk, we explore two topological phases, respectively associated to non zero Chern number and Z2 invariant, for two examples of kagome lattice physical systems.

First, we are interested by the kagome magnet Co3Sn2S2. It shows an impressive behavior of the QAH conductivity driven by the interplay between ferromagnetism in the z direction and antiferromagnetism in the xy plane. Motivated by these facts, we show how such a tuning of the QAH conductivity via the external tuning of the magnetic order can be described.

Then, we investigate the topological phases of a spin-orbit coupled tight-binding model with flux on the kagome lattice. This model is time-reversal invariant and shows Z2 topological insulating phases. We show the stability of the topological phase towards spin-flip processes and different types of on-site potentials. To describe the topological properties of the system we use a numerical approach based on the twisted boundary conditions and we develop an analytical approach related to smooth fields in the Brillouin Zone.