Theoretical study of magnetic topological insulators

Abstract

In recent years, the discovery of topological insulators brought a topological classification of materials and opened a new field in condensed matter physics. Due to the nontrivial topological properties, the topological insulators have insulating bulk and metallic edge/surface relating to some exotic physics such as quantum anomalous Hall effect, quantum spin Hall effect, and magneto-electric effect. Followed realizations of the Z2 topological insulators in two and three dimensions, the quantum anomalous Hall effect was realized in the magnetic-doped topological insulators very recently, which attracts intensive interest. In this thesis, the magnetic topological insulators as a consequence of time-reversal symmetry breaking in the Z2 topological insulators in two or three dimensions are studied. As an introduction, a review of the topological insulators including some relevant theories is given. The approaches involved in this study are also presented. The results can be

summarized in two parts. First, the quantum anomalous Hall effect can be found on the two-dimensional decorated lattice with spin-orbit coupling and electron-electron interaction. Without interaction, this model exhibits the quantum spin Hall effect and has at bands in the middle of the spectra. A at-band ferrimagnetism which breaks the time-reversal symmetry and a charge-density wave can be induced by the electron-electron interaction. Altogether they can modulate the Chern number of the system and give rise to the quantum anomalous Hall effect. In the second part, the realization of the quantum anomalous Hall effect in magnetic-doped topological insulator thin films is investigated. With an effective Hamiltonian of the surface states of a topological insulator thin _lm, the condition of the quantum anomalous Hall effect and the behavior of the longitudinal and Hall conductivity is given, which agrees with the experimental results. The effects of the structural inversion asymmetry potential and the particle-hole symmetry breaking term are studied. With a thin _lm model of the three-dimensional topological insulator, it is shown that the lateral surface states account for the non-quantized value of the Hall conductance and the nonzero longitudinal conductance. The quantized Hall conductance restores when the lateral surface state electrons are thoroughly localized by disorder. The quantum anomalous Hall phase in magnetic topological insulator thin film in the present of disorder is also studied. The disorder will shrink the regime of the quantum anomalous Hall effect in a thick film and becomes an obstacle to the realization of the quantum anomalous Hall effect.