Disordered Phase Transition And Localization Effects In Higher-order Topological Systems

Since the discovery of topological insulators,there is a rapid development in the related fields and many novel topological states have been discovered successively.In particular,high-order topological insulators have attracted extensive attention in recent years due to their unique bulk-boundary correspondence.Meanwhile,the study of disorder effects in topological systems is the key to the understanding of its topological features.However,since higher-order topological insulators are protected by point groups and space groups,the corresponding topological properties are generally believed to be difficult to preserve under disorder.With the further study of high-order topological systems in recent years,the real-space topological invariant(e.g.electric quadrupole moment)of high-order topological insulators has been proposed.It has been proved that higher-order topological insulators are robust and protected by chiral or particle-hole symmetry.However,the relationship between the electric quadrupole moment and the mobility band gap is not clear because the influence of the unique bulk-edge correspondence in the disordered higher order topological insulators is ignored in previous studies.In this thesis,we study the disordered phase transition and localization effect of two-dimensional higher-order topological insulators,and propose a topological invariant called spin chern number,which is directly related to the mobility gap.We concentrate on two different cases:(1)bulk-corner correspondence and(2)edge-corner correspondence.For the bulk-corner correspondence case,the numerical results show the existence of the mobility gaps,and the spin number gives the same phase diagram as the electric quadrupole moment.Therefore,the electric quadrupole moment is a topological invariant that protected by the mobility gap under strong disorder.For the edge-corner correspondence case,we show that the bulk mobility gap and edge band gaps of HOTIs are no longer closed simultaneously.This effect is accompanied by the inconsistency between the spin chem number and the electric quadrupole moment under disorder.Different from the traditional topological states,we also find the disordered phase transition from nontrivial phase to trivial phase based on band renormalization.Finally,based on the above results,we give the possible phase transition processes of high-order topological insulators under disorder.In summary,starting from different bulk-boundary correspondence,this thesis clarifies the relationship between the evolutions of the gap and different topological invariants in the disordered phase transition of the system,and obtains a clear phase transition process.At the same time,we also reveal the underlying physical mechanisms for the rich disordered phase transitions of high-order topological insulators,which provide a certain theoretical basis for related experimental studies.