Stability Of Topological Phase Research Articles

Competition of Quantum Anomalous Hall States and Charge Density Wave in a Correlated Topological Model

We investigate the topological phase transition driven by non-local electronic correlations in a realistic quantum anomalous Hall model consisting of dxy –d x 2 – y 2 orbitals. Three topologically distinct phases defined in the non-interacting limit evolve to different charge density wave phases under correlations. Two conspicuous conclusions were obtained: The topological phase transition does not involve gap-closing and the dynamical fluctuations significantly suppress the charge order favored by the next nearest neighbor interaction. Our study sheds light on the stability of topological phase under electronic correlations, and we demonstrate a positive role played by dynamical fluctuations that is distinct to all previous studies on correlated topological states.

Ab initiostudy of nontrivial topological phases in corundum-structured(M2O3)/(Al2O3)5multilayers

\textit{Ab initio} calculations have been performed on hexagonal layers of M$_2$O$_3$ (M being several transition metals of the $5d$ series) sandwiched by a band insulator such as Al$_2$O$_3$ that provides the honeycomb lattice where the $5d$ electrons reside. This corundum-structure-based superlattice is the most obvious way to design a honeycomb lattice with transition metal cations avoiding the use of largely polar surfaces. We obtain that this system supports the presence of Dirac cones at the Fermi level that open up with the introduction of spin-orbit coupling at various fillings of the $5d$ band. The DFT calculations performed in this work show that the $5d^5$ situation is always a trivial insulator, whereas the $5d^8$ filling presents topological insulating configurations which evolve into a trivial state with increasing tensile strain or on-site Coulomb potential U. However, LDA+U calculations show a stable antiferromagnetic solution for the $5d^8$ case at every U value, which would break time reversal symmetry and could affect the topological properties of the system. We also discuss the similarities with the buckled honeycomb lattice obtained using perovskite (111) bilayers previously studied in literature, in particular for the $5d^5$ and $5d^8$ configurations. This work provides some clues on the stability of topological phases using metal oxides in general.

On the stability of topological phases on a lattice

We study the stability of anyonic models on lattices to perturbations. We establish a cluster expansion for the energy of the perturbed models and use it to study the stability of the models to local perturbations. We show that the spectral gap is stable when the model is defined on a sphere, so that there is no ground state degeneracy. We then consider the toric code Hamiltonian on a torus with a class of abelian perturbations and show that it is stable when the torus directions are taken to infinity simultaneously, and is unstable when the thin torus limit is taken.