Motivated by recent experiments, we investigate the quantum spin Hall state in 2D topological insulator/ferromagnetic metal planar junctions by means of a tight-binding model and linear response theory. We demonstrate that whether the edge state Dirac cone is submerged into the ferromagnetic subbands and the direction of the magnetization dramatically affect how the edge state percolates into the ferromagnet. Despite the percolation, spin-momentum locking of the edge state remains robust in the topological insulator region. In addition, laminar flows of room temperature persistent charge and spin currents near the interface are uncovered, and the current-induced spin torque is found to be entirely field-like due to the real wave functions of the percolated edge state and the quantum well state of the ferromagnet.

Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the curvature function diverges and changes sign at certain high symmetry points in the Brillouin zone. These generic properties suggest the introduction of a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. { We apply this scheme to a variety of interacting topological insulators in different dimensions and symmetry classes. We demonstrate that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases with very little numerical effort.} Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality in the examples studied.

We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase transitions, and using interacting Su-Schrieffer-Heeger model as an example. From the many-body spectral function, we find that closing of the bulk gap remains a defining feature even if the topological phase transition is driven by interactions. The existence of edge state in the presence of interactions can be captured by means of a T -matrix formalism combined with Dyson's equation, and the bulk-edge correspondence is shown to be satisfied even in the presence of interactions. The critical exponent of the edge state decay length is shown to be affiliated with the same universality class as the noninteracting limit. arXiv:1905.02583v1 [cond-mat.str-el]

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