Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

Abstract

We theoretically demonstrate non-Hermitian indirect interaction between two magnetic impurities placed at the interface between a 3D topological insulator and a ferromagnetic metal. The coupling of topological insulator and the ferromagnet introduces not only Zeeman exchange field on the surface states but also broadening to transfer the charge and spin between the surface states of the topological insulator and the metallic states of the ferromagnet. While the former provides bandgap at the charge neutrality point, the latter causes non-Hermiticity. Using the Green’s function method, we calculate the range functions of magnetic impurity interactions. We show that the charge decay rate provides a coupling between evanescent modes near the bandgap and traveling modes near the band edge. However, the spin decay rate induces a stronger coupling than the charge decay rate so that higher energy traveling modes can be coupled to lower energy evanescent ones. This results in a non-monotonic behavior of the range functions in terms of distance and decay rates in the subgap regime. In the over gap regime, depending on the type of decay rate and on the distance, the amplitude of spatial oscillations would be damped or promoted.

Transition Characteristics of Non‐Hermitian Skin Effects in a Zigzag Lattice Without Chiral Symmetry

“…However, many physical systems hold energy exchange from the ambient environment, and some may even exhibit asymmetrical spatial couplings, rendering the intrinsic Hamiltonian non-Hermitian. [7][8][9][10][11][12] Interestingly, different from conventional Hermitian system, non-Hermitian system, either classical or quantum, has recently become an emergent research front and has attracted rapidly growing interest in past decades, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] which shows abundant characteristics in its complex energy bands and thereby brings about many novel physical phenomena seen in broad physical settings such as optical crystals, [32][33][34][35] mechanical lattices, [36][37][38] electric circuits, [39][40][41][42] acoustic systems, [43][44][45][46] and many others. [47][48][49] The eigen-energy of a non-Hermitian Hamiltonian is usually complex, but it has been f...…”