Topological phases of electrons induced by electron-magnon interactions

TL;DR

The paper tackles how to realize electronic topological phases without relying on strong spin–orbit coupling or external magnetic fields by leveraging electron–magnon interactions. Using a Green's-function formalism and Holstein–Primakoff spin rotations, it shows that the topology of magnons can be transferred to adjacent electrons, producing quantum Hall and quantum spin Hall insulators in honeycomb trilayer structures. It analyzes both spin-conserving and non-conserving cases, demonstrating DM-induced gaps and quantized Hall responses, and introduces a Z2 framework via Wilson loops for inversion- and SOC-like effects. The work outlines material platforms such as kagome/honeycomb magnets and magnet/metal heterostructures where this topology-transfer mechanism can be realized and tuned by temperature, DM strength, and stacking, offering a route to engineer topological electronics in magnetic systems.

Abstract

Topological phases of electrons such as topological insulators and quantum Hall states typically require strong spin-orbit coupling or magnetic fields. In this study, we consider an electron system coupled to a spin system, where electrons interact with magnons, quasiparticles of spin waves. We show that the interaction between electrons and magnons transfers the effect of symmetry breaking in the spin system to the electron system, whereby a non-trivial topological phase can be induced in the electron system that is otherwise topologically trivial. Through this ``topology transfer'' mechanism, we demonstrate the realization of various topological phases, including quantum Hall and quantum spin Hall insulators, in simple ferromagnetic spin systems, without requiring strong spin-orbit coupling or external magnetic field for electron systems.

Figures (13)

• Figure 1: Schematic of magnon-assisted electron hopping leading to a topological electronic phase. Hoppings of electrons (yellow balls) and magnons (blue balls) are shown in real space. Focusing on the initial state and final state, the electron hops to the next-nearest-neighbor site with acquiring the phase factor.
• Figure 2: Feynman diagrams for the lowest-order electron self-energy contributions: (a) The correction term $\Sigma_{cor}$ [Eq. \ref{['General_Sigma_cor']}], (b) the scattering term $\Sigma_{sca}$ [Eq. \ref{['General_Sigma_sca']}], and (c) the tadpole term $\Sigma_{tad}$ [Eq. \ref{['General_Sigma_tad']}].
• Figure 3: Schematic picture of three-layer honeycomb lattice model. (a) Electron system sandwiched by top and bottom spin systems. Top and bottom layers are ferromagnetically ordered in an anti-parallel way. (b) Honeycomb lattice structure of each layer. Relevant vectors for electron hopping and spin interactions are indicated.
• Figure 4: Spectral function of electrons. (a) A spectral function without self-energy along the high-symmetry path ($\eta/t_1=0.01$). (b) A spectral function with self-energy ($D/t_1=0.0$, $\eta/t_1=0.01$). (c) Spectral function $A_{\vb*{k},\omega}$ at the $K$ point as a function of DM interaction ($\eta/t_1=0.002$). We use following parameters: $t_2/t_1=0.0$, $J_1/t_1=0.05$, $J_2/t_1=0.01$, $J_{ex}/t_1=0.5$, $S=1$, $\Delta_z/t_1=0.005$ and $\varepsilon_F/t_1=0.0$
• Figure 5: Band energy and the Hall conductivity of the effective Hamiltonian of a multi-layer system. (a) Energy band of the effective Hamiltonian ($\varepsilon_F=0.0$). (b) The energy gap at the $K$ point of the effective Hamiltonian as a function of DM interaction. (c) Hall conductivity $\sigma_{xy}$ as a function of the $\varepsilon_F$ at the zero temperature. We use following parameters: $t_2/t_1=0.0$, $J_1/t_1=0.05$, $J_2/t_1=0.01$, $D/t_1=0.02$, $J_{ex}/t_1=0.5$, $S=1$, $\Delta_z/t_1=0.005$ and $\eta/t_1=0.02$.