Phase modulation of snake state transport at complex domain walls of magnetic topological insulators

Snake state emerges at the domain wall of magnetic topological insulator heterojunctions. Their wavelength and transmission are governed by the dynamical phase accumulated along the wall. We theoretically investigate snake-state transmission through complex domain walls, and domain crosses and networks. Our main findings reveal that: First, fluctuations in the domain wall magnetization direction reconstruct the phase and spatial current distribution, leading to disorder-renormalized oscillations in the transmission coefficient. Second, in asymmetric heterojunctions with magnetizationsM1andM2on the two sides, the snake wavelength scales as1/(M1-m0)(M2-m0), wherem0is a material parameter. Third, transmission through a Néel domain cross is configuration-dependent: unity for a vortex and less than unity for an antivortex, explained by the phase accumulated around the cross center. Finally, for domain wall networks, Bloch walls host antichiral edge states, whereas Néel walls exhibit global interference of all domain-wall states. These results fill a gap in understanding electronic transport in complex domain structures of magnetic topological insulators and offer insights into transport behavior near the coercive field.