Angular momentum invoked band inversions in mirror symmetry protected topological states

Topology-Engineered Orbital Hall Effect in Two-Dimensional Ferromagnets

“…However, in spite of extensive efforts so far, effective control of the OHE still remains elusive, which presents a key challenge for practical applications of the effect. It is generally accepted that a topological phase transition (TPT) is always accompanied by the exchange of orbital components between conduction and valence bands, referred to as band inversion. − The band inversion is a physical phenomenon that can lead to unique states at the surfaceas pointed out already by William Shockley back in 1939and to date it is widely used to conceptualize the emergence of different topological states and topological boundary modes. , A key observation is that a band inversion directly invokes the OAM of the inverted states, with distinct orbital components characterized by different OAM eigenvalues, , shedding light on the profound potential of band inversion, instigated by a TPT, in modulating the OHE. While the effect of symmetry breaking on the OHE has been considered from models in nonmagnetic materials, magnetic materials offer much more versatility in realizing TPTs, and the control of the OHE by TPTs in ferromagnets remains a great challenge with strong practical implications.…”