Coexistence of quantum spin Hall and magnetic states in zigzag bismuth nanoribbons

Chemical modifications and/or simple vertical stacking of disparate van der Waals layered crystals can be used as a materials design approach for creating novel phases of matter. Here, using ab initio computations, we demonstrate the realization of an unusual state in a bismuth nanoribbon decorated with nitrogen atoms along one of the edges. In this phase, the quantum spin Hall state on one edge of the nanoribbon coexists with the ferromagnetism on the other edge. Such a coexistence is made possible by the short-range nature of the exchange interactions on the magnetic edge. As a result, the quantum spin Hall state on the opposite edge of the nanoribbon does not feel the local breaking of time-reversal symmetry on the magnetic edge. While the edge with quantum spin Hall state exhibits the typical spin-helical texture associated with the state, the magnetic edge displays $± k$-asymmetry due to the interplay of Rashba and exchange effects. The latter is also a half-metal and can generate a fully spin-polarized current. We demonstrate that this coexistence of states is robust and that it is exhibited even when the nitrogen-decorated nanoribbon is placed on a substrate. In addition, with a proof-of-principle heterostructure, composed of an undecorated bismuth nanoribbon on hexagonal boron nitride, we show that this mixture of states can potentially exist even without passivation with nitrogen-atoms. In the heterostructure, an unequal relaxation along the two edges of the nanoribbon is found to be responsible for the coexistence of two states.