Emergence of Dirac and quantum spin Hall states in fluorinated monolayer As and AsSb

Using first-principles calculations, we investigate the electronic and vibrational properties of monolayer As and AsSb. While the pristine monolayers are semiconductors (direct band gap at the $\mathrm{\Gamma }$ point), fluorination results in Dirac cones at the K points. Fluorinated monolayer As shows a band gap of 0.16 eV due to spin-orbit coupling, and fluorinated monolayer AsSb a larger band gap of 0.37 eV due to inversion symmetry breaking. Spin-orbit coupling induces spin splitting similar to monolayer ${\mathrm{MoS}}_2$. Phonon calculations confirm that both materials are dynamically stable. Calculations of the edge states of nanoribbons by the tight-binding method demonstrate that fluorinated monolayer As is topologically nontrivial in contrast to fluorinated monolayer AsSb.

Figure 1

(a) Atomic structure of pristine ML As. (b) Side view and (c) top view of fluorinated ML As. (d) Brillouin zone of the hexagonal lattice.

Figure 2

Band structure and density of states of (a,b) pristine ML As, (c,d) pristine ML AsSb, (e,f) fluorinated ML As, and (g,h) fluorinated ML AsSb.

Figure 3

Effect of strain: (a) Size of the band gap in fluorinated ML As and AsSb, and (b) spin splitting at the K valleys in fluorinated ML AsSb.

Figure 4

Phonon spectrum of (a) pristine ML As, (b) pristine ML AsSb, (c) fluorinated ML As, and (d) fluorinated ML AsSb.

Figure 5

Charge density difference of (a) pristine ML As and (b) fluorinated ML As with respect to isolated As atoms (isovalue: 0.05 electrons/Å${}^3)$.

Figure 6

Tight-binding band structure of fluorinated ML (a) As and (b) AsSb zigzag nanoribbons. The size of the circles quantifies the projection on the edge atoms and red/blue color corresponds to spin-up/down.