Analysis of electronic properties of hexagonal and triangular Bismuth quantum dot with different edges in the presence of magnetic field

We investigate energy spectra of Bi honeycomb quantum dots (BiQDs) considering buckled hexagonal and triangular structures with zigzag and armchair edges. We apply the four-orbital tight-binding approach. By using of the probability density of states, we distinguish some edge states in the regime of the band gap of Bi monolayer. We see that the number of edge states of zigzag (armchair) triangular BiQDs is more than the number of edge states of zigzag (armchair) hexagonal BiQDs. Also, we investigated energy spectra of hexagonal and triangular BiQDs with zigzag and armchair edges in the presence of the perpendicular magnetic fields. In the low and strong magnetic fields, there are relativistic Landau levels in the electronic spectra of BiQDs (in the hexagonal and triangular boundary conditions). Moreover, we show that edge atoms have more important roles in the formation of the line connectors between i and | i + 1 | Landau levels of hexagonal BiQDs than ones that are in the triangular BiQDs. In the middle numbers of the magnetic fields, more states collapse into Landau levels in which bulk atoms have a significant role to constitute them in both hexagonal and triangular BiQDs. Furthermore as the same as Bi nanoribbon spectrum, there are some helical edge modes in the band gap regions of Bi monolayer in which edge atoms are responsible to form them. These helical edge modes have topological properties.