Size effects on atomic collapse in the dice lattice.

We study the role of size effects on atomic collapse of charged impurity in the flat band system. The tight-binding simulations are made for the dice lattice with circular quantum dot shapes. It is shown that the mixing of in-gap edge states with bound states in impurity potential leads to increasing the critical charge value.

Current distribution and group velocities for electronic states onα-T3lattice ribbons in a magnetic field.

We study the group velocities of electronic states and distributions of currents inα-T3lattice ribbons under a uniform perpendicular magnetic field. Using the effective low-energy model we analyze all possible simple configurations of lattice termination with zigzag and armchair boundaries. We show that the edge current depends on the type of zigzag termination, and can be zero or finite near the edge.

Electronic states of pseudospin-1 fermions in [Formula: see text] lattice ribbons in a magnetic field.

The electronic states on a finite width [Formula: see text] ribbon in a magnetic field are studied in the framework of low-energy effective theory. Both zigzag and armchair types of boundary conditions are analyzed. The analytical solutions are compared with the results of numerical tight-binding calculations.