Current distribution and group velocities for electronic states on $\alpha-\mathcal{T}_3$ lattice ribbons in a magnetic field

TL;DR

This paper investigates the electronic group velocities and edge current distributions in $ ext{T}_3$ lattice ribbons under magnetic fields, revealing how edge termination and lattice parameters influence current flow and edge state formation.

Contribution

It provides a detailed analysis of how lattice termination and the parameter $ ext{alpha}$ affect edge currents and states in $ ext{T}_3$ lattice ribbons under magnetic fields.

Findings

Edge current depends on zigzag termination type.

Nonzero edge current indicates propagating edge states.

Distinct current distribution for $ ext{alpha}=1$ compared to other values.

Abstract

We study the group velocities of electronic states and distributions of currents in $\alpha-\mathcal{T}_3$ lattice 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. Also similar dependence is observed in the case of armchair termination and is related to the size of the ribbon. The nonzero current flowing along the edge can be used a signature of formation of propagating edge states. Also we show the qualitative difference in the distribution of the edge current between the case of $\alpha=1$ (dice model) and other values of model parameter $\alpha\neq 1$ for armchair-terminated ribbons.