Electronic Properties of $\alpha-\mathcal{T}_3$ Quantum Dots in Magnetic Fields

TL;DR

This paper investigates the electronic properties and charge transport in $oldsymbol{ extalpha- ext{T}_3}$ quantum dots under magnetic fields, using analytical and numerical methods to explore effects of boundaries, disorder, and the interpolating lattice structure.

Contribution

It provides a combined analytical and numerical analysis of $oldsymbol{ extalpha- ext{T}_3}$ quantum dots in magnetic fields, including boundary conditions, transport, and disorder effects, which is novel in this context.

Findings

Eigenvalue solutions for quantum dots with boundary conditions.

Analysis of conductance and local density of states.

Impact of disorder on electronic properties.

Abstract

We address the electronic properties of quantum dots in the two-dimensional $\alpha-\mathcal{T}_3$ lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue problem for an isolated quantum dot in the low-energy, long-wavelength approximation where the system is described by an effective Dirac-like Hamiltonian that interpolates between the graphene (pseudospin 1/2) and Dice (pseudospin 1) limits. Results are compared to a full numerical (finite-mass) tight-binding lattice calculation. In a second step we analyse charge transport through a contacted $\alpha-\mathcal{T}_3$ quantum dot in a magnetic field by calculating the local density of states and the conductance within the kernel polynomial and Landauer-B\"uttiker approaches. Thereby the influence of a disordered environment is discussed as well.