Continuous limit of a tight-binding model on a hexagonal disk in a magnetic field: size dependence on energy level

Abstract

This study considers the energy level of a charged particle on a large hexagonal lattice in a magnetic field. The discretized Schrödinger equation on a hexagonal lattice, which can be expressed as a special case of a tight-binding model is derived, and its energy level is numerically calculated. The size dependence of the energy level near zero for large radii is considered by analyzing the asymptotic behavior of the zeros of the Laguerre function, which is the radical wavefunction of the continuous Schrödinger equation. Additionally, the splitting of the Landau level due to the finite size of a hexagonal disk is discussed.

Orbital magnetic susceptibility of zigzag carbon nanobelts: a tight-binding study

“…In the continuous limit of a → 0, the Hamiltonian (43) can be approximately regarded as (p + e ⃗ A) 2 /2m, where p and m are the momentum operator and effective mass related to γ, respectively [27,28]. Combining equation ( 5) with equation ( 4) leads to…”