Zero-energy states of graphene triangular quantum dots in a magnetic field

TL;DR

This paper develops a tight-binding model to study zero-energy states in triangular graphene quantum dots under magnetic fields, revealing how magnetic fields influence degeneracy and energy gaps.

Contribution

It provides a semi-analytical description of zero-energy states in magnetic fields, showing the magnetic field's role in closing energy gaps and modulating degeneracy.

Findings

Zero-energy states form a degenerate shell similar to the 0th Landau level.

Magnetic field closes the energy gap in graphene quantum dots.

Degeneracy of the shell is maintained despite magnetic field variations.

Abstract

We present a tight-binding theory of triangular graphene quantum dots (TGQD) with zigzag edge and broken sublattice symmetry in external magnetic field. The lateral size quantization opens an energy gap and broken sublattice symmetry results in a shell of degenerate states at the Fermi level. We derive a semi-analytical form for zero-energy states in a magnetic field and show that the shell remains degenerate in a magnetic field, in analogy to the 0th Landau level of bulk graphene. The magnetic field closes the energy gap and leads to the crossing of valence and conduction states with the zero-energy states, modulating the degeneracy of the shell. The closing of the gap with increasing magnetic field is present in all graphene quantum dot structures investigated irrespective of shape and edge termination.