Resonant, non-resonant, and anomalous states of Dirac electrons in a parabolic well in the presence of magnetic fields

TL;DR

This paper explores the unique spectral properties of Dirac electrons in a parabolic quantum dot under magnetic fields, revealing resonant, non-resonant, and anomalous states with potential experimental implications.

Contribution

It introduces a detailed analysis of how Dirac electrons exhibit resonant and anomalous states in a parabolic well under magnetic fields, highlighting properties unique to massless Dirac fermions.

Findings

Resonant quasi-bound states exist for both positive and negative energies.

Negative energy resonant states are unique to massless Dirac fermions.

States transform into anomalous states with characteristic probability density peaks.

Abstract

We report on several new basic properties of a parabolic dot in the presence of a magnetic field. The ratio between the potential strength and the Landau level (LL) energy spacing serves as the coupling constant of this problem. In the weak coupling limit the energy spectrum in each Hilbert subspace of an angular momentum consists of discrete LLs of graphene. In the intermediate coupling regime non-resonant states form a closely spaced energy spectrum. We find, counter-intuitively, that resonant quasi-boundstates of both positive and negative energies exist in the spectrum. The presence of resonant quasi-boundstates of negative energies are a unique property of massless Dirac fermions. As the strong coupling limit is approached resonant and non-resonant states transform into anomalous states, whose probability densities develop a narrow peak inside the well and another broad peak under the potential barrier. These properties may investigated experimentally by measuring optical transition energies that can be described by a scaling function of the coupling constant.