arXiv subjects

R. Van Pottelberge

Publications and source records attributed to R. Van Pottelberge.

4 recordsLinked to original sources

arXiv2021

Coulomb impurity on a Dice lattice: atomic collapse and bound states

The modification of the quantum states in a Dice lattice due to a Coulomb impurity are investigated. The energy band structure of a pristine Dice lattice consists of a Dirac cone and a flat band at the Dirac point. We use the tight binding formalism and find that the flat band states transform into a set of discrete bound states whose electron density is localized on a ring around the impurity mainly on two of the three sublattices. The energy is proportional to the strength of the Coulomb impurity. Beyond a critical strength of the Coulomb potential atomic collapse states appear that have some similarity with those found in graphene with the difference that the flat band states contribute with an additional ring-like electron density that is spatially decoupled from the atomic collapse part. At large value of the strength of the Coulomb impurity the flat band bound states anti-cross with the atomic collapse states.

cond-mat.mes-hall↗

arXiv2019

Tunable circular dipolelike system in graphene: Mixed electron-hole states

Coupled electron-hole states are realized in a system consisting of a combination of an electrostatic potential barrier and ring-shaped potential well, which resembles a circular dipole. A perpendicular magnetic field induces confined states inside the Landau gaps which are mainly located at the barrier or ring. Hybridizations between the barrier and ring states are seen as anticrossings in the energy spectrum. As a consequence, the energy levels show an oscillating dependence on the electrostatic potential strength in combination with an oscillating migration of the wave functions between the barrier and ring. At the anticrossing points the quantum state consists of a mixture of electron and hole. The present system mimics closely the behavior of a relativistic dipole on gapped graphene.

cond-mat.mes-hall↗

arXiv2018

Electrical dipole on gapped graphene: Bound states and atomic collapse

We investigate the energy spectrum, wave functions, and local density of states of an electrical dipole placed on a sheet of gapped graphene as function of the charge strength Zα for different sizes of the dipole and for different regularization parameters. The dipole is modeled as consisting of a positive and negative charge. Bound states are found within the gap region with some energy levels that anticross and others that cross as function of the impurity strength Zα. The anticrossings are more pronounced and move to higher charges Zα when the length of the dipole decreases. These energy levels turn into atomic collapse states when they enter the positive (or negative) energy continuum. A smooth transition from the single-impurity behavior to the dipole one is observed: The states diving towards the continuum in the single-impurity case are gradually replaced by a series of anticrossings that represent a continuation of the diving states in the single-impurity case. By studying the local density of states at the edge of the dipole we show how the series of anticrossings persist in the positive and negative continuum.

cond-mat.mes-hall↗

arXiv2018

Comment on "Impurity spectra of graphene under electric and magnetic fields"

In a recent publication [Phys. Rev. B $\textbf{89}$, 155403 (2014)], the authors investigated the spectrum of a Coulomb impurity in graphene in the presence of magnetic and electric fields using the coupled series expansion approach. In the first part of their publication they investigated how Coulomb impurity states collapse in the presence of a perpendicular magnetic field. We argue that the obtained spectrum does not give information about the atomic collapse and that their interpretation of the spectrum regarding atomic collapse is not correct. We also argue that the obtained results are only valid up to the dimensionless charge $\mid α\mid=0.5$ and in order to obtain correct results for $α>0.5$ a proper regularisation of the Coulomb interaction is required. Here we present the correct numerical results for the spectrum for arbitrary values of $α$.

cond-mat.mes-hall↗