Pawel Potasz

Magnetism and Correlations in Fractionally Filled Degenerate Shells of Graphene Quantum Dots

We show that the ground state and magnetization of the macroscopically degenerate shell of electronic states in triangular gated graphene quantum dots depends on the filling fraction of the shell. The effect of degeneracy, finite size, and electron-electron interactions are treated nonperturbatively using a combination of density functional theory, tight-binding, Hartree-Fock and configuration interaction methods. We show that electronic correlations play a crucial role in determining the nature of the ground state as a function of filling fraction of the degenerate shell at the Fermi level. We find that the half-filled charge neutral shell leads to full spin polarization but this magnetic moment can be completely destroyed by adding a single electron.

Effect of edge reconstruction and passivation on zero-energy states and magnetism in triangular graphene quantum dots with zigzag edges

We present the results of ab-initio density functional theory based calculations of the stability and reconstruction of zigzag edges in triangular graphene quantum dots. We show that, while the reconstructed pentagon-heptagon zigzag edge structure is more stable in the absence of hydrogen, ideal zigzag edges are energetically favored by hydrogen passivation. Zero-energy band exists in both structures when passivated by hydrogen, however in case of pentagon-heptagon zigzag, this band is found to have stronger dispersion, leading to the loss of net magnetization.

Electric-field controlled spin in bilayer triangular graphene quantum dots

In this work, we investigate electronic and magnetic properties of bilayer triangular graphene quantum dots with zigzag edges under external vertical electric-field. We show that the magnetic moment of bilayer triangular graphene quantum dots can be controlled by the vertical electric-field. Without the electric-field, the magnetic moments of the two layers are shown to be coupled ferromagnetically. Using configuration interaction and mean-field calculations based on tight-binding model, we demonstrate that the ferromagnetism can be either turned off or reduced to a single electron/hole spin. The single electron spin is hence isolated in a charge neutral structure by the application of an electric-field, independent of the size of the quantum dot and without decoherence due to contacts. The electric-field control of the ferromagnetism [33] and isolation of a single spin opens new applications in spintronics and quantum information processing[34–38]. Figure 1a shows two possibilities for building a bilayer triangular graphene quantum dot (BQD) using two single layer triangular quantum dots (TGQD) of comparable sizes, with zigzag edges. We consider AB Bernal stacking, where the A sublattice of the top layer (A2, shown in blue color) is on top of the B sublattice of the bottom layer (B1, shown in red). On the left hand side, the two TGQDs are of the same size. In this configuration,

Graphene Quantum Dots

Single particle properties of graphene quantum dots.- Electron-electron interaction in gated graphene nanostructures.- Magnetic properties of gated graphene nanostructures.- Optical properties of graphene nanostructures.

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

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.

Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles.

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. By modeling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island, and crystallographic direction of the edges, reflecting its topological protection.

Fractional Chern insulator phase at the transition between checkerboard and Lieb lattices

The stability of

Single-Particle Properties of Graphene Quantum Dots

\nu=1/3

Spin–orbit coupling and optical detection of spin polarisation in triangular graphene quantum dots

Fractional Chern Insulator (FCI) phase is analysed on the example of checkerboard lattice undergoing a transition into Lieb lattice. The transition is performed by the addition of a second sublattice, whose coupling to the checkerboard sites is controlled by sublattice staggered potential. We investigate the influence of these sites on the many body energy gap between three lowest energy states and the fourth state. We consider cases with different complex phases acquired in hopping and a model with a flattened topologically nontrivial band. We find that an interaction with the additional sites either open the single-particle gap or enlarge the existing one, which translates into similar effect on the many-particle gap. Evidences of FCI phase for a region in a parameter space with larger energy gap are shown by looking at momenta of the three-fold degenerate ground state, spectral flow, and quasihole excitation spectrum.

Electron–Electron Interactions in Graphene Quantum Dots

This chapter describes the size, shape and edge dependence of the electronic properties of graphene quantum dots obtained using the empirical tight-binding model. The effective mass extension of the TB model is discussed, including the effect of the magnetic field. The one-band TB model is extended to the \(sp^2\) TB model and spin-orbit coupling is introduced, followed by the Kane-Mele Hamiltonian and the spin Hall effect in nanoribbons. Triangular quantum dots and rings with zigzag edges as examples of quantum dots with broken sublattice symmetry and a shell of degenerate states at the Fermi level are described. Graphene ribbons and twisted graphene Mobius ribbons as examples of topological insulators where topology is introduced through geometry are discussed.