Field Dependence Of Energy Levels Research Articles

Magnetic field dependence of energy levels in biased bilayer graphene quantum dots

Using the tight-binding approach, we study the influence of a perpendicular magnetic field on the energy levels of hexagonal, triangular, and circular bilayer graphene (BLG) quantum dots (QDs) with zigzag and armchair edges. We obtain the energy levels for AB (Bernal)-stacked BLG QDs in both the absence and the presence of a perpendicular electric field (i.e., biased BLG QDs). We find different regions in the spectrum of biased QDs with respect to the crossing point between the lowest-electron and -hole Landau levels of a biased BLG sheet. Those different regions correspond to electron states that are localized at the center, edge, or corner of the BLG QD. Quantum Hall corner states are found to be absent in circular BLG QDs. The spatial symmetry of the carrier density distribution is related to the symmetry of the confinement potential, the position of zigzag edges, and the presence or absence of interlayer inversion symmetry.

Bound states and magnetic field induced valley splitting in gate-tunable graphene quantum dots

The magnetic field dependence of energy levels in gapped single-layer and bilayer graphene quantum dots (QDs) defined by electrostatic gates is studied analytically in terms of the Dirac equation. Due to the absence of sharp edges in these types of QDs, the valley degree of freedom is a good quantum number. We show that its degeneracy is efficiently and controllably broken by a magnetic field applied perpendicular to the graphene plane. This opens up a feasible route to create well-defined and well-controlled spin and valley qubits in graphene QDs. We also point out the similarities and differences in the spectrum between single-layer and bilayer graphene quantum dots. Striking in the case of bilayer graphene is the anomalous bulk Landau level (LL) that crosses the gap, which results in crossings of QD states with this bulk LL at large magnetic fields in stark contrast to the single-layer case where this LL is absent. The tunability of the gap in the bilayer case allows us to observe different regimes of level spacings directly related to the formation of a pronounced ``sombrero'' in the bulk band structure. We discuss the applicability of such QDs to control and measure the valley isospin and their potential use for hosting and controlling spin qubits.

Artificial Atoms: New Boxes for Electrons

Just as atoms are natural boxes that contain electrons, quantum dots--small structures in which electrons can be trapped--can be studied as artificial atoms. In his Perspective, McEuen discusses results reported in the same issue on new studies of artificial atoms. Kouwenhoven et al. studied the magnetic field dependence of energy levels in a quantum dot. Stewart et al. report studies of irregularly shaped dots containing many electrons, analogous to transuranic elements. Finally, Schedelbeck et al. report experiments in which two quantum dots were coupled together to form artificial molecules.

Quantum interference effects on the electron conduction through negative-potential regions

The quantum interference effects on transport properties of quantum wires including some large obstacles with a negative potential are studied in the presence of a magnetic field. It is found that the magnetoconductance has a quasiperiodic dip structure in the high magnetic field regime. We show that the dips are attributed to an Aharonov-Bohm-type effect and that the period reflects the ring area lying between the inner and outer orbits for the negative-potential region. The effects of the potential edge structure on the conductance are also discussed. The current density around the obstacles and the magnetic field dependence of energy levels are calculated to investigate whole features of the conductance.