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

2009
##### Authors
Recher, Patrik
Nilsson, Johan
Trauzettel, Björn
Journal article
##### Published in
Physical Review / B ; 79 (2009). - 85407
##### Abstract
The magnetic field dependence of energy levels in gapped single- 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- 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 Mexican hat in the bulk bandstructure. We discuss the applicability of such QDs to control and measure the valley isospin and their potential use for hosting and controlling spin qubits.
530 Physics
##### Cite This
ISO 690RECHER, Patrik, Johan NILSSON, Guido BURKARD, Björn TRAUZETTEL, 2009. Bound states and magnetic field-induced valley splitting in gate-tunable graphene quantum dots. In: Physical Review / B. 79, 85407. Available under: doi: 10.1103/PhysRevB.79.085407
BibTex
@article{Recher2009Bound-4860,
year={2009},
doi={10.1103/PhysRevB.79.085407},
title={Bound states and magnetic field-induced valley splitting in gate-tunable graphene quantum dots},
volume={79},
journal={Physical Review / B},
author={Recher, Patrik and Nilsson, Johan and Burkard, Guido and Trauzettel, Björn},
note={Article Number: 85407}
}

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<dcterms:abstract xml:lang="eng">The magnetic field dependence of energy levels in gapped single- 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- 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  Mexican hat  in the bulk bandstructure. We discuss the applicability of such QDs to control and measure the valley isospin and their potential use for hosting and controlling spin qubits.</dcterms:abstract>
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