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

TL;DR

This paper analytically investigates how magnetic fields influence energy levels and valley degeneracy in electrostatically defined graphene quantum dots, highlighting mechanisms to control valley and spin qubits in both single- and bilayer graphene.

Contribution

It provides an analytical study of magnetic field effects on valley splitting in graphene quantum dots, revealing controllable valley degeneracy breaking and differences between single- and bilayer graphene.

Findings

Magnetic field breaks valley degeneracy in graphene QDs.

Bilayer graphene exhibits an anomalous bulk Landau level crossing the gap.

The gap tunability in bilayer graphene enables different level spacing regimes.

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.