Abstract
The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in bilayer graphene. So far, these approaches suffer from edge disorder or insufficiently controlled localization of electrons. Here we realize an alternative strategy in monolayer graphene, by combining a homogeneous magnetic field and electrostatic confinement. Using the tip of a scanning tunneling microscope, we induce a confining potential in the Landau gaps of bulk graphene without the need for physical edges. Gating the localized states toward the Fermi energy leads to regular charging sequences with more than 40 Coulomb peaks exhibiting typical addition energies of 7–20 meV. Orbital splittings of 4–10 meV and a valley splitting of about 3 meV for the first orbital state can be deduced. These experimental observations are quantitatively reproduced by tight binding calculations, which include the interactions of the graphene with the aligned hexagonal boron nitride substrate. The demonstrated confinement approach appears suitable to create quantum dots with well-defined wave function properties beyond the reach of traditional techniques.
Highlights
The charge carriers in graphene at low energies, described as massless Dirac quasiparticles,[1] are expected to feature long spin coherence times.[2−5] Exploiting this property requires precise manipulation of individual Dirac electrons
Orbital splittings of 4−10 meV and a valley splitting of about 3 meV for the first orbital state can be deduced. These experimental observations are quantitatively reproduced by tight binding calculations, which include the interactions of the graphene with the aligned hexagonal boron nitride substrate
Landau quantization helps to overcome Klein tunneling by opening band gaps.[21−23] An elegant method to exploit this by combining a magnetic field and an electrostatic potential has been proposed theoretically.[29−31] indications of such
Summary
Information). (b) Energy diagram in real space: Fermi energy EF, black dashed line; local band bending Egr, magenta line; states belonging to electron (hole) LLs, blue (red); bulk LLs, 1, 0, −1. We use the STM tip as source of the electrostatic potential and as gate for the QD states and to sequence the energy level spectrum of the QD as the states cross EF, that is, as the charge on the QD changes by ±e This leads to a step in the tunneling current I(Vtip) and a corresponding charging peak in the differential conductance dI/dVtip. Because the measurement captures the QD level spacings as charging peak distances ΔV, they need to be converted to Eadd via the tip lever arm αtip The latter relates a change of Vtip to its induced shift of the QD state energies. We distinguish two regimes in the sequence of spin degenerate states crossing (Figure 4e) exhibits Δkτ ≲
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