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Register a new userGraphene quantum dots in perpendicular magnetic fields
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Added by
Johannes Guettinger
Publication date
2009
fields
Physics
and research's language is
English
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We report transport experiments on graphene quantum dots. We focus on excited state spectra in the near vicinity of the charge neutrality point and signatures of the electron-hole crossover as a function of a perpendicular magnetic field. Coulomb blockade resonances of a 50 nm wide and 80 nm long dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 40 states as a function of the back gate voltage can be interpreted in terms of the unique evolution of the diamagnetic spectrum of a graphene dot including the formation of the E = 0 Landau level, situated in the center of the transport gap, and marking the electron-hole crossover.
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Using the tight-binding approximation we calculated the magnetic susceptibility of graphene quantum dots (GQD) of different geometrical shapes and sizes, smaller than the magnetic length, when the magnetic properties are governed by the electron edge states. Two types of edge states can be discerned: the zero-energy states (ZES) located exactly at the zero-energy Dirac point, and the dispersed edge states (DES) with the energy close, but not exactly equal to zero. DES are responsible for the temperature independent diamagnetic response, while ZES provide the temperature dependent spin Curie paramagnetism. The hexagonal, circular and randomly shaped GQDs contain mainly DES and, as a result, they are diamagnetic. The edge states of the triangular GQDs are ZES and these dots reveal the interplay between the spin paramagnetism, dominating for small dots and at low temperatures, and bulk orbital diamagnetism, dominating for large dots and at high temperatures.
We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched single-layer graphene flake with two narrow constrictions separating a 140 nm diameter island from source and drain graphene contacts. Lateral graphene gates are used to electrostatically tune the device. Measurements of Coulomb resonances, including constriction resonances and Coulomb diamonds prove the functionality of the graphene quantum dot with a charging energy of around 4.5 meV. We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level. Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.
In a recent comment (arXiv:1607.06081), Falaye et al. claim that there are certain flaws in our publication (Phys. Rev. B, 78, 195427 (2008)). We point out that our results, in particular the analytic derivation of the energy spectrum of a circular graphene quantum dot exposed to a perpendicular magnetic field, are correct and equivalent to the result of Falaye et al. A misleading notation error is corrected.
We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called $Lambda$ levels).
We have studied the transport properties of a large graphene double quantum dot under the influence of background disorder potential and magnetic field. At low temperatures, the evolution of the charge-stability diagram as a function of B-field is investigated up to 10 Tesla. Our results indicate that the charging energy of quantum dot is reduced, and hence the size of the dot increases, at high magnetic field. We provide an explanation of our results using a tight-binding model, which describes the charge redistribution in a disordered graphene quantum dot via the formation of Landau levels and edge states. Our model suggests that the tunnel barriers separating different electron/hole puddles in a dot become transparent at high B-fields, resulting in the charge delocalization and reduced charging energy observed experimentally.
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