Quantized States, Berry Phases, and Wedding Cakes in Graphene Quantum Dots

The wave nature of quantum mechanics is revealed when the particle’s de Broglie wavelength becomes comparable to the system length scale. Quantum dots (QD) offer an ideal platform for studying the interplay between quantum confinement, caused by spatial constraints or by large magnetic fields via cyclotron motion, and interaction effects. Recently, the ability to apply local nanometer scale gate potentials in graphene heterostructures has enabled the creation of QDs for Dirac particles. Graphene QDs are formed inside circular p-n junction [1,2], where one has detailed control of electron orbits by means of local gate potentials and magnetic fields. In this talk, I describe scanning tunneling spectroscopy measurements of the energy spectrum of graphene QDs as a function of energy, spatial position, and magnetic field. In zero field, the Dirac quasiparticles are confined by Klein scattering at large incident angle at the p-n junction boundary. The confined carriers give rise to an intricate eigenstate spectrum, characterized by radial and angular momentum quantum numbers, creating a multi-electron artificial atom [1]. Applying a weak magnetic field results in a sudden and giant increase in energy for certain angular momentum states of the QD, creating a discontinuity in the energy spectrum as a function of magnetic field [2]. This behavior results from a π-Berry phase, which I show can be turned on and off with magnetic field. With increased applied magnetic field, the QD states are observed to condense into Landau levels, providing a direct visualization of the transition from spatial to magnetic confinement, along with “wedding cake” profiles arising from interaction effects [3].

[1]. Y. Zhao, J. Wyrick, F. D. Natterer, J. F. Rodriquez-Nieva et al., Science 348, 672 (2015).
[2]. F. Ghahari, D. Walkup, C. Gutiérrez, J. F. Rodriguez-Nieva et al., Science 356, 845 (2017).
[3]. C. Gutiérrez, D. Walkup, F. Ghahari, Cyprian Lewandowski et al., (submitted).