Title: Whispering galleries and Berry Phase Switches in Circular Graphene Resonators

Abstract:

Ballistic propagation and the light-like dispersion of graphene charge carriers make graphene an attractive platform for optics-inspired graphene electronics where gate tunable potentials can control electron refraction and transmission. In analogy to optical wave propagation in lenses,mirrors and metamaterials, gate potentials can be used to create Fabry-Pérot interferometers and a negative index of refraction for Veselago lensing. In circular geometries, gate potentials caninduce whispering gallery modes (WGM), similar to optical and acousticwhispering galleries [1,2] albeit on a much smaller length scale. Klein scattering of Dirac carriers plays a centralrole in determining the coherent propagation of electron waves in theseresonators. In this talk, I examinecircular electron resonators in graphene produced with p-n junction rings in two ways: 1) a traveling resonator producedby the tip potential [1], and 2) a fixed resonator produced by impurity chargesin the underlying boron nitride insulator [2]. The spectrum of WGM modes in these resonators are mapped as a functionof energy, position, and magnetic field with the scanning tunneling microscope. Here I show that the Berry phase associatedwith the topological singular Dirac point in graphene gives rise to a sudden and giant increase in energy of the WGM states in the circular graphenep-n junction resonators when verysmall magnetic fields are applied. ThisBerry phase can be switched on and off with field changes on the order of 5 mT,which may prove useful in future optoelectronic graphene deviceapplications. These results agree wellwith recent theory on Klein scattering in graphene electron resonators [3].
1. Y. Zhao, J. Wyrick, F. D. Natterer, J. F.Rodriquez-Nieva et al., Science 348, 672 (2015).
2. Juwon Lee etal., Nature Physics advanceonline publication, DOI: 10.1038/NPHYS3805, (2016).
3. J.F. Rodriguez-Nieva and L. S. Levitov, arXiv:1508.06609