Whispering Galleries and Berry Phase Switches in Circular Graphene Resonators
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 acoustic whispering galleries [1,2] albeit on a much smaller length scale. Klein scattering of Dirac carriers plays a central role in determining the coherent propagation of electron waves in these resonators. In this talk, I examine circular electron resonators in graphene produced with p-n junction rings in two ways: 1) a traveling resonator produced by the tip potential , and 2) a fixed resonator produced by impurity charges in the underlying boron nitride insulator . The spectrum of WGM modes in these resonators are mapped as a function of energy, position, and magnetic field with the scanning tunneling microscope. Here I show that the Berry phase associated with the topological singular Dirac point in graphene gives rise to a sudden and giant increase in energy of the WGM states in the circular graphene p-n junction resonators when very small magnetic fields are applied. This Berry phase can be switched on and off with field changes on the order of 5 mT, which may prove useful in future optoelectronic graphene device applications. These results agree well with recent theory on Klein scattering in graphene electron resonators .
1. Y. Zhao, J. Wyrick, F. D. Natterer, J. F. Rodriquez-Nieva et al., Science 348, 672 (2015).
2. Juwon Lee et al., Nature Physics advance online publication, DOI: 10.1038/NPHYS3805, (2016).
3. J.F. Rodriguez-Nieva and L. S. Levitov, arXiv:1508.06609