Abstract
The Berry phase of wave functions is a key quantity to understand various low-energy properties of matter, among which electric polarisation, orbital magnetism, as well as topological and ultra-relativistic phenomena. Standard approaches to probe the Berry phase in solids rely on the electron dynamics in response to electromagnetic forces. In graphene, probing the Berry phase π of the massless relativistic electrons requires an external magnetic field. Here, we show that the Berry phase also affects the static response of the electrons to a single atomic scatterer, through wavefront dislocations in the surrounding standing-wave interference. This provides a new experimental method to measure the graphene Berry phase in the absence of any magnetic field and demonstrates that local disorder can be exploited as probe of topological quantum matter in scanning tunnelling microscopy experiments.
Highlights
In quantum mechanics, the phase of the wave function is arbitrary
Experimental measurements in graphene relied on magnetic cyclotron orbits enclosing this phase singularity in momentum space
We have demonstrated instead that one can materialize the phase singularity directly in real space with an atomic scatterer
Summary
The phase of the wave function is (locally) arbitrary. This U(1) gauge invariance allows observable manifestations of the wave-function phase through cyclic evolutions. As a consequence the waves functions pick a π Berry phase when travelling around a Dirac point This topological feature of graphene’s band structure has been demonstrated beautifully for electrons confined in whispering gallery modes in this material [4]. In a semi-classical picture, the confined electrons can be viewed as bouncing from circular p–n junctions created by the electrostatic potential of a Scanning Tunnelling Microscope (STM) tip or a charge embedded in the substrate They perform loops that do not enclose the Dirac points in momentum space. The inclusion provokes abrupt changes in the energy spectrum of the resonator Such spectral features result from the π-quantised Berry phase picked up by the wave functions orbiting around a Dirac point. It relies on disorder-induced standing-wave interference resolved in scanning tunnelling microscopy (STM)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
