Measuring the Berry phase of graphene from wavefront dislocations in Friedel oscillations

TL;DR

This paper demonstrates a novel method to measure the Berry phase in graphene through wavefront dislocations in Friedel oscillations, eliminating the need for external magnetic fields and providing insights into the topological properties of electronic wavefunctions.

Contribution

It introduces a new real-space technique to determine graphene's Berry phase by analyzing topological defects in Friedel oscillations caused by chemisorbed hydrogen atoms.

Findings

Edge dislocations in Friedel oscillations reveal Berry phase information.

The method allows measurement of topological properties without external magnetic fields.

Electronic dispersion can be simultaneously extracted from Friedel oscillations.

Abstract

Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore of crucial importance for technological applications. While the spectral distribution in energy bands is routinely measured by various techniques, it is more difficult to access the topological properties of band structures such as the Berry phase {\gamma}. It is usually thought that measuring the Berry phase requires applying external electromagnetic forces because these allow realizing the adiabatic transport on closed trajectories along which quantum mechanical wave-functions pick up the Berry phase. In graphene, the anomalous quantum Hall effect results from the Berry phase {\gamma} = {\pi} picked up by massless relativistic electrons along cyclotron orbits and proves the existence of Dirac cones. Contradicting this belief, we demonstrate that the Berry phase of graphene can be measured in absence of any external magnetic field. We observe edge dislocations in the Friedel oscillations formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry in describing these topological defects as phase singularities of complex fields, we show that the number of additional wave-fronts in the dislocation is a real space measurement of the pseudo spin winding, i.e. graphene's Berry phase. Since the electronic dispersion can also be retrieved from Friedel oscillations, our study establishes the electronic density as a powerful observable to determine both the dispersion relation and topological properties of wavefunctions. This could have profound consequences for the study of the band-structure topology of relativistic and gapped phases in solids.