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

Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore crucial for technological applications. Although the spectral distribution in energy bands is routinely measured by various techniques1, it is more difficult to access the topological properties of band structures such as the quantized Berry phase, γ, which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle2. In graphene, the quantized Berry phase γ = π accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories3. Contradicting this belief, here we demonstrate that the Berry phase of graphene can be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge density ρ (Friedel oscillations) that are formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry6 in describing these topological defects as phase singularities of complex fields, we show that the number of additional wavefronts in the dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be determined from Friedel oscillations7, our study establishes the charge density as a powerful observable with which 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.

Valley polarization assisted spin polarization in two dimensions.

Valleytronics is rapidly emerging as an exciting area of basic and applied research. In two-dimensional systems, valley polarization can dramatically modify physical properties through electron-electron interactions as demonstrated by such phenomena as the fractional quantum Hall effect and the metal-insulator transition. Here, we address the electrons' spin alignment in a magnetic field in silicon-on-insulator quantum wells under valley polarization. In stark contrast to expectations from a non-interacting model, we show experimentally that less magnetic field can be required to fully spin polarize a valley-polarized system than a valley-degenerate one. Furthermore, we show that these observations are quantitatively described by parameter-free ab initio quantum Monte Carlo simulations. We interpret the results as a manifestation of the greater stability of the spin- and valley-degenerate system against ferromagnetic instability and Wigner crystalization, which in turn suggests the existence of a new strongly correlated electron liquid at low electron densities.

Metallic behaviour in SOI quantum wells with strong intervalley scattering.

The fundamental properties of valleys are recently attracting growing attention due to electrons in new and topical materials possessing this degree-of-freedom and recent proposals for valleytronics devices. In silicon MOSFETs, the interest has a longer history since the valley degree of freedom had been identified as a key parameter in the observation of the controversial "metallic behaviour" in two dimensions. However, while it has been recently demonstrated that lifting valley degeneracy can destroy the metallic behaviour, little is known about the role of intervalley scattering. Here, we show that the metallic behaviour can be observed in the presence of strong intervalley scattering in silicon on insulator (SOI) quantum wells. Analysis of the conductivity in terms of quantum corrections reveals that interactions are much stronger in SOI than in conventional MOSFETs, leading to the metallic behaviour despite the strong intervalley scattering.

Impact of valley polarization on the resistivity in two dimensions.

We examine the temperature dependence of resistivity in a two-dimensional electron system formed in a silicon-on-insulator quantum well. The device allows us to tune the valley splitting continuously in addition to the electron density. Our data provide a global picture of how the resistivity and its temperature dependence change with valley polarization. At the boundary between valley-polarized and partially polarized regions, we demonstrate that there is an insulating contribution from spin-degenerate electrons occupying the upper valley-subband edge.

Boundary-mediated electron-electron interactions in quantum point contacts.

An unusual increase of the conductance with temperature is observed in clean quantum point contacts for conductances larger than 2(e2/h). At the same time, a positive magnetoresistance arises at high temperatures. A model accounting for electron-electron interactions mediated by boundaries (scattering on Friedel oscillations) qualitatively describes the observation. It is supported by a numerical simulation at zero magnetic field.