What can we learn from Friedel oscillations in 2d semimetals?
par Clément Dutreix, Laboratoire de Physique, ENS de Lyon
Mardi 25 Avril, 14h, Salle des séminaires (215), 2ème étage, Bâtiment A4N
During this seminar, we will revisit the natural problem of elastic scattering through a localised impurity in (quastwo-dimensional (semmetals. Such an impurity is responsible for quantum interferences known as Friedel oscillations, i.e., long-range oscillations in the electronic density whose algebraic decay with the distance to the impurity was shown to be universal in every dimension .
However, the observation of Friedel oscillations in graphene via scanning tunnelling microscopy (STM) actually taught us that their algebraic decay can be different from the one in a two-dimensional electron gas and is, in this sense, non-universal . This non-universality has been related to the impossibility for the graphene electrons to be backscattered.
On the one hand, we shall see how such non-universal behaviours of Friedel oscillations may be used in STM experiments to characterise a two-dimensional topological Lifshitz transition, namely the Dirac cone merging transition .
On the other hand, we will discuss Friedel oscillations in a quasi-two-dimensional semimetal, that is, rhombohedral N-layer graphene, one of the two most stable staking of graphene layers experimentally isolated. We will show that, even when Friedel oscillations exhibits conventional algebraic decay, there exists additional observable oscillations from which we can reconstruct the whole low-energy Bloch band structure of the material. This suggests that it would additionally be possible to image the 𝜋-quantised Berry phases that topologically protect the existence of nodal points in the semimetallic spectrum from STM experiments .
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 C. Dutreix, M. I. Katsnelson, Phys. Rev. B 93, 035413 (2016)