18 Décembre – Thesis defense - Jonathan Atteia

14 h Amphi - Building B6 (University of Bordeaux / Talence)

Topology and electronic transport in Dirac systems under irradiation.

This thesis presents a theoretical work done in the field of condensed matter physics, and in particular solid state physics. This field of physics aims at describing the behaviour of electrons in crystalline materials at very low temperature to observe effects characteristic of quantum physics at the mesoscopic scale.
This thesis lies at the interface between two types of materials : graphene and topological insulators. Graphene is a monoatomic layer of carbon atoms arranged in a honeycomb lattice that presents a wide range of striking properties in optics, mechanics and electronics. Topological insulators are materials that are insulators in the bulk and conduct electricity at the edges. This characteristic originates from a topological property of the electrons in the bulk. Topology is a branch of mathematics that aims to describe objects globally retaining only characteristics invariant under smooth deformations. The edge states of topological insulators are robust to certain king of perturbations such as disorder created by impurities in the bulk. The link between these two topics is two-fold. On one hand, the first models of band topological insulators were formulated for graphene, by Haldane in 1988 and Kane and Mele in 2005, opening the way to the discovery of 2D and 3D topological insulators in materials with strong spin-orbit coupling. On the other hand, it was predicted that graphene, even without spin-orbit coupling, turns to a topological insulator under irradiation by an electromagnetic wave. In this thesis, we follow two directions in parallel : describe the topological properties on one hand, and the electronic transport properties on the other hand.
First, we review the tight-binding model of graphene, and the effective model that describes low-energy electrons as massless Dirac fermions. We then introduce the Haldane model, a simple model defined on the honeycomb lattice that presents non-trivial bands characterised by a topological invariant, the Chern number. Due to this topological property, this model possesses a chiral edge state that propagates around the sample and a quantized Hall conductance. When graphene is irradiated by a laser with a frequency larger than the graphene bandwidth, it acquires a dynamical gap similar to the topological gap of the Haldane model. When the frequency is lowered, we show that topological transitions happens and that different edge states appear.
The main work of this thesis is the study of electronic transport in irradiated graphene in a regime of experimentally achievable parameters. A graphene sheet is connected to two electrodes with a potential difference that generates a current. We compute the differential conductance of the sample according to Landauer-Büttiker formalism extended to periodically driven systems. Using this simple formalism, we are able to obtain the conductance as a function of the geometry of the sample and of several parameters such as the chemical potential, the frequency and the intensity of the electromagnetic wave.
Another kind of topological insulator is the quantum spin Hall insulator. This type of phase possesses two edge states in which opposite spins propagate in opposite directions. The second work of this thesis concerns electronic transport through this irradiated edge state. We observe the apparition of a pumped current in the absence of a potential difference. We observe two regimes : a quantized adiabatic at low frequency, and a non-quantized linear response regime at high frequency. Compared to previous studies, we show an important effect originating from the presence of electrodes.

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