Magnétisme orbital et aspects géométriques de la théorie des bandes

Abstract : My research project has been to studythe orbital magnetic response of a electron gas inthe periodic potential of a crystal. Its purpose isto generalize Landau’s diamagnetism and Peierls’formula for one-band crystals. The main goal wasto generalize Peierls’ work to any number of bands.Then, I applied the obtained formula to 2-bandsystems in order to highlight the role of interbandeffects in the orbital susceptibility. The susceptibilitycan be written using Berry curvature, quantityassociated to interband effects, as well as the metrictensor. In particular, I show that a band isulatorcan have a non-vanishing magnetic responseeven if the chemical potential lies in the gap. Moreover,I study a model where the geometric propertiescan be tuned without changing the dispersionrelation. This tuning can drastically modifythe orbital magnetic response.
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Arnaud Raoux. Magnétisme orbital et aspects géométriques de la théorie des bandes. Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]. Université Paris-Saclay, 2017. Français. ⟨NNT : 2017SACLS041⟩. ⟨tel-01480954⟩

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