# Groupe de Physique Statistique

## Equipe 106, Institut Jean Lamour

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### Séminaire de groupe

 Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number Gunnar Möller Cavendish Laboratory, Cambridge University jeudi 24 septembre 2015 , 10h25 Salle de séminaire du groupe de Physique Statistique We will discuss the many-body physics that is realised by interacting particles occupying topological flat bands of the Harper-Hofstadter model with Chern number $|C|>1$ [1,2]. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor, $\nu$, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors $\nu = r/(r|C| +1)$ for bosons, or $\nu = r/(2r|C| +1)$ for fermions. This series includes a bosonic integer quantum Hall state (bIQHE) in $|C|=2$ bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions, with characteristics matching the predictions of composite fermion theory. Finally, we discuss how band-geometric measures influence the stability of generic fractional Chern insulator phases, providing evidence that the many-body gap correlates not only with the flatness of the Berry-curvature, but additionally we demonstrate also the influence of the Fubini-Study metric tensor [3]. [1] G. MÃ¶ller, N.R. Cooper, Phys. Rev. Lett. 103, 105303 (2009). [2] G. MÃ¶ller, N.R. Cooper, Phys. Rev. Lett. 115, 126401 (2015); arXiv:1504.06623. [3] T. Jackson, GM, R. Roy, Nature Communications (2015), in press; arxiv:1408.0843.