## SCL Seminar by Milica Milovanovic

SCL's Milica Milovanovic presented a seminar:

"On the geometrical description of fractional Chern insulators"

Abstract:

After the prediction and realization of topological insulators [1], which may be described as systems with integer quantum Hall effect physics without external magnetic field and Landau levels, there is an increasing interest in fractional Chern insulators (FCIs), interacting systems which without magnetic field would support fractional quantum Hall (FQH) physics [2]. In the case of FCIs the role of the fixed Landau level is played by a Bloch band with a non-trivial Chern number. The structure of the Bloch band depends on the underlying lattice, and may be quantified by Berry curvature and Fubini-Study (quantum distance) metric that depend on Bloch momentum in Brillouin zone. The usual FQH effect would correspond to a uniform background: constant curvature and metric with a fixed relationship.

In this talk [3] we will study the static structure factor of the FCI Laughlin-like state and provide analytical forms for this quantity in the long distance limit. In the course of this we will identify averaged over Brillouin zone Fubini Study metric as the relevant metric in the long distance limit. We will discuss under which conditions the static structure factor will assume the usual behavior of Laughlin-like FQH system i.e. the scenario of Girvin, MacDonald, and Platzman [Phys. Rev. B 32, 8458 (1986)], and study the influence of the departure of the averaged over Brilloin zone Fubini-Study metric from its FQH value. This departure appears in the long distance analysis as an effective change of the filling factor. According to our exact diagonalization results on the Haldane model and analytical considerations we find persistence of FCI state even in this region of the parameter space.

[1] M.Z. Hasan and C.L, Kane, "Colloquium: Topological Insulators", Rev. Mod. Phys. 82, 3045 (2010)

[2] R. Roy and S.L. Sondhi, "Fractional Quantum Hall Effect without Landau levels", Physics 4, 46 (2011); M. Daghofer and M. Haque, "Toward Fractional Quantum Hall Physics with Cold Atoms", Physics 6, 49 (2013)

[3] E. Dobardzic, M.V. Milovanovic, and N. Regnault, arXiv:1303.7131