Discovery of the Fractional Quantum Anomalous Hall Effect in Moire MoTe2

Abstract

The impact of the integer and fractional quantum Hall effects on condensed matter physics can hardly be overstated. Their discovery in the 1980s and the subsequent theoretical interpretation by Thouless et al., Laughlin, Jain, Halperin, and others has resulted in a completely new way of thinking about condensed matter. We now understand that there are quantum phases beyond those described via Landau symmetry-breaking theory - that is, phases with topological order. The physics of fractional quantum Hall phases is particularly rich, leading to concepts such as charge fractionalization, composite fermions, and non-Abelian anyon excitations. Beyond their fundamental interest, non-Abelian anyons could lead to topologically-protected quantum computation. However, the massive magnetic fields and millikelvin temperatures necessary for fractional quantum Hall physics make experiments extremely difficult. Lattice systems showing a quantized Hall effect at zero magnetic field without the formation of Landau levels - Chern insulators - were first proposed by Haldane. More recently, systems hosting lattice versions of fractional quantum Hall states, or fractional Chern insulators (FCIs), have been explored theoretically. The quantized Hall effect at zero field - the quantum anomalous Hall effect - was observed experimentally in 2012. The natural question then arises: are there systems which show the fractional quantum anomalous Hall effect? In this dissertation, we answer in the affirmative. By forming a heterostructure of two monolayers of van der Waals semiconductor MoTe2 with a small twist angle, a moire superlattice can be realized. Surprisingly, this superlattice meets all the criteria to host an FCI - topological bands, strong correlations, and spontaneous time reversal symmetry breaking. Using optical probes, we observe ferromagnetism arising from strong correlations between doped holes over a large region of phase space. Optical Landau fan diagrams, compared with the expected Streda formula dispersion for topological states, provide the first signature of a zero-field FCI. Transport measurements at zero magnetic field reveal not only an integer quantized Hall resistance at full filling of the moire Chern band, but also fractionally quantized Hall resistance at multiple fractional fillings. These results constitute the first experimental observation of the fractional quantum anomalous Hall effect. This groundbreaking discovery sets up the search for more FCI phases, including those hosting zero-field non-Abelian anyons. We take a first step in this direction, using the optical response of the system to find signatures of a zero-field composite Fermi liquid. The composite Fermi liquid is the parent state of fractional phases which host Abelian anyon excitations - and, possibly, phases which host non-Abelian ones as well.