Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers

Abstract

Remarkable recent experiments have observed fractional quantum anomalous Hall effects at zero field and unusually high temperatures in twisted semiconductor bilayer <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>t</a:mi><a:msub><a:mi>MoTe</a:mi><a:mn>2</a:mn></a:msub></a:mrow></a:math>, hence realizing the first genuine fractional Chern insulators. Intriguing observations in these experiments, such as the absence of integer Hall effects at twist angles where a fractional Hall effect is observed, do however remain unexplained. The experimental phase diagram as a function of twist angle remains to be established. By a comprehensive numerical study, including entanglement spectroscopy, we show that band mixing has large qualitative and quantitative effects on the energetics of competing states and their energy gaps throughout the twist angle range <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>θ</b:mi><b:mo>≤</b:mo><b:msup><b:mn>4</b:mn><b:mo>∘</b:mo></b:msup></b:mrow></b:math>. This lays the foundation for a detailed realistic study of a rich variety of strongly correlated moiré superlattices and an understanding of the phase diagram of these fascinating systems. Published by the American Physical Society 2024