Unconventional Fractional Phases in Multi-Band Vortexable Systems

TL;DR

This paper explores novel fractional quantum Hall states in multi-band vortexable systems with flat bands, revealing phenomena that differ from traditional Landau levels and are driven by moire lattice effects and quantum geometry.

Contribution

It introduces new fractional quantum Hall states in vortexable multi-band systems, highlighting their unique properties and origins beyond conventional Landau level physics.

Findings

Discovery of fractional states with unconventional Hall conductance

Identification of the role of moire lattice commensurability

Demonstration of deviations from Landau level behavior

Abstract

In this Letter, we study topological flat bands with distinct features that deviate from conventional Landau level behavior. We show that even in the ideal quantum geometry limit, moire flat band systems can exhibit physical phenomena fundamentally different from Landau levels without lattices. In particular, we find new fractional quantum Hall states emerging from multi-band vortexable systems, where multiple exactly flat bands appear at the Fermi energy. While the set of bands as a whole exhibits ideal quantum geometry, individual bands separately lose vortexability, and thus making them very different from a stack of Landau levels. At certain filling fractions, we find fractional states whose Hall conductivity deviates from the filling factor. Through careful numerical and analytical studies, we rule out all known mechanisms--such as fractional quantum Hall crystals or separate filling of trivial and topological bands--as possible explanations. Leveraging the exact solvability of vortexable systems, we use analytic Bloch wavefunctions to uncover the origin of these new fractional states, which arises from the commensurability between the moire unit cell and the magnetic unit cell of an emergent effective magnetic field.