Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit

Abstract

In the presence of strong electronic interactions, a partially filled Chern band may stabilize a fractional Chern insulator (FCI) state, the zero-field analog of the fractional quantum Hall phase. While FCIs have long been hypothesized, feasible solid-state realizations only recently emerged, largely due to the rise of moiré materials. In these systems, the quantum geometry of the electronic bands plays a critical role in stabilizing the FCI in the presence of competing correlated phases. In the limit of ``ideal'' quantum geometry, where the quantum geometry is identical to that of Landau levels, this role is well understood. However, in more realistic scenarios only empiric numerical evidence exists, accentuating the need for a clear understanding of the mechanism by which the FCI deteriorates moving further away from these ideal conditions. We introduce and analyze an anisotropic model of a $\left|C\right|=1$ Chern insulator, whereupon partial filling of its bands, an FCI phase is stabilized over a certain parameter regime. We incorporate strong electronic interaction analytically by employing a coupled-wires approach, studying the FCI stability and its relation to the the quantum metric. We identify an unusual anti-FCI phase benefiting from non-ideal geometry, generically subdominant to the FCI. However, its presence hinders the formation of FCI in favor of other competitive phases at fractional fillings, such as the charge density wave. Though quite peculiar, this anti-FCI phase may have already been observed in experiments at high magnetic fields. This establish a direct link between quantum geometry and FCI stability in a tractable model far from any ideal band conditions, and illuminates a unique mechanism of FCI deterioration.

Published version

References in corpus (24)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Fractional quantum Hall states at zero magnetic field
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Spectroscopy Signatures of Electron Correlations in a Trilayer Graphene/hBN Moiré Superlattice
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Topological Lattice Models with Constant Berry Curvature
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Magnetic field stabilized Wigner crystal states in a graphene moiré superlattice
• General scatterings and electronic states in the quantum-wire network of moiré systems

Cited by in corpus (8)

• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Quantum Geometric Kohn-Luttinger Superconductivity
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Entropy-Enhanced Fractional Quantum Anomalous Hall Effect
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Geometric transport signatures of strained multi-Weyl semimetals
• Designing (higher) Hall crystals
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires