Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs

Abstract

Topological flat moiré bands with nearly ideal quantum geometry have been identified in homobilayer transition metal dichalcogenide moiré superlattices, and are thought to be crucial for understanding the fractional Chern insulating states recently observed therein. Previous work proposed viewing the system using an adiabatic approximation that replaces the position-dependence of the layer spinor with a nonuniform periodic effective magnetic field. When the local zero-point kinetic energy of this magnetic field cancels identically against that of an effective Zeeman energy, a Bloch-band version of Aharonov-Casher zero-energy modes, which we refer to as Aharonov-Casher band, emerges leading to ideal quantum geometry. Here, we critically examine the validity of the adiabatic approximation and identify the parameter regimes under which Aharonov-Casher bands emerge. We show that the adiabatic approximation is accurate for a wide range of parameters including those realized in experiments. Furthermore, we show that while the cancellation leading to the emergence of Aharonov-Casher bands is generally not possible beyond the leading Fourier harmonic, the leading harmonic is the dominant term in the Fourier expansions of the zero-point kinetic energy and Zeeman energy. As a result, the leading harmonic expansion accurately captures the trend of the bandwidth and quantum geometry, though it may fail to quantitatively reproduce more detailed information about the bands such as the Berry curvature distribution.

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• Theory of Generalized Landau Levels and Implication for non-Abelian States
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• Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides
• Intraband collective excitations in fractional Chern insulators are dark
• Quantum Geometry and the Hidden Scales in Materials
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Moiré Band Engineering in Twisted Trilayer WSe2
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Optical properties, plasmons, and orbital Skyrme textures in twisted TMDs
• Geometric transport signatures of strained multi-Weyl semimetals
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Topological Order in Neural Wavefunctions
• Orbital Description of Landau Levels
• Robustness of real-space topology in moiré systems
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• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory