Closed-form wavefunctions for charge-e spin polarons in SU(2) Chern ferromagnets are exact eigenstates in ideal Chern-1 bands with contact interactions and remain stable variational states when quantum geometry is controlled.
Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The discovery of fractional quantum anomalous Hall (FQAH) states in two-dimensional heterostructures has opened the door to realizing phases of dispersing anyons. Here, we develop an analytically controlled theory of anyon dispersion in FQAH states realized in ideal or Aharonov-Casher (AC) bands by projecting interactions onto the space of Laughlin quasiholes. Constructing quasihole momentum eigenstates allows efficient evaluation of the single quasihole dispersion using Monte Carlo. We find that the quasihole bandwidth grows with increasing quantum-geometry inhomogeneity of the AC band and with increasing interaction screening length. For realistic parameters relevant to the bands of twisted MoTe${}_2$, the quasihole bandwidth is of order 1 meV and increases with increasing displacement field, suggesting that itinerant-anyon physics may play an important role in sufficiently clean samples. Furthermore, we develop a microscopic Lagrangian framework in terms of a quasihole guiding-center coordinate, which reproduces the momentum-space formula for the dispersion. This approach reveals that quasihole dispersion originates from the combined effects of an interaction-generated periodic potential, arising from non-uniform quantum geometry of the single particle bands, and the quasihole many-body Berry phase arising from the background magnetic field. The latter endows the guiding-center coordinate with a noncommutative structure, converting the periodic potential into a finite dispersion. Finally, we outline how this framework generalizes to multiple quasiholes, enabling a microscopic theory of charged excitations in FQAH systems that retains only the anyon degrees of freedom.
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Anyon Bloch bands in ideal FCIs have m-fold degeneracy in the magnetic BZ and bandwidth controlled by quantum geometry non-uniformity, with higher harmonics strongly suppressing dispersion through emergent symmetries.
Tuning reciprocal-lattice Fourier components of density modulations allows arbitrary enhancement of the FCI gap within projected flat-band theory and rescales the full low-energy spectrum to match Landau-level FQHS.
Tunneling probes can measure anyon dispersion via quasiparticle interference patterns and continuum thresholds in fractional Chern insulators.
An exciton forms a bound state with a quasihole in a 1/3-filled fractional Chern insulator, with spectral signatures and binding energies of order 1 meV accessible to optical experiments.
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Microsopic Theory of Spin Polarons in Chern Ferromagnets
Closed-form wavefunctions for charge-e spin polarons in SU(2) Chern ferromagnets are exact eigenstates in ideal Chern-1 bands with contact interactions and remain stable variational states when quantum geometry is controlled.
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Dispersion of Anyon Bloch Bands
Anyon Bloch bands in ideal FCIs have m-fold degeneracy in the magnetic BZ and bandwidth controlled by quantum geometry non-uniformity, with higher harmonics strongly suppressing dispersion through emergent symmetries.
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How Similar Can Fractional Chern Insulators Be to Fractional Quantum Hall States? Moir\'e-Enhanced Gaps and Excitation-Spectrum Correspondence
Tuning reciprocal-lattice Fourier components of density modulations allows arbitrary enhancement of the FCI gap within projected flat-band theory and rescales the full low-energy spectrum to match Landau-level FQHS.
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Measuring anyon dispersion with tunneling probes
Tunneling probes can measure anyon dispersion via quasiparticle interference patterns and continuum thresholds in fractional Chern insulators.
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Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints
An exciton forms a bound state with a quasihole in a 1/3-filled fractional Chern insulator, with spectral signatures and binding energies of order 1 meV accessible to optical experiments.
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