Non-Abelian Fractional Quantum Anomalous Hall States and First Landau Level Physics in Second Moir\'e Band of Twisted Bilayer MoTe2
Utilizing the realistic continuum description of twisted bilayer MoTe2 and many-body exact diagonalization calculation, we establish that the second moir\'e band of twisted bilayer MoTe2, at a small twist angle of approximately 2{\deg}, serves as an optimal platform for achieving the long-sough...
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Zusammenfassung: | Utilizing the realistic continuum description of twisted bilayer MoTe2 and
many-body exact diagonalization calculation, we establish that the second
moir\'e band of twisted bilayer MoTe2, at a small twist angle of approximately
2{\deg}, serves as an optimal platform for achieving the long-sought
non-Abelian fractional quantum anomalous Hall states without the need for
external magnetic fields. Across a wide parameter range, our exact
diagonalization calculations reveal that the half-filled second moir\'e band
demonstrates the ground state degeneracy and spectral flows, which are
consistent with the pfaffian state in the first Landau level. We further
elucidate that the emergence of the non-Abelian state is deeply connected to
the remarkable similarity between the second moir\'e band and the first Landau
level. Essentially, the band not only exhibits characteristics akin to the
first Landau level,
$\frac{1}{2\pi}\int_\mathrm{BZ}\mathrm{d}^2\mathbf{k}\:\mathrm{tr}\:\eta(\mathbf{k})
\approx 3$ where $\eta_{ab}(\mathbf{k})$ is the Fubini-Study metric of the
band, but also that its projected Coulomb interaction closely mirrors the
Haldane pseudopotentials of the first Landau level. Motivated from this
observation, we introduce a novel metric of "first Landau level"-ness of a
band, which quantitatively measures the alignment of the projected Coulomb
interaction with the Haldane pseudopotentials in Landau levels. This metric is
then compared with the global phase diagram of the half-filled second moir\'e
band, revealing its utility in predicting the parameter region of the
non-Abelian state. In addition, we uncover that the first and third moir\'e
bands closely resemble the lowest and second Landau levels, revealing a
remarkable sequential equivalence between the moir\'e bands and Landau levels.
We finally discuss the potential implications on experiments. |
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DOI: | 10.48550/arxiv.2403.19155 |