Sublattice structure and topology in spontaneously crystallized electronic states
arxiv(2024)
摘要
The prediction and realization of the quantum anomalous Hall effect are often
intimately connected to honeycomb lattices in which the sublattice degree of
freedom plays a central role in the nontrivial topology. Two-dimensional Wigner
crystals, on the other hand, form triangular lattices without sublattice
degrees of freedom, resulting in a topologically trivial state. In this Letter,
we discuss the possibility of spontaneously formed honeycomb-lattice crystals
that exhibit the quantum anomalous Hall effect. Starting from a single-band
system with nontrivial quantum geometry, we derive the mean-field energy
functional of a class of crystal states and express it as a model of sublattice
pseudospins in momentum space. We find that nontrivial quantum geometry leads
to extra terms in the pseudospin model that break an effective `time-reversal
symmetry' and favor a topologically nontrivial pseudospin texture. When the
effects of these extra terms dominate over the ferromagnetic exchange coupling
between pseudospins, the anomalous Hall crystal state becomes energetically
favorable over the trivial Wigner crystal state.
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