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Topological Phononics in Twisted Bilayer Graphene Moiré Superlattices with Verifiable Anomalous Acoustic Resonances_基于转角双层石墨烯摩尔超晶格的拓扑声子学与可验证的异常声学共振

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Topological Phononics in Twisted Bilayer Graphene Moiré Superlattices with Verifiable Anomalous Acoustic Resonances_基于转角双层石墨烯摩尔超晶格的拓扑声子学与可验证的异常声学共振

Abstract

This paper extends the topological-phonon framework to the twisted bilayer graphene (TBG) system. Based on the magic-angle flat bands predicted by the Bistritzer-MacDonald continuum model, we demonstrate that electron-phonon coupling in the moiré superlattice can engender a novel topological collective excitation — the Moiré Phonon Topological Polaron (MPTP). Under the unified description of the topological soliton field ϕ 6 theory, the MPTP carries a winding number and a valley topological charge, and obeys non-Abelian U(1) Z2 braiding statistics. The theoretical framework yields two independent, falsifiable experimental predictions: (1) a giant nonlinear acoustic resonance peak described by a quantised Duffing equation with a well-defined power threshold (1–10 W) and frequency hysteresis; (2) an acoustic frequency comb whose sideband spacing is μ proportional to both the MPTP topological charge and the moiré superlattice period ( ) with stable Δf ∝ Q/ℓmo irˊe phase locking. All experimental verification protocols employ existing, mature, commercially available equipment (vector network analyser, interdigital transducer, cryostat), and the flat-band filling factor can be continuously tuned via gate voltage — a unique experimental degree of freedom of TBG compared with other topologicalphonon candidate systems. Confirmation of the MPTP would open an entirely new pathway for acoustically controlling strongly correlated states in moiré flat bands. Keywords: topological phononics, twisted bilayer graphene, moiré superlattice, moiré phonon topological polaron, non-Abelian statistics, acoustic frequency comb

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