Neutral phasons in moire ladders heterostructures

A charge density wave (CDW) is a periodic modulation of charge density that breaks translational symmetry. In incommensurate CDWs, the Goldstone excitation, or phason, reflects collective gapless phase fluctuations. We study a chiral-symmetric, half-filled, four-band ladder moiré model with a relative shift \(\delta=p/q\), resulting in a moiré supercell comprising \(q\) composite cells. The moiré potential compresses layer bands into narrow minibands near the Fermi level, leading to prominent peaks in the density of states (DOS) at low energies and a periodic electronic spectrum. Including Coulomb interactions, we find an incommensurate CDW characterized by a rung-odd density wave where charge modulation is out of phase between ladder legs, resulting in long-lived neutral phason excitations. The phason speed is determined by the density-wave phase stiffness and compressibility, controlled by \(\delta\). This model could enhance the understanding of quantum phase transitions between pinned and unpinned CDW states, the coexistence of CDWs and superconductivity, and the potential for topological properties in certain CDW states with coupled spin and charge orders.