Excitonic Charge Density Waves in Moire Ladders

Abstract

An incommensurate charge density wave (CDW) is a periodic modulation of charge that breaks translational symmetry incongruently with the underlying lattice. Its low-energy excitations, the phason, are collective, gapless phase fluctuations. We study a half-filled, four-band ladder model where a shift \(\delta = p/q\) between the legs leads to a supercell of \(q\) composite cells. The moir\'e potential narrows minibands near the Fermi level, resulting in additional peaks in the density of states, whose separation is controlled by \(\delta\). The inclusion of short-range Coulomb interactions leads to an excitonic incommensurate CDW state. We identify the oscillations in its amplitude with a gapped Higgs collective mode and a lowest-energy Goldstone mode, realized by long-lived neutral phasons whose propagation velocity is governed by the shift \(\delta\) and the inter-leg tunneling amplitude. Our results show that even the slightest interlayer mismatches can strongly modify both charge-ordering patterns and low-energy bosonic excitations in layered materials, and suggest that the enigmatic CDW phase in the quasi-one-dimensional compound \(\rm HfTe_3 \) is excitonic in nature.