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Excitonic Charge Density Waves in Moire Ladders

Paula Mellado, Francisco Muñoz, Javiera Cabezas-Escares

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 $δ=p/q$ between the legs leads to a supercell of q composite cells. The moiré potential narrows minibands near the Fermi level, resulting in additional peaks in the density of states, whose separation is controlled by $δ$. 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 δ 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 HfTe3 is excitonic in nature.

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 between the legs leads to a supercell of q composite cells. The moiré potential narrows minibands near the Fermi level, resulting in additional peaks in the density of states, whose separation is controlled by . 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 δ 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 HfTe3 is excitonic in nature.

Paper Structure

This paper contains 3 equations, 4 figures.

Figures (4)

  • Figure 1: (a) The moire ladder model. (b-d) Band spectra of the kinetic Hamiltonian $H(k)$ in the EBZ at (b) $\delta=1$, (c) $\frac{19}{20}$ and (d) $\frac{17}{20}$.
  • Figure 2: DOS at T=0 and (a) $\delta=1$, (b) $\delta=\frac{17}{20}$. (c) Band spectra of the minibands $H_{\rm RBZ}$, in the RBZ.
  • Figure 3: Spectral function at $\delta=\frac{19}{20}$ and $T=1-\delta$ computed from (a) the single particle retarded Green function, (b) the two-particle RPA susceptibility.
  • Figure 4: (a) Distorted structure of HfTe$_3$, the distortion is exaggerated, Te chains are highlighted. (b) Bulk bandstructure; the darker the color, the stronger the projection on the Te chains. Subbands of a $12\times1$ supercell of a HfTe$_3$ monolayer, without (c) and with (d) the modulation. (e) Changes of the charge around each atom, bright blue/red is $\pm0.002e$.