Misconceptions associated with the origin of charge density waves

Figures & data

Figure 1. Illustration of the Peirls picture. (a) Atomic model of a 1D chain with lattice constant a above T_c. (b) Atomic model of the 1D chain with lattice constant changing to 2a below T_c. (c) Free electron band of the 1D chain above T_c. (d) Free electron band of the 1D chain below T_c with a gap opening at k_F. (e) Plots of the real part of Linhard function for 1D, 2D and 3D free electron gas models. (f) Phonon energy of 1D atomic chain at different temperature.

Table 1. Comparison of the key features of typical CDW materials with Peierls’ model.

	Peierls’ model (1D atomic chain)	TTF-TCNQ (Quasi-1D material)	NbSe2 (Quasi-2D material)	Sn/Ge or Pb/Ge (2D films on surface)	Cuprates
Fermi Surface Nesting	√	√ [27]	X [30–32]	√ [37,38]	√ [64,69,70]
Sharp Peak in Lindhard Function	√	√ [23]	X [30–32]	√ [38]	√ [32]
Kohn Anomaly	√	√ [25]	√ [20]	√ [39,40]	X [32]
Structural Transition	√	√ [24]	√ [15–19]	√ [37,38]	√ [67,68]
Metal–insulator Transition	√	√ [22]	X [34]	√ [37]	X [69]

Figure 2. Illustration of the CDW state of TTF-TCNQ. (a) STM image at 63 K showing the normal state. (b) STM image at 36 K showing the CDW state. Reprinted with permission from Ref. [26]. Copyright (2003) by the American Physical Society. (c) ARPES intensity mapping at E_F of TTF-TCNQ at 60 K, showing a clear 1D FSN. Reprinted with permission from Ref. [27]. Copyright (2013) by the Physical Society of Japan. (d) Resistivity vs. temperature measurements showing a clear metal–insulator transition at 55 K [22]. (e) Inelastic neutron scattering results of the acoustic phonon dispersion showing a strong Kohn anomaly [25].

Figure 3. Origin of the CDW in NbSe₂. (a) Fermi Surface Contours [10] with the experimental [16,17] shown. (b) Reχ(q) and (c) Imχ(q) calculated from experimental data [10] along the ΓM direction. (d) Extracted EPC matrix element [32]. (e) Measured phonon dispersion (points) at T = 8 K [20] and calculated soft phonon behaviour (solid line) using and an approximation for the bare phonon (dashed line) dispersion [32].

Figure 4. EPC associated with apical oxygen A_1g phonon mode in optimally doped Bi₂Sr₂CaCu₂O_8+δ [32]. (a) Fit to the measured phonon dispersion [83] as a function of momentum. (b) Fit to the measured linewidth as a function of momentum. (c) extracted from the phonon [83] and ARPES [82] data.

Figure 5. Resistivity vs. temperature measurements for typical CDW materials. (a) 1D chain TTF-TCNQ [22]. (b) 1D chain NbSe₃ [85]. (c) 2D layered NbSe₂ [34].

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