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Magnetic, ESR, and NMR Properties
Published in Jean-Pierre Farges, Organic Conductors, 2022
Peierls pointed out in 1955 that a one-dimensional metallic chain is not stable at T = 0 K, against a periodic lattice distortion of wave vector 2kF, as the result of electron-phonon coupling, opening a gap 2Δ at the Fermi level. From this fact a collective electronic state results called a charge density wave (CDW). In the limit where U, the intrasite Coulomb repulsion, is infinite, since a given k state cannot be occupied by more than one electron, the conduction band will be filled from -2kF up to +2kF (if we still define kF for noninteracting electrons). Similarly to the 2kF Peierls instability, the system is also unstable at T = 0 K against a periodic lattice distortion which now occurs at the wave vector 4kF. In a half-filled band, the big U limit leads to a Mott-Hubbard insulator.
Towards a Universal Model of High Energy Density Capacitors
Published in Ranjusha Rajagopalan, Avinash Balakrishnan, Innovations in Engineered Porous Materials for Energy Generation and Storage Applications, 2018
Francisco Javier Quintero Cortes, Andres Suarez, Jonathan Phillips
The surface state formation concept is based on polarisation across a very thin insulating layer (Lunkenheimer et al. 2009). This concept is confusing as atomic scale polarisation is assumed to occur in electric double layers, but the theoretical dielectric values derived are less than 30 in all cases (see Table 2). Charge-density wave (CDW) are variations in the electronic charge density is a periodic function of position that may be incommensurate with the crystal lattice. In theory this leads to the formation of net dipoles between the layers and concomitantly high dielectric values (Whangbo and Subramanian 2006, Dumas et al. 1983, Gruner 1988, Fleming et al. 1986, Cava et al. 1986). It is notable that this behaviour is generally observed only at very high frequency (Wuttig et al. 2007, Zhang et al. 2005).
Layer-Structured Thermoelectric Materials: Fundamentals, Strategies and Progress
Published in Kuan Yew Cheong, Two-Dimensional Nanostructures for Energy-Related Applications, 2017
Charge Density Waves (CDWs) are periodic modulations of the electronic charge density – a standing wave in the electronic wave functions created by combining electron states moving in opposite directions (Rhyee et al. 2009b). CDWs and strong electron-phonon coupling and Peierls instabilities, have been used to lower κ of In4Se3-x crystal. In4Se3-x crystal shows very strong anisotropic thermoelectric properties. A very low κ of < 0.74 Wm−1 K−1 at 705 k along the b-c plane is observed in the Se deficiency In4Se3-x crystal while the κ along a-b plane is higher than that along b-c plane, but still achieves a relatively low value of ~1.1 Wm−1> K−1 at 705 K (Rhyee et al. 2009a). Through fundamental analysis, three aspects are responsible for the obtained low κ, including: (a) the in-plane Peierls lattice distortion and CDW instability result in the low κ along b-c plane in In4Se2.35, (b) the van der Waals interaction between In-Se layers along a axis leads to the low κ along a-b plane in In4Se2.35 and (c) the defect-induced phonon scattering at the Se-defect sites are further lowering κ with increasing the Se deficiency. Such a low κ finally results in a peak ZT of 1.48 at 705 K along the b-c plane, indicating In4Se3-x as a potential material for recycling waste heat in the mid-temperature range (500–900 K).
Local Nonequilibrium Electron Transport in Metals after Femtosecond Laser Pulses: A Multi-Temperature Hyperbolic Model
Published in Nanoscale and Microscale Thermophysical Engineering, 2021
Dai [31] extended the concept of the TTHM [10, 18, 22, 23] to the case of energy exchanges in a generalized N-carrier system. A finite difference scheme was developed for solving the hyperbolic and the difference between the hyperbolic model and the corresponding parabolic model was shown numerically [31]. Tao et al. [33] extended the TTHM to the three-temperature case to investigate the electron-phonon mechanism in three classes of low-dimensional systems (CeTe3, graphite, and VO2). While the phonon and the charge density wave (CDW) heat capacities assumed to be different, the CDW thermal conductivity is assumed to be equal to the phonon thermal conductivity. It was demonstrated by numerical calculations that the three temperature model is essential to tie the optical, electronic, and nuclear energies together in order to deduce coupling constants.
Elastic properties at the charge density wave phase transitions in TbTe3, ErTe3 and HoTe3
Published in Phase Transitions, 2022
Although the amount of work for the electronic properties have been made in Rare Earth Tritellurides [4, 5], only a few studies for the elastic properties have been performed. Hereafter we present a comparative study of the elastic properties in TbTe, ErTe and HoTe. We reexamine the measurements of the elastic stiffness components at the lower CDW phase transition in the three ErTe, HoTe and TbTe compounds [15,16] in order to analyze the striking temperature dependence of the velocity of the longitudinal modes and observed in the incommensurate ordered phase at low temperatures. The observed elastic anomalies have their origin in the micoscopic mechanisms attributed to ordering and their interaction with the strain at the upper and lower CDW phase transition. The appearance of incommensurate phases in dielectric materials has been intensively studied [17, 18] and displacive structural phase transition can be described within the context of lattice dynamics. It is expected that from the behavior of the elastic functions around the phase transitions informations about the interaction mechanisms between the strain and the order parameter and its corresponding excitations (soft phonons, amplitudons) can be obtained. In contrast charge density wave systems undergo displacive transitions driven by a Fermi surface instability of the conduction electrons. The resulting atomic displacement spatially modulated with a wave vector (where is the Fermi wavevector) lowers the electronic energy of the system and is accompanied by a periodic modulation of the electronic charge density and the formation of a gap at the Fermi level.