Charge density wave

A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such a CDW, like those in a superconductor, can flow through a linear chain compound en masse, in a highly correlated fashion. Unlike a superconductor, however, the electric CDW current often flows in a jerky fashion, much like water dripping from a faucet due to its electrostatic properties. In a CDW, the combined effects of pinning (due to impurities) and electrostatic interactions (due to the net electric charges of any CDW kinks) likely play critical roles in the CDW current's jerky behavior, as discussed in sections 4 & 5 below. A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such a CDW, like those in a superconductor, can flow through a linear chain compound en masse, in a highly correlated fashion. Unlike a superconductor, however, the electric CDW current often flows in a jerky fashion, much like water dripping from a faucet due to its electrostatic properties. In a CDW, the combined effects of pinning (due to impurities) and electrostatic interactions (due to the net electric charges of any CDW kinks) likely play critical roles in the CDW current's jerky behavior, as discussed in sections 4 & 5 below. Most CDW's in metallic crystals form due to the wave-like nature of electrons – a manifestation of quantum mechanical wave-particle duality – causing the electronic charge density to become spatially modulated, i.e., to form periodic 'bumps' in charge. This standing wave affects each electronic wave function, and is created by combining electron states, or wavefunctions, of opposite momenta. The effect is somewhat analogous to the standing wave in a guitar string, which can be viewed as the combination of two interfering, traveling waves moving in opposite directions (see interference (wave propagation)). The CDW in electronic charge is accompanied by a periodic distortion – essentially a superlattice – of the atomic lattice. The metallic crystals look like thin shiny ribbons (e.g., quasi-1-D NbSe3 crystals) or shiny flat sheets (e.g., quasi-2-D, 1T-TaS2 crystals). The CDW's existence was first predicted in the 1930s by Rudolf Peierls. He argued that a 1-D metal would be unstable to the formation of energy gaps at the Fermi wavevectors ±kF, which reduce the energies of the filled electronic states at ±kF as compared to their original Fermi energy EF. The temperature below which such gaps form is known as the Peierls transition temperature, TP. The electron spins are spatially modulated to form a standing spin wave in a spin density wave (SDW). A SDW can be viewed as two CDWs for the spin-up and spin-down subbands, whose charge modulations are 180° out-of-phase. In 1954, Herbert Fröhlich proposed a microscopic theory, in which energy gaps at ±kF would form below a transition temperature as a result of the interaction between the electrons and phonons of wavevector Q=2kF. Conduction at high temperatures is metallic in a quasi-1-D conductor, whose Fermi surface consists of fairly flat sheets perpendicular to the chain direction at ±kF. The electrons near the Fermi surface couple strongly with the phonons of 'nesting' wave number Q = 2kF. The 2kF mode thus becomes softened as a result of the electron-phonon interaction. The 2kF phonon mode frequency decreases with decreasing temperature, and finally goes to zero at the Peierls transition temperature. Since phonons are bosons, this mode becomes macroscopically occupied at lower temperatures, and is manifested by a static periodic lattice distortion. At the same time, an electronic CDW forms, and the Peierls gap opens up at ±kF. Below the Peierls transition temperature, a complete Peierls gap leads to thermally activated behavior in the conductivity due to normal uncondensed electrons. However, a CDW whose wavelength is incommensurate with the underlying atomic lattice, i.e., where the CDW wavelength is not an integer multiple of the lattice constant, would have no preferred position, or phase φ, in its charge modulation ρ0 + ρ1cos. Fröhlich thus proposed that the CDW could move and, moreover, that the Peierls gaps would be displaced in momentum space along with the entire Fermi sea, leading to an electric current proportional to dφ/dt. However, as discussed in subsequent sections, even an incommensurate CDW cannot move freely, but is pinned by impurities. Moreover, interaction with normal carriers leads to dissipative transport, unlike a superconductor. Several quasi-2-D systems, including layered transition metal dichalcogenides, undergo Peierls transitions to form quasi-2-D CDWs. These result from multiple nesting wavevectors coupling different flat regions of the Fermi surface. The charge modulation can either form a honeycomb lattice with hexagonal symmetry or a checkerboard pattern. A concomitant periodic lattice displacement accompanies the CDW and has been directly observed in 1T-TaS2 using cryogenic electron microscopy. In 2012, evidence for competing, incipient CDW phases were reported for layered cuprate high-temperature superconductors such as YBCO. Early studies of quasi-1-D conductors were motivated by a proposal, in 1964, that certain types of polymer chain compounds could exhibit superconductivity with a high critical temperature Tc. The theory was based on the idea that pairing of electrons in the BCS theory of superconductivity could be mediated by interactions of conducting electrons in one chain with nonconducting electrons in some side chains. (By contrast, electron pairing is mediated by phonons, or vibrating ions, in the BCS theory of conventional superconductors.) Since light electrons, instead of heavy ions, would lead to the formation of Cooper pairs, their characteristic frequency and, hence, energy scale and Tc would be enhanced. Organic materials, such as TTF-TCNQ were measured and studied theoretically in the 1970s. These materials were found to undergo a metal-insulator, rather than superconducting, transition. It was eventually established that such experiments represented the first observations of the Peierls transition. The first evidence for CDW transport in inorganic linear chain compounds, such as transition metal trichalcogenides, was reported in 1976 by Monceau et al., who observed enhanced electrical conduction at increased electric fields in NbSe3. The nonlinear contribution to the electrical conductivity σ vs. field E was fit to a Landau-Zener tunneling characteristic ~ exp (see Landau–Zener formula), but it was soon realized that the characteristic Zener field E0 was far too small to represent Zener tunneling of normal electrons across the Peierls gap. Subsequent experiments showed a sharp threshold electric field, as well as peaks in the noise spectrum (narrow band noise) whose fundamental frequency scales with the CDW current. These and other experiments (e.g.,) confirm that the CDW collectively carries an electric current in a jerky fashion above the threshold field.