Charge density wave

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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.^[1][2][3] 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 ±k_F, which reduce the energies of the filled electronic states at ±k_F as compared to their original Fermi energy E_F.^[4] The temperature below which such gaps form is known as the Peierls transition temperature, T_P.

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.