Theory of phason drag effect on thermoelectricity

Lee, Rice, and Anderson, in their monumental paper [Solid State Commun. 14, 703 (1974)], proved the existence of a collective mode describing the coupled motion of electron density and phonons in a one-dimensional incommensurate charge density wave in the Peierls state. This mode, which represents the coherent sliding motion of electrons and lattice distortions and affects low-energy transport properties, is described by the phase of the complex order parameter of the Peierls condensate, leading to Fr\"ohlich superconductivity in pure systems. Once spatial disorder is present, however, the phason is pinned, and the system is transformed into an insulating ground state: a dramatic change. Since phasons can be considered an ultimate phonon drag effect, it is of interest to see its effects on thermoelectricity, which is studied in the present paper based on linear response theory of Kubo and Luttinger. The result indicates that a large absolute value of the Seebeck coefficient proportional to the square root of the resistivity is expected at low temperatures ${k}_{\mathrm{B}}T/\mathrm{\ensuremath{\Delta}}\ensuremath{\ll}1$ ($\mathrm{\ensuremath{\Delta}}$ is the Peierls gap) with a sign opposite to the electronic contributions in the absence of the Peierls gap.