Energy spectrum of an incommensurate charge-density wave: Potassium and sodium

The conduction-electron energy spectrum is calculated for K and Na taking into account the periodic potential 2αcos(→Q·→r) of the charge-density wave. Accordingly, the Schr\"odinger equation includes this term in addition to a pseudopotential 2βcos(→G·→r) caused by the ionic lattice. →Q and →G are nearly parallel, and differ in magnitude by only a few percent. As a consequence three families of higher-order gaps in E(→k) arise: "minigaps," characterized by wave vectors (n+1)→Q-n→G; "heterodyne gaps," with periodicities n(→G-→Q); "second-zone minigaps," with periodicities (n+1)→G-n→Q. The energy-gap surfaces of the first two families truncate the Fermi surface and cause the open orbits observed by Coulter and Datars in high-field magnetoresistance. They should also lead to new optical-absorption bands in the far infrared.