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

New optical-absorption edges of a metal having a charge-density-wave ground state arise from transitions across charge-density-wave energy gaps. If the charge-density-wave wave vector Q{→} is incommensurate with the reciprocal-lattice vector G{→}, three families of higher-order gaps in E(k{→}) arise: ``minigaps,'' characterized by wave vectors (n+1)Q{→}-nG{→}; ``heterodyne gaps,'' with periodicities n(G{→}-Q{→}); and ``second-zone minigaps,'' with periodicities (n+1)G{→}-nQ{→}. The energy-gap surfaces of the first two families truncate the Fermi surface and lead to additional absorption edges in the far-infrared region. The absorption peaks associated with the first three minigaps are calculated for K and Na, and are found to be an order of magnitude larger than both the interband absorption and the main charge-density-wave peak. However, they are much smaller than the room-temperature Drude absorption. Consequently, a search for far-infrared edges must be carried out at low temperature, and in samples for which the orientation of Q{→} allows observation of the Mayer--El Naby anomaly.