Structure of the moving piezoelectric polaron

Both the intermediate-coupling theory and a strong-coupling theory appropriate for a moving polaron give an anomalous energy-momentum relation, E(P), for the piezoelectric polaron. This relation starts out quadratic at small P, but at large P it asymptotes to a straight line with slope equal to the speed of sound s. It is shown that the states represented by this anomalous E vs. P relation are such that the electron is clothed by its concomitant lattice distortion and that this lattice distortion becomes larger as the polaron velocity v-->s. This indicates that in this limit an increasing number of phonons are gathering in the "phonon cloud" around the electron. In both theories the constant lattice-potential surfaces become flattened in the forward and backward directions as the polaron starts to move.