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Energy-momentum relation for polarons confined to one dimension

1986; American Physical Society; Volume: 33; Issue: 12 Linguagem: Inglês

10.1103/physrevb.33.8284

1095-3795

E. S. Hellman, J. S. Harris,

Physics of Superconductivity and Magnetism

Electrons confined to one dimension (1D) in a quantum wire structure or in a large magnetic field can interact with unconfined phonon modes. For interactions with polar optical phonons treated to first order in perturbation theory, the infinite density of states at wave vector k=0 for one-dimensional electrons results in a divergent phonon emission rate by electrons with energy equal to that of the longitudinal-optical phonon, \ensuremath{\Elzxh}${\ensuremath{\omega}}_{\mathrm{LO}}$. We have done a variational calculation of the dispersion relation for the single 1D electron-phonon (polaron) system in the weak-coupling limit which shows significant energy lowering at wave vector ${\mathit{k}}_{\mathrm{LO}}$=(2${\mathrm{m}}^{\mathrm{*}}$${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}$/\ensuremath{\Elzxh}${)}^{1/2}$ and a bending over for larger k. The dispersion relation is calculated for GaAs in large magnetic fields. We propose that the space charge of polarons below the phonon energy accounts for the size of the sequential phonon emission effect reported by Hickmott et al. [Phys. Rev. Lett. 52, 2053 (1984)].