Effects of the Electron-Phonon Interaction on the Cyclotron Resonance of Parabolic Quantum Wells in a Tilted Magnetic Field

doi:10.1006/aphy.1994.1066

Annals of Physics

Volume 233, Issue 2, 1 August 1994, Pages 214-247

https://doi.org/10.1006/aphy.1994.1066 Get rights and content

Abstract

We study in detail the interaction of electrons confined in one spatial direction in a parabolic quantum well with longitudinal-optical (LO) phonons, in a tilted magnetic field. The polaron correction to the electron levels and the polaron cyclotron mass are calculated using second-order perturbation theory. We present analytic and numerical results for the energy levels and the polaron cyclotron mass in dependence on the strength and the tilt angle of the applied magnetic field. It is shown that the electron-phonon induced corrections of the electron levels and, especially, the polaron cyclotron mass are very sensitive according to the tilt angle. For the case of an in-plane magnetic field it depends on the ratio of the confinement energy and the LO phonon energy whether cyclotron resonance results in a resonant magnetopolaron or not.

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Cited by (15)

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The interaction of quasi-one-dimensional electrons and longitudinal-optical (LO) phonons in the presense of a quantizing magnetic field is calculated. Results are detailed presented for the polaron correction to the subband energies, the polaron cyclotron mass and the polaron effective mass. The calculations are done by using different approaches, Rayleigh–Schrödinger perturbation theory, Wigner–Brillouin perturbation theory, improved Wigner–Brillouin perturbation theory and Green's function technique. In the framework of a diagrammatic approach a modified Hartree–Fock approximation is developed, which allows the calculation of the quasi-particle properties of lower-dimensional semiconductor nanostructures in the subband space. It is shown that the Rayleigh–Schrödinger perturbation theory, improved Wigner–Brillouin perturbation theory and the modified Hartree–Fock approximation well describe the ground-state renormalization, but only the improved Wigner–Brillouin perturbation theory and the modified Hartree–Fock approximation well describe the bend-over and pinning behaviour of the subbands at the boundary of the phonon continuum. Rayleigh–Schrödinger and Wigner–Brillouin perturbation theories fail for the calculation of the renormalization of the excited subband energies in quantum-well wires with strong confining potential even for vanishing magnetic field and polaron momentum. In addition to the symmetric scattering processes, which are the only processes involved in the self-energy of the old-fashioned perturbation theories, Green's function technique allows also to calculate the contribution of all asymmetric scattering processes of two electrons by exchanging an optical phonon.
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Applying the Feynman variational principle, we analyze the basic polaron parameters – the ground-state energy, the polaron effective mass, the number of phonons in the polaron cloud, and the polaron radius – for a three-axis ellipsoidal potential well. Numerical calculations are performed for the specific cases when the potential well determines (i) a cylindrical quantum wire, (ii) a planar quantum wire, and (iii) a spherical quantum dot. The polaron parameters are derived analytically for the limiting cases of large and small cross-section sizes of a quantum wire, and of large and small radii of a quantum dot. A boundary between the weak and strong coupling regions is studied as a function of sizes of the structures under consideration. It is shown that with confinement strengthening, regions of the weak and intermediate coupling shorten, while the strong-coupling region widens. For a “squeezed” polaron state in a quantum dot, when the radius of confinement R is smaller than the polaron radius $R_{p} =(ℏ/ m ̄ ω_{0})^{1/2}$ (with the electron band mass $m ̄$ and the LO phonon frequency ω₀), the electron–phonon coupling constant α is scaled as αR_p/R.
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Regular ArticleEffects of the Electron-Phonon Interaction on the Cyclotron Resonance of Parabolic Quantum Wells in a Tilted Magnetic Field

Abstract

Regular Article
Effects of the Electron-Phonon Interaction on the Cyclotron Resonance of Parabolic Quantum Wells in a Tilted Magnetic Field