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Physical review. B, Condensed matter

Collective interband excitations in the Raman spectra of quantum wires

Maura Sassetti, Franco Napoli, Bernhard Krämer

Published Mar 15, 1999• 11 citations
Publisher

Abstract

A unifying theory for the collective interband excitations of the interacting electrons in a quantum wire with several occupied subbands is developed by using the bosonization method. Interband spin- and charge-density excitations for two subbands are treated in detail. The results are used to clarify the physical nature of the interband modes detected in recent Raman scattering experiments, especially the so-called single-particle excitations.

DOI
10.1103/physrevb.59.7297

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A unifying theory for the collective interband excitations of the interacting electrons in a quantum wire with several occupied subbands is developed by using the bosonization method. Interband spin- and charge-density excitations for two subbands are treated in detail. The results are used to clarify the physical nature of the interband modes detected in recent Raman scattering experiments, especially the so-called single-particle excitations.
Using the bosonization technique, we develop a theory for the Raman scattering of the interacting electrons in quantum wires. The energy spectra of the collective excitations in a two-subband model are given. The density correlation functions for the Raman cross section are calculated. The charge and spin density excitations observed in recent Raman experiments are identified. Hitherto unexplained “single particle excitations” which appear near resonance and are independent of the relative polarization of incoming and scattered light are shown to originate in higher order spin density excitations, which can be evaluated due to the bosonization. For the intraband excitations, the peak strengths in the Raman cross section as a function of the frequency of the incoming light is explicitely calculated. Power law behaviors depending on the strength of the interaction are predicted.
Abstract Using the bosonization technique, we develop a theory for the Raman scattering of the interacting electrons in quantum wires. The energy spectra of the collective excitations in a two‐subband model are given. The density correlation functions for the Raman cross section are calculated. The charge and spin density excitations observed in recent Raman experiments are identified. Hitherto unexplained “single particle excitations” which appear near resonance and are independent of the relative polarization of incoming and scattered light are shown to originate in higher order spin density excitations, which can be evaluated due to the bosonization. For the intraband excitations, the peak strengths in the Raman cross section as a function of the frequency of the incoming light is explicitely calculated. Power law behaviors depending on the strength of the interaction are predicted.
The bosonisation technique is used to calculate the resonant Raman spectrum of a quantum wire with two electronic sub-bands occupied. Close to resonance, the cross-section at frequencies in the region of the inter–sub-band transitions shows distinct peaks in parallel polarisation of the incident and scattered light that are signature of collective higher-order spin density excitations . This is in striking contrast to the conventional selection rule for non-resonant Raman scattering according to which spin modes can appear only in perpendicular polarisation. We predict a new selection rule for the excitations observed near resonance, namely that, apart from charge density excitations, only spin modes with positive group velocities can appear as peaks in the spectra in parallel configuration close to resonance. The results are consistent with all of the presently available experimental data.
We systematically investigate the mode dispersion and spectral weight of the elementary excitation spectra in one-dimensional continuum and lattice electron systems by using the RPA, the Luttinger liquid model, and the Hubbard model. Both charge and spin excitations are studied in detail and compared among the theoretical models. For the lattice Hubbard model we use both Bethe-ansatz equations and Lanczos-Gagliano method to calculate dispersion and spectral weight separately. We discuss the theoretically calculated elementary excitation spectra in terms of the experimental inelastic light (Raman) scattering spectroscopy of one-dimensional (1D) semiconductor quantum wire systems. Our results show that in the polarized (i.e., non-spin-flip) Raman-scattering spectroscopy, only the 1D charge density excitations should show up with observable spectral weight with the single-particle excitations (in random-phase approximation) or singlet spin excitations (in the Luttinger model and the Hubbard model) having negligible spectral weight. The depolarized (spin-flip) Raman-scattering spectra manifest the spin density or the triplet spin excitations. We also provide a qualitative comparison between the continuum and the lattice 1D elementary excitation spectra.