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Annalen der Physik

Luttinger‐liquid features in the resonant Raman spectra of quantum wires

Maura Sassetti, B. Krämer

Published Nov 1, 1998• 0 citations
Publisher

Abstract

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.

DOI
10.1002/andp.199851005-620

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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.
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.
A theory of resonant Raman scattering spectroscopy of one-dimensional electronic systems is developed on the assumptions that (i) the excitations of the one-dimensional electronic system are described by the Luttinger-liquid model, (ii) Raman processes involve virtual excitations from a filled valence band to an empty state of the one-dimensional electronic system, and (iii) excitonic interactions between the valence and conduction bands may be neglected. Closed form analytic expressions are obtained for the Raman scattering cross sections, and are evaluated analytically and numerically for scattering in the polarized channel, revealing a ``double-peak'' structure with the lower peak involving multispinon excitations with total spin S=0S=0S=0 and the higher peak being the conventional plasmon. A key feature of our results is a nontrivial power-law dependence, involving the Luttinger-liquid exponents, of the dependence of the Raman cross sections on the difference of the laser frequency from resonance. We find that near resonance the calculated ratio of intensity in the lower energy feature to the intensity in the higher energy feature saturates at a value of the order of unity (times a factor of the ratio of the velocities of the two modes). We explicate the differences between the ``Luttinger-liquid'' and ``Fermi-liquid'' calculations of resonant Raman spectroscopy (RRS) spectra and argue that excitonic effects, neglected in all treatments so far, are essential for explaining the intensity ratios observed in quantum wires. We also discuss other Luttinger-liquid features which may be observed in future RRS experiments.
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.