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arXiv:cond-mat/0002287 · Physical review. B, Condensed matter

Tomonaga-Luttinger features in the resonant Raman spectra of quantum wires

B. Krämer, Maura Sassetti

Published Aug 15, 2000• 10 citations
arXivHTMLPDF

Abstract

The differential cross section for resonant Raman scattering from the collective modes in a one-dimensional system of interacting electrons is calculated nonperturbatively using the bosonization method. The results indicate that resonant Raman spectroscopy is a powerful tool for studying Tomonaga-Luttinger liquid behavior in quasi-one-dimensional electron systems.

DOI
10.1103/physrevb.62.4238

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The differential cross section for resonant Raman scattering from the collective modes in a one-dimensional system of interacting electrons is calculated nonperturbatively using the bosonization method. The results indicate that resonant Raman spectroscopy is a powerful tool for studying Tomonaga-Luttinger liquid behavior in quasi-one-dimensional electron systems.
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.
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.
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.
We derive the dynamical structure factor for an inhomogeneous Tomonaga-Luttinger liquid (TLL) as can be formed in a confined strongly interacting one-dimensional gas. In view of the current experimental progress in the field, we provide a simple analytic expression for the light-scattering cross section, requiring only the knowledge of the density dependence of the ground-state energy as it can be extracted, e.g., from exact or quantum Monte Carlo (QMC) techniques and a Thomas-Fermi description. We apply the result to the case of one-dimensional quantum bosonic gases with dipolar interaction in a harmonic trap, using an energy functional deduced from QMC computations. We find a universal scaling behavior peculiar to the TLL, a signature that can be probed eventually by Bragg spectroscopy in experimental realizations of such systems.
This chapter presents the energy spectrum and the momentum distribution of the Frohlich–Toyozawa–Luttinger liquid. The one-dimensional many-electron problem has generated renewed interest after the discovery of quasi-one dimensional solids such as carbon nanotubes, quantum wires, and other one-dimensional systems. Tomonaga was the first to solve the one-dimensional interacting fermion problem exactly using bosonization and certain approximations regarding the commutator of the density operators. Marino considered a one-dimensional acoustic many-polaron Hamiltonian within the framework of the Luttinger model and showed that for a certain range of the coupling constants the system would exhibit a metallic behavior because the spectrum contains gapless collective excitations of polaronic plasmons. Rao et al. have exactly solved the one-dimensional interacting electron problem within the framework of Luttinger model incorporating both the electron-optical-phonon interaction and the electron-acoustic-phonon interaction along with the electron-electron interaction to obtain the energy spectrum.