Collective Excitations in Realistic Quantum Wires

We have used the Hartree-Fock Random Phase Approximation (HFRPA) to study the interacting electron gas in a quantum wire. The spectra of intersubband spin-flip excitations reveal a considerable red shift with respect to single-particle HF energies. That signals on appearance of collective intersubband spind-density excitations due to the exchange interaction. The long wavelength dispersions of the intrasubband collective spin-density excitations are linear, but the sound velocities are renormalised due to the exchange interaction and screening. The in-phase intrasubband charge-density excitation has the long wavelength form q[− ln(q)]1/2. We found good qualitative agreement of our results with experimental observations. A semiconductor quantum wire can be fabricated by applying a voltage with a microstructured gate to a 2D electron gas. The single-particle energy (SPE) spectrum typically consists of subbands separated by several meV . At a 1D electron density about 10cm more than one subband can be occupied. In recent years progress has been made in spectroscopic study of such systems. In angular resolved Raman spectra of GaAs quantum wires[1, 2, 3], collective spin-density excitations (SDE) and charge-density excitations (CDE, or plasmons) were observed. The measured spectra cover from low to high frequency, and for low-frequency intrasubband excitations, the wave-vector dependence of the spin-wave energy was found to be linear. The correct interpretation of these experiments allows us not only to understand the interesting physical processes, but also to access important physical parameters. The exchange interaction is crucial to the collective intrasubband and intersubband SDE. Similar to the direct long range Coulomb interaction which leads to the depolarisation shift of single-particle excitations and to the appearance of collective plasma modes, exchange interaction gives rise to the red-shift of SPE. If the redshift is sufficiently large, the collective SDE with a sizable oscillator strength splits off the continuum of SPE. For semiconductor quantum wells, such split-off appears in the Hartree-Fock Random Phase Approximation (HF-RPA)[4, 5, 6, 7]. Thus, it is important to perform a HF-RPA analysis on collective electron excitations in a realistic GaAs quantum wire with full Coulomb interaction, and compare the results with measured spectra[2, 3]. The selfconsistent and conserving[8] HF-RPA is suitable for this task, because we will calculate the two-particle spectra but not single-particle properties. As in using any approximation, the HF-RPA calculation also contains error. However, our HF-RPA results agree very well with experimental measurements. In this Letter we will first outline the HF-RPA method to express the spin or charge correlation functions in terms of the corresponding spinor charge-density induced