Electron–phonon interaction in a spin–orbit coupled quantum wire with a gap

Abstract

Interaction between electron and acoustic phonon in an in-plane magnetic field induced gapped quantum wire with Rashba spin-orbit interaction is studied. We calculate acoustic phonon limited resistivity (ρ) and phonon-drag thermopower (Sg) due to two well known mechanisms of electronphonon interaction namely, deformation potential (DP) and piezoelectric (PE) scattering. In the so called Bloch-Gruneisen temperature limit both ρ and Sg depend on temperature (T ) in a power law fashion i.e. ρ or Sg ∼ T ν T . For resistivity, νT takes the value 5 and 3 due to DP and PE scattering respectively. On the other hand, νT is 4 and 2 due to DP and PE scattering, respectively for phonondrag thermopower. Additionally, we find numerically that νT depends on Rashba parameter (α) and electron density (n). The dependence of νT on α becomes more prominent at lower density. We also study the variations of ρ and Sg with carrier density in the Bloch-Gruneisen regime. Through a numerical analysis a similar power law dependence ρ or Sg ∼ n −νn is established in which the effective exponent νn undergoes a smooth transition from a low density behavior to a high density behavior. At a higher density regime, νn matches excellently with the value obtained from theoretical arguments. Approximate analytical expressions for both resistivity and phonon-drag thermopower in the Bloch-Gruneisen regime are given.

Optical Absorption in Semiconductor Nanowire Mediated by Electron-Polar Optical Phonon and Spin-Orbit Interactions

“…The SOC arising from the inversion asymmetry in a bulk crystal is called Dresselhaus SOC and has both a k-linear and a k-cubic terms [21]. The influence of the SOC on electron states [22][23][24][25][26][27][28][29][30][31][32][33] and related phenomena [34][35][36][37][38][39] in QWR have been successively studied experimentally and theoretically.…”