1. Abstract

1. Collective Excitations in an interacting electron gas with Rashba spin-orbit coupling Sergej Konschuh and Mikhail Pletyukhov Institut für Theoretische Physik - Universität Regensburg -93053 Regensburg- Germany Institut für Theoretische Festkörperphysik - Universität Karlsruhe - 76135 Karlsruhe - Germany 1. Abstract 5. Renormalized density response matrix 8. Polarization & Sy – magnetic susceptibility In the two dimensional electron gas (2DEG) the Rashba spin-orbit (SO) coupling induces the momentum-dependent spin splitting of the conduction band. Response functions of this system are modified due to the possible intersubband transitions. We present the charge and spin density response functions of an interacting 2DEG with the Rashba SO coupling to an external time-dependent, non-uniform and spin-dependent potential. We study collective charge density excitations (CDE) and spin density excitation (SDE) modes in the clean regime (i.e., impurity scattering is neglected). We identify the regime when the usually small spin-charge response function produces a notable effect. Effect of avoided crossing A convenient approach - Equation of Motions (EoM) Account of e-e interactions: Hubbard approximation (direct and exchange Coulomb terms) Result: Black lines: collective charge and spin density excitation modes Red lines: mixed spin-charge modes by virtue of Cy Structure factor neglecting Cy including Cy Renormalized response functions (in the basis) 2. Rashba spin-orbit coupling Spin-charge response is small Neglecting it we obtain: Rashba spin-orbit coupling arises due to the inversion asymmetryof the microscopic confining potential of the 2DEG. w z Hamiltonian of the 2DEG with the Rashba SO coupling - Rashba coupling constant - effective mass 6. Polarization operator Structure factor neglecting Cy including Cy Dispersion relations spin texture Contour plots of the structure factor of polarization operator Left: without SO coupling Right: including SO coupling, neglecting Cy Wigner-Seitz parameter in 2D: Eigenstates spin is not conserved! Projectors onto the eigenstates SO – attenuation of the plasmon spectrum in the intersubband region of the particle-hole excitations. The latter is defined by (blue lines) The dispersion of collective mode is given by 3. Density response matrix 9. Spin response to electric field Particle-hole excitations are allowed for A linear response of a system to external perturbation is given by the density response matrix Renormalized spin response function to inhomogeneous longitudinal electric field applied in the x-direction 7. Sx and Sz magnetic susceptibilities Kubo formula: After analytical continuation: - Fermi function In the basis the matrix is sparse Particle-hole excitation region: Experimental observation: inelastic Raman spectroscopy Intensity of the scattered light polarization vectors of incident and scattered light Structure factor 9. Summary Charge-charge, charge-spin and spin-spin response functions of the 2DEG with Rashba are calculated in the clean limit. Coulomb interaction is further taken into account in the framework of the Equations of Motion in the Hubbard approximation (RPA + exchange). The dispersions and lifetimes of the collective charge and spin density excitations are studied using the renormalized response functions. Dispersions of the collective SDE modes are given by