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Physical review. B, Condensed matter

Collective excitations in an asymmetrically spin-polarized quantum well

D. C. Marinescu, J. J. Quinn

Published Nov 15, 1998• 2 citations
Publisher

Abstract

We present a phenomenological picture for the many-body excitations of a two-dimensional electron gas in a quantum well spin polarized by a dc magnetic field at an angle $\ensuremath{\theta}$ with the axis of the well. In the framework of the Landau theory of charged Fermi liquids, we determine the frequencies of collective modes by solving a transport equation for quasiparticles in the local electromagnetic field associated with the charge- and spin-density fluctuations. In the long-wavelength limit, analytic solutions for $\ensuremath{\omega}(\stackrel{\ensuremath{\rightarrow}}{q})$ are obtained as functions of the degree of spin polarization and of the angle $\ensuremath{\theta}.$

DOI
10.1103/physrevb.58.13762

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We present a phenomenological picture for the many-body excitations of a two-dimensional electron gas in a quantum well spin polarized by a dc magnetic field at an angle \ensuremathθ\ensuremath{\theta}\ensuremathθ with the axis of the well. In the framework of the Landau theory of charged Fermi liquids, we determine the frequencies of collective modes by solving a transport equation for quasiparticles in the local electromagnetic field associated with the charge- and spin-density fluctuations. In the long-wavelength limit, analytic solutions for \ensuremathω(q\ensuremath→)\ensuremath{\omega}(\stackrel{\ensuremath{\rightarrow}}{q})\ensuremathω(q\ensuremath→​) are obtained as functions of the degree of spin polarization and of the angle \ensuremathθ.\ensuremath{\theta}.\ensuremathθ.
We present the microscopic derivation of a quasiparticle pseudo-Hamiltonian for an infinitesimally polarized electron liquid. The Hamiltonian is expressed in terms of suitably defined quasiparticle operators. Our approach is based on a canonical transformation which allows one to replace the bare Coulombic coupling between the interacting electrons with an effective interaction between quasiparticles in which collective charge and spin fluctuations are explicitly accounted for. The relevant matrix elements of the charge and spin-density operators enter our theory via linear-response functions: the charge response, the longitudinal and transverse spin responses, and the mixed charge-spin response. These susceptibilities are in turn expressed in terms of the appropriate many-body local fields. As a consequence our method can be seen as an attempt to satisfactorily include in a self-consistent manner the effects of the vertex corrections associated with charge and spin-fluctuations of the electron liquid. As a result useful expressions for the quasiparticle energy and the effective interaction between two quasiparticles are determined. These can, in turn, be employed in a microscopic determination of the parameters of the Landau theory of the Fermi liquid. The generalization of our results to a multicomponent system is also discussed.
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The general interaction between quasiparticles and particle-hole excitations in a neutral Fermi system at T=0T=0T=0 is investigated. Density and spin-density fluctuations and collective modes are treated on an equal basis. Use is made of Ward identities to relate the vertex function $\ensuremath{\Gamma}$ to the quasiparticle self-energy $\ensuremath{\Sigma}$, and logarithmic corrections to the self-energy are obtained. The coefficients of the logarithmic terms are calculated analytically in terms of known Landau parameters.
We study the appearance of a sharp collective mode which features transverse current fluctuations within the bosonization approach to interacting two-dimensional Fermi liquids. This mode is analogous to the shear sound modes in elastic media, and, unlike the conventional zero sound mode, it is damped in weakly interacting Fermi liquids and only separates away from the particle-hole continuum when the quasiparticle mass becomes twice the transport mass ${m}^{*}\ensuremath{\gtrsim}2m$. The shear sound should be present in a large class of interacting charged and neutral Fermi liquids especially those proximate to critical points where the quasiparticle mass diverges. In metals this mode remains linearly dispersing in the presence of the long-ranged Coulomb force, unlike the conventional zero sound mode which becomes the plasma mode. We also detail a quick path between bosonization and classical Landau's Fermi liquid theory by constructing a mapping between the solutions of the classical kinetic equation and the quantized bosonic eigenmodes. By further mapping the kinetic equation into a one-dimensional tight-binding model we solve for the entire spectrum of collective and incoherent particle-hole excitations of Fermi liquids with nonzero F0{F}_{0}F0​ and F1{F}_{1}F1​ Landau parameters.
A Fermi liquid with spin-orbit coupling (SOC) is expected to support a new set of collective modes: oscillations of magnetization in the absence of the magnetic field. We show that these modes are damped by the electron-electron interaction even in the limit of an infinitely long wavelength (q=0). The linewidth of the collective mode is on the order of Δ¯2/E(F), where Δ¯ is a characteristic spin-orbit energy splitting and E(F) is the Fermi energy. Such damping is in stark contrast to known damping mechanisms of both charge and spin collective modes in the absence of SOC, all of which disappear at q=0, and arises because none of the components of total spin is conserved in the presence of SOC.
We present numerical calculations of the effect of electron-electron interactions on the quasiparticle properties such as the effective mass and the Land\'e ggg-factor in a GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs triangular quantum well from which the spin susceptibility is obtained. For this purpose, we consider quantum many-body effects associated with charge- and spin-density fluctuations induced many-body vertex corrections. The approach is based on the many-body local-field factors which are extracted from Fermi hypernetted-chain self-consistent calculation through the fluctuation-dissipation theorem. We find the spin susceptibility in good agreement with the recent experimental measurements and quantum Monte Carlo simulation data for such a system in the weak and intermediate coupling limits.