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Physical Review Letters

Spin-Density Response Function in a 2D Electron System under a Magnetic Field

Kanako Yoshizawa, Natsuko Hirano, Kazuo Takayanagi

Published Aug 8, 2003• 4 citations
Publisher

Abstract

We study the spin density response function in a two-dimensional electron system under a strong perpendicular magnetic field. The theoretical framework is the extended RPA which takes into account all the second order self-energies of particle-hole propagators. Our results reproduce the data obtained by a light scattering experiment. We clarify how the extended RPA explains the empirical findings which are different even qualitatively from the RPA response. Especially the important role played by the two-particle-two-hole degrees of freedom is stressed.

DOI
10.1103/physrevlett.91.066802

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We study the spin density response function in a two-dimensional electron system under a strong perpendicular magnetic field. The theoretical framework is the extended RPA which takes into account all the second order self-energies of particle-hole propagators. Our results reproduce the data obtained by a light scattering experiment. We clarify how the extended RPA explains the empirical findings which are different even qualitatively from the RPA response. Especially the important role played by the two-particle-two-hole degrees of freedom is stressed.
Dynamical density and spin responses of a two-dimensional fermion system are studied with the self-consistent second-order perturbation theory using a model Hamiltonian. Special attention is paid to the density response at a large wave vector, where it was reported that a sharp mode develops below the particle-hole continuum in two-dimensional liquid 3{}^{3}3He. We find that at a large wave vector, a peak in the dynamical density structure factor shifts to lower energy as interaction sets in, but it is not sharp enough to represent a well-defined mode because of the strong damping effect of the quasiparticles. We point out that it is necessary to treat the large damping effect properly in explaining the propagating mode found in two-dimensional liquid 3{}^{3}3He.
In noninteracting two-dimensional (2D) electron systems, the extended states ``float up'' in energy in the vanishing perpendicular magnetic field ${B}_{\ensuremath{\perp}},$ giving rise to an insulator. However, in strongly interacting 2D systems, the extended states remain at a finite energy as ${B}_{\ensuremath{\perp}}\ensuremath{\rightarrow}0,$ thus allowing conduction. Here we show that polarizing the electrons' spins in strongly interacting systems causes the extended states to once more ``float up'' in energy, as they do for noninteracting electrons. The difference between extended states that float up (an insulator) or remain at a constant energy (a metal) is thus unambiguously tied to the existence of the spins.
Introduction and guide to the chapter Linear response functions contain a wealth of information about the physical properties of a many-body system. In the case of the electron liquid, for example, the density–density response function provides a unified framework for the understanding of different phenomena such as static screening, effective interaction, collective modes, electron energy loss spectra (inelastic scattering of electrons), and Raman spectra (inelastic scattering of photons). The spin–spin response function provides the corresponding information for the spin density fluctuations as probed, for example, by cross-polarized Raman scattering experiments, in which the incident and scattered photon have perpendicular polarizations, or by spin-flip electron energy loss spectroscopy, in which the incoming and outgoing electrons have opposite spin orientations. As we have seen, the Hartree–Fock approximation describes each electron as an independent particle moving in a self-consistent field generated by all the other electrons. There is no correlation between this self-consistent field and the instantaneous position of the electron. Reality is however quite different: whenever an electron moves, it acts on the surrounding electrons, causing a collective disturbance which eventually feeds back on its own motion. In order to study these effects we need, first of all, to learn how the electron liquid as a whole responds to disturbances caused by the charge, the spin, and the current of a single electron. The linear response theory of Chapter 3 provides the natural framework for this description. Strictly speaking, the linear response functions describe the readjustments of the electronic density, spin, or current, in response to externally controlled fields.
Two-dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many-particle ground state and its excitations are studied in detail at fractional filling factors for spin-polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.
Two-dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many-particle ground state and its excitations are studied in detail at fractional filling factors for spin-polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.
The parametrized form of local-field corrections is introduced to construct the dielectric function and the nonlocal spin susceptibility that describe the dielectric properties of a paramagnetic degenerate electron liquid in two dimensions beyond the random-phase approximation (RPA). The parameters that take into account the spin-parallel and spin-antiparallel electron-electron interactions at short distances are determined in such a way that the response functions correctly give the Monte Carlo values for the compressibility and the spin susceptibility, respectively, in the long-wavelength limit. The local-field correction thus obtained is compared with that in the Hubbard approximation; the static dielectric function and the spin susceptibility are also compared with those in the RPA. It is found that the sign of the static dielectric function depends on both the dimensionless coupling constant and the wave number, which is a feature markedly different from the RPA results.