Inelastic light scattering by 2D electron system with SO interaction
© Chaplik et al.; licensee Springer. 2012
Received: 16 July 2012
Accepted: 2 September 2012
Published: 28 September 2012
Inelastic light scattering by electrons of a two-dimensional system taking into account the Rashba spin-orbit interaction (SOI) in the conduction band is theoretically investigated. The case of resonance scattering (frequencies of incident and scattered light are close to the effective distance between conduction and spin-split-off bands of the AIIIBV-type semiconductor) is considered. As opposed to the case of SOI absence, the plasmon peak in the scattering occurs even at strictly perpendicular polarizations of the incident and scattered waves. Under definite geometry, one can observe the spectrum features conditioned by only single-particle transitions. In the general case of elliptically polarized incident and scattered light, the amplitude of the plasmon peak turns out to be sensitive to the sign of the SOI coupling.
It is well known that the spectrum of light scattering by a two-dimensional (2D) electron system is characterized by two contributions. One of them is determined by charge density excitations which is commonly called screened scattering. The shift of frequency equals the 2D plasmon frequency. The maximum of intensity of the corresponding peak in light scattering is reached when polarizations are parallel, and it is equal to 0 when polarizations are perpendicular.
The other contribution corresponds to single-particle excitations (SPE). The typical frequency shift is of the order q v F , where q is the wave vector transfer and v F is the Fermi velocity. The intensity of this peak is maximal for perpendicular polarizations of the incident and scattered waves. As to polarized scattering, the SPE contribution strongly depends on the resonance parameter (see): if the incident frequency is close to the effective bandgap (including the Moss-Burstein shift), the SPE peak can be comparable with the plasmon one.
The SOI substantially changes the spectrum of inelastic light scattering. A new peak (of a nontrivial shape) appears with the frequency shift equal to the spin splitting at the Fermi momentum. The polarization dependences are changed qualitatively. The plasmon peak can occur even at crossed polarizations. Finally, the left to right symmetry of circularly polarized incident light is violated: the cross section is invariant under simultaneous change of signs of polarizations and the SOI constant. This allows, in principle, to determine the sign of the Rashba constant experimentally.
Expressions for the scattering cross section
where f β ≡ f(ε β ), f(ε) is the Fermi distribution function, ε β is the energy of an electron in the conduction band, and.
where E g is the effective bandgap width,, P ≡ p cv /m0 is the Kane parameter, e1,2 are the polarizations of incident and scattered photons, and σ are the Pauli matrices. We treat here the enhanced resonant factor A in Equation 5 just as a constant that is true for not extremely resonant regime: the denominator in Equation 5 is much larger than the Fermi energy of electrons. We do this in order to simplify calculations because our main goal in this paper is to demonstrate the qualitatively new features of the scattering process due to spin-orbit interaction.
The values of Z and are given by expressions for L1 and in Equation 2 with γ replaced by γ2.
The contribution R1 determines the scattering of light by fluctuations of charge density. The value R2 determines unscreened mechanism of scattering and corresponds to single-particle excitations. It can be shown that in the absence of SOI in the conduction band, the values of Z and and, respectively, R3 and R4 are equal to 0 identically.
Results and discussion
Thus, allowing SOI essentially (qualitatively) changes the spectrum of inelastic light scattering by a 2D electron system. It should be especially noted that in the absence of external magnetic field, the symmetry between left and right polarizations is violated.
This research has been supported in part by RFBR grant nos. 11-02-00730 and 11-02-12142.
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