Stochastic Faraday rotation induced by the electric current fluctuations in nanosystems

Abstract

We demonstrate theoretically that in gyrotropic semiconductors and semiconductor nanosystems the Brownian motion of electrons results in temporal fluctuations of the polarization plane of light passing through or reflected from the structure, i.e., in stochastic Faraday or Kerr rotation effects. The theory of the effects is developed for a number of prominent gyrotropic systems such as bulk tellurium, ensembles of chiral carbon nanotubes, and GaAs-based quantum wells of different crystallographic orientations. We show that the power spectrum of these fluctuations in thermal equilibrium is proportional to the ac conductivity of the system. We evaluate contributions resulting from the fluctuations of the electric current, as well as of spin, valley polarization, and the spin current to the noise of the Faraday/Kerr rotation. Hence, all-optical measurements of the Faraday and Kerr rotation noise provide an access to the transport properties of the semiconductor systems.

Magnetospatial dispersion of semiconductor quantum wells

“…We can estimate the SIA parameter as ξ ∼ (e/ c)a 2 z lh1,hh1 , where a is the hole localization length in the QW structure, see Eq. (17). For a = 8 nm we get ξ ∼ (z lh1,hh1 /a) nmT −1 .…”

“…The polarization parameters of the reflected light observed in the experiment, Eq. ( 5), are given by [4,17]…”

Theory of optically detected spin noise in nanosystems

“…In this case the Faraday rotation noise spectrum is determined by the current noise spectrum [179]. The effects of this kind are possible in any gyrotropic system, for example, for ensembles of chiral nanotubes [180], and GaAs-based quantum wells with the crystallographic orientation [001] for the oblique incidence of light [181] (in this case the contribution of the spin current noise is also possible).…”

“…From this expression one can see, that k x transforms in the same was as σ z , so the fluctuations of the current along the x axis can lead to the rotation of the polarization plane of the incident light along with the spin noise. After the reflection of the incident wave, the polarization conversion is determined by the off-diagonal reflection coefficient [179] r xy = −r yx = P s s z + P j j x ,…”