Spin and Valley Noise in Two-Dimensional Dirac Materials

We develop a theory for optical Faraday rotation noise in two-dimensional Dirac materials. In contrast to spin noise in conventional semiconductors, we find that the Faraday rotation fluctuations are influenced not only by spins but also the valley degrees of freedom attributed to intervalley scattering processes. We illustrate our theory with two-dimensional transition-metal dichalcogenides and discuss signatures of spin and valley noise in the Faraday noise power spectrum. We propose optical Faraday noise spectroscopy as a technique for probing both spin and valley relaxation dynamics in two-dimensional Dirac materials.

Figure 1

Total noise power spectrum (solid black) and its valley (dashed blue) and spin (dashed red) components at ${\mathrm{\Omega }}_{\mathrm{eff}}>1/T_s,1/T_v$ with $T_s=31.42\mathrm{ns}$, $T_v=3.14\mathrm{ns}$, and ${\mathrm{\Omega }}_{\text{SO}}/2\pi =7\mathrm{GHz}$. (a) ${\mathrm{\Omega }}_L/2\pi =3.5\mathrm{GHz}$ (${\mathrm{\Omega }}_L<{\mathrm{\Omega }}_{\text{SO}}$), and (b) ${\mathrm{\Omega }}_L/2\pi =15\mathrm{GHz}$ (${\mathrm{\Omega }}_L>{\mathrm{\Omega }}_{\text{SO}}$). Faraday rotation is assumed equally sensitive to valley and spin (${\mathcal{L}}_{-}=0$).

Figure 2

Spin noise power spectrum at different values of the external in-plane magnetic field (along $x$) for $T_v\ll T_s$ and (a) $1/T_v\lesssim {\mathrm{\Omega }}_{\text{SO}}$ (${\mathrm{\Omega }}_{\text{SO}}/2\pi =480\mathrm{GHz}$) and (b) $1/T_v>{\mathrm{\Omega }}_{\text{SO}}$ (${\mathrm{\Omega }}_{\text{SO}}/2\pi =48\mathrm{GHz}$). Values of parameters used are $g$ factor $g=2$, $T_s=2\mathrm{ns}$, $T_v=1\mathrm{ps}$.