Tuning Valley Polarization in a ${\mathrm{WSe}}_2$ Monolayer with a Tiny Magnetic Field

In monolayers of semiconducting transition metal dichalcogenides, the light helicity (${\sigma }^{+}$ or ${\sigma }^{-}$) is locked to the valley degree of freedom, leading to the possibility of optical initialization of distinct valley populations. However, an extremely rapid valley pseudospin relaxation (at the time scale of picoseconds) occurring for optically bright (electric-dipole active) excitons imposes some limitations on the development of opto-valleytronics. Here, we show that valley pseudospin relaxation of excitons can be significantly suppressed in a ${\mathrm{WSe}}_2$ monolayer, a direct-gap two-dimensional semiconductor with the exciton ground state being optically dark. We demonstrate that the already inefficient relaxation of the exciton pseudospin in such a system can be suppressed even further by the application of a tiny magnetic field of about 100 mT. Time-resolved spectroscopy reveals the pseudospin dynamics to be a two-step relaxation process. An initial decay of the pseudospin occurs at the level of dark excitons on a time scale of 100 ps, which is tunable with a magnetic field. This decay is followed by even longer decay ($>1\mathrm{ns}$), once the dark excitons form more complex pseudo-particles allowing for their radiative recombination. Our findings of slow valley pseudospin relaxation easily manipulated by the magnetic field open new prospects for engineering the dynamics of the valley pseudospin in transition metal dichalcogenides.

Popular Summary

The single-monolayer-thick layers of semiconducting transition metal dichalcogenides have a unique band structure consisting of two nonequivalent minima (valleys) of valence and conduction bands. This structure induces a novel degree of freedom—valley pseudospin—that, in analogy to the electronic spin in conventional semiconductors, may be exploited to store quantum information. However, a severe limitation for practical realization of this concept is imposed by the extremely short (i.e., picosecond) lifetime of the optically active electron-hole pairs (bright excitons) in such materials. Here, we focus on so-called dark excitons, show how to optically address their valley pseudospin, and demonstrate that it is conserved for orders of magnitude longer than for bright excitons.

Our experiment involves samples of tungsten diselenide monolayer, a two-dimensional semiconductor, held at low temperatures ($T=5\mathrm{K}$) in helium gas. We create dark excitons in a chosen valley using circularly polarized nonresonant optical excitation. We probe the dynamics of the valley pseudospin relaxation of these dark excitons using polarization and time-resolved measurements of the emission from low-energy localized excitons, which we show to be a product of the dark exciton relaxation. We determine the pseudospin depolarization time of the dark excitons to be roughly 100 ps, which is significantly longer than that of bright excitons. This dark exciton depolarization channel can be completely switched off by a tiny magnetic field less than 100 mT in strength.

Our findings reveal the hidden potential of dark excitons in the emerging field of opto-valleytronics. We anticipate that this potential will be exploited in future investigations of valley pseudospin in quantum information storage.

Figure 1

(a) PL spectra of a representative ${\mathrm{WSe}}_2$ monolayer (at $T=6.5\mathrm{K}$) excited with the ${\sigma }^{-}$ polarized light at $E=1915\mathrm{meV}$. The spectra were measured at zero field (solid lines) and at a magnetic field of 100 mT applied in the Faraday geometry (dashed lines). For each field, the spectra were detected in the two circular polarizations of opposite helicities (as indicated). (b) Color-scale map presenting the circular polarization degree of monolayer ${\mathrm{WSe}}_2$ PL as a function of magnetic field and emission energy. The plotted degree is obtained as an average of the two polarization degrees determined under the ${\sigma }^{-}$ and ${\sigma }^{+}$ polarized excitation. A pronounced decrease of the polarization degree at zero field is visible in the energy range corresponding to the emission of localized excitons. (c) Cross section presenting the magnetic-field dependence of the circular polarization degree of the localized excitons PL integrated over the emission energy ranging from $E=1650\mathrm{meV}$ to $E=1715\mathrm{meV}$. The solid line represents a fit with a formula $\mathcal{P}(B)\propto 1-\alpha /[1+(B-B_{\mathrm{rem}}{)}^2/B_0^2]$ accounting for the Lorentzian-like field dependence of the valley pseudospin relaxation rate in line with similar effects observed for real spins in conventional semiconductors [1, 23, 24, 25]. The parameter $\alpha$ corresponds to the percentage amplitude of the magnetic-field-induced dip in the polarization degree, $B_0$ represents the HWHM of the dip, while $B_{\mathrm{rem}}$ accounts for the remanent field of a superconducting coil. (d,e) The amplitude $\alpha$ (d) and HWHM $B_0$ (e) of the dip in the polarization degree determined for different emission energies.

Figure 2

(a) The circular polarization degree of the ${\mathrm{WSe}}_2$ monolayer PL measured vs the magnetic field in the energy range between $E=1650\mathrm{meV}$ and $E=1715\mathrm{meV}$, which corresponds to the emission band of the localized excitons. Each set of data points corresponds to a different orientation of the magnetic field, which is quantified by the angle ${\alpha }_B$ between the field vector and the out-of-plane direction $z$ [as schematically depicted in (b)]. The angles ${\alpha }_B$ were determined with an accuracy of less than 2°. (c) The inverse width $1/B_{1/2}$ of the magnetic-field-induced dip in the circular polarization degree as a function of $\cos ({\alpha }_B)$. The solid line represents the linear fit.

Figure 3

(a,b) Time-resolved PL of the localized excitons integrated over the emission energy ranging from $E=1635\mathrm{meV}$ to $E=1710\mathrm{meV}$. The temporal profiles were measured under the ${\sigma }^{+}$ polarized pulsed excitation at $E=1915\mathrm{meV}$ in two circular polarizations of detection and for two values of the magnetic field: $B=0$ (a) and $B=100\mathrm{mT}$ (b). The instrument response profile measured using a backscattered laser is shown for reference. (c) The circular polarization degree of the localized excitons emission measured under circularly polarized excitation as a function of time after the laser pulse for $B=0$ and $B=100\mathrm{mT}$. The temporal profile of the circular polarization degree showing no observable polarization under linearly polarized excitation is displayed for comparison. The solid lines in (a–c) represent the fit to the experimental data with the rate-equation model described in the text. (d) A scheme of the states and transitions included in the rate-equation model (a quantitative description of the model, together with the list of parameters used, is provided in Ref. [28]). The horizontal lines indicate the states, while the arrows mark the transitions. The color indicates the valley polarization (red: ${\sigma }^{+}$; blue: ${\sigma }^{-}$).