Magnetic Control of Valley Pseudospin in Monolayer WSe2

The peak splitting due to the valley Zeeman effect is small compared to the width of the photoluminescence (PL) peaks so care must be taken in determining the Zeeman splitting. The peaks are slightly asymmetric, with shape varying somewhat with magnetic field, and do not conform well to a Gaussian or Lorentzian peak shape. We use two methods to determine the peak position and hence the Zeeman splitting, both of which make no assumptions about the peak shape. As shown in Figure 1c, they agree very well. The first, “max point”, simply finds the 15 points in each spectrum with the most counts and assigns the peak position to the median value of these points. This method is insensitive to the trion peak, which is too far away to influence these points; however, it is more sensitive to noise as it only considers a few points. The second method, “weighted average”, computes the “center of mass” of the peak, , where is the PL spectral density and E is photon energy. In this method the effect of noise is greatly reduced because it makes use of all the several hundred points that make up the spectrum, but on the other hand it is more sensitive to the trion peak, which will tend to over-weight the low-energy side of the peak. However, since the valley exciton Zeeman splitting is small and we are interested in the difference between the σ+ and σpeaks, the weak trion effects on both peaks tend to balance each other out. The data in Fig. 1c and Fig. S1a are from two different samples. We can see that the splitting as a function of magnetic field obtained by these two different methods has little difference.