  In graphene on transition metal dichalcogenides, proximity-induced Rashba and
spin-valley Zeeman SOCs can coexist that modify graphene's electronic band
differently. Here, we show that the Landau levels (LLs) are also affected by
these SOCs distinctively enough to estimate their relative strengths from the
Landau fan diagram. Using a simple theoretical model, we calculated the LL
spectrums of graphene for different SOC strengths, and found that when the
total SOC is strong enough (i.e., when it is comparable to the half of the
energy gap between the LLs of an intrinsic graphene), the corresponding LLs
will split and cross with others depending sensitively on the relative
strengths of the SOC terms. To demonstrate how one can use it to estimate the
relative SOC strengths, we first identified the four key features that are well
separated from the complex background and can be compared with experiment
directly, and used them to show that in our sample, the Rashba SOC is stronger
than the spin-valley Zeeman SOC that is consistent with other spectroscopic
measurements. Our study therefore provides a simple and practical strategy to
analyze the LL spectrum in graphene with SOC before carrying out more in-depth
measurements.
