Landau-Level Spectrum and the Effect of Spin–Orbit Coupling in Monolayer Graphene on Transition Metal Dichalcogenides

Abstract

In graphene on transition metal dichalcogenides, two types of spin–orbit coupling (SOC)—Rashba and spin–valley Zeeman SOCs—can coexist that modify graphene's electronic band differently. Herein, it is shown that the Landau levels (LLs) are also affected by these SOCs distinctively enough to estimate their relative strengths from the Landau fan diagram. A simple theoretical model is used to calculate the LL spectra of graphene for different SOC strengths, revealing 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, the four key features that are well separated from the complex background are first identified and compared with experiment to show that in the sample investigated, the Rashba SOC is stronger than the spin–valley Zeeman SOC consistent with other spectroscopic measurements. The study therefore provides a simple and practical strategy to analyze the LL spectrum in graphene with SOC before carrying out more in-depth measurements.