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Ionic liquid gated field-effect transistors (FETs) based on semiconductingtransition metal dichalcogenides (TMDs) are used to study a rich variety ofextremely interesting physical phenomena, but important aspects of how chargecarriers are accumulated in these systems are not understood. We address theseissues by means of a systematic experimental study of transport in monolayerMoSe$_2$ and WSe$_2$ as a function of magnetic field and gate voltage,exploring accumulated densities of carriers ranging from approximately10$^{14}$ cm$^{-2}$ holes in the valence band to 4x10$^{14}$ cm$^{-2}$electrons in the conduction band. We identify the conditions when the chemicalpotential enters different valleys in the monolayer band structure (the K and Qvalley in the conduction band and the two spin-split K-valleys in the valenceband) and find that an independent electron picture describes the occupation ofstates well. Unexpectedly, however, the experiments show very large changes inthe device capacitance when multiple valleys are occupied that are not at allcompatible with the commonly expected quantum capacitance contribution of thesesystems, $\textit{C}$$_Q$=$\textit{e}^2$/(d$\mu$/d$\textit{n}$). Thisunexpected behavior is attributed to the presence of a cross quantumcapacitance, which originates from screening of the electric field generated bycharges on one plate from charges sitting on the other plate. Our findingstherefore reveal an important contribution to the capacitance of physicalsystems that had been virtually entirely neglected until now. (short abstractdue to size limitations - full abstract in the manuscript)

Band filling and cross quantum capacitance in ion gated semiconducting transition metal dichalcogenide monolayers