Critical Considerations for Observing Cross Quantum Capacitance in Electric-Double-Layer-Gated Transistors Based on Two-Dimensional Crystals

Cross quantum capacitance (CQC) has been proposed as an extension to traditional quantum capacitance (TQC) in systems where strong interfacial screening between spatially separated charge layers modifies the total capacitance—particularly in electric-double-layer-gated transistors (EDLTs) based on two-dimensional (2D) crystals. In this work, we revisit a theoretical model of CQC to evaluate its relevance under experimentally realistic conditions. By systematically analyzing the model’s behavior across key parameter spaces, we identify the specific conditions under which CQC leads to the non-monotonic dependence of capacitance on inter-plate distance—a proposed experimental signature of CQC. However, we find that these conditions—requiring similar effective masses, high charge densities, and strong charge asymmetry—are highly restrictive and difficult to realize in typical EDLTs. Instead, we highlight a more experimentally accessible regime in which CQC enhances total capacitance beyond TQC predictions, even in the absence of non-monotonicity. These results clarify the limitations of the existing model and suggest concrete strategies for probing CQC in nanoscale devices, emphasizing the need for new theoretical frameworks that explicitly incorporate both ionic and electronic conductors.