A paper by the Erfu Liu Group and collaborators, “Excitonic Stark Response Induced by Quantum Capacitance in van der Waals Heterostructures,” has been published in Physical Review Letters. Xiangzhi Hong, a doctoral student at Nanjing University, is the first author, and Associate Professor Erfu Liu is the corresponding author. Congratulations to Xiangzhi Hong, Associate Professor Erfu Liu, and all coauthors.
In two-dimensional van der Waals heterostructures, top and bottom gates can tune carrier density and the out-of-plane electric field. The commonly used geometric capacitor model estimates the internal field from the applied voltages and device geometry. Interfacial charge transfer changes the charge distribution, however, and a finite electronic density of states introduces quantum capacitance. Together, these effects can make the actual internal field differ from the geometric prediction.
The team built a dual-gated device combining monolayer graphene and bilayer MoS₂, encapsulated in hexagonal boron nitride. Two interlayer excitons in bilayer MoS₂ have opposite out-of-plane electric dipoles, so their Stark shifts respond in opposite directions to a local electric field. Reflection-contrast measurements at about 6 K showed that the exciton energies still changed with doping when the externally applied gate field was held at zero, departing from the geometric model.
To identify the source of this discrepancy, the researchers compared bottom-gate and top-gate scans. In the former, the gate-induced and transferred-charge-induced fields change in the same direction. In the latter, the geometric model predicts that their changes cancel. Yet the top-gate scans produced different energy shifts for the two oppositely oriented excitons, indicating that the internal field was not fully canceled.
Exciton energies are also affected by many-body screening. The team compared the 1s and 2s states of both interlayer excitons and found that their level spacings changed nearly identically with doping. Together with an analysis of band-gap renormalization, this supports a largely symmetric many-body contribution. Taking the energy difference between the two exciton branches suppresses that contribution and isolates the residual Stark response.
The researchers attribute the residual response to graphene’s quantum capacitance. Part of the applied gate voltage changes graphene’s chemical potential, so less charge is transferred than the purely geometric model predicts. The carrier-induced field therefore does not fully cancel the gate-induced field. With graphene quantum capacitance included, the model describes the measured exciton splitting without additional fitting parameters. Experimental calibration further shows that changes in the splitting can be used to measure graphene’s local chemical potential quantitatively.
These results show that quantum-capacitance corrections matter when interfacial charge transfer occurs and quantum capacitance is comparable to the relevant geometric capacitance. Differential spectroscopy of opposite-dipole excitons offers a micrometer-scale optical probe of local electronic properties at buried interfaces under operating conditions.
Professor Baigeng Wang contributed to the theoretical interpretation. Takashi Taniguchi and Kenji Watanabe at the National Institute for Materials Science provided the hexagonal boron nitride crystals used in device fabrication.
Paper: Physical Review Letters 137, 186902 (2026).
