Quantum capacitance in two-dimensional TMDC semiconductors: effects of temperature, electric field, and spin–valley Zeeman field

We investigate the dependence of quantum capacitance $$\left({C}_{\text{Q}}\right)$$ C Q on the Fermi energy $$\left({E}_{\text{F}}\right)$$ E F in two-dimensional semiconductor materials belonging to the transition metal dichalcogenide (TMDC) family, taking into account the influences of external electric fields, Zeeman fields, and temperature. At low temperatures, distinct peaks and abrupt steps are clearly observed; whereas, at room temperature, these features are suppressed owing to thermal broadening from the Fermi–Dirac distribution. When external electric fields and Zeeman field components are introduced, the structure of $${C}_{\text{Q}}$$ C Q becomes more complex, exhibiting step-like features and deep valleys around the Fermi level. These reflect energy level splitting induced by spin–orbit coupling and valley polarization. A comparison among MoS2, MoSe2, WS2, and WSe2 reveals significant differences in the band gap width and density of states. These results demonstrate that the quantum capacitance in TMDCs is sensitive to external parameters, highlighting its potential for applications in quantum electronic devices, high-sensitivity sensors, and spintronic technologies based on two-dimensional materials. Graphical abstract