Working with Tobias Holder, Ilia showed that an insulator's intrinsic capacitance comes from virtual transitions between occupied and empty bands. Its size is set by the quantum metric divided by the spectral gap, linking dielectric response to the real-space spread of the occupied wavefunctions.
The result applies across several classes of insulators, including Landau levels, hBN-aligned twisted bilayer graphene, and diamond. In the quantum Hall limit the capacitance is quantized, while in diamond the unusually large refractive index acquires a topological origin.
Read The quantum geometric origin of capacitance in insulators, published in Nature Communications.
