Theory of multidimensional quantum capacitance and its application to spin and charge discrimination in quantum dot arrays

Quantum states of a few-particle system capacitively coupled to metal gate can be discriminated by measuring the quantum capacitance, which identified with second derivative energy respect voltage. This approach is here generalized multivoltage case, through introduction capacitance matrix. The matrix formalism allows us determine dependence on direction voltage oscillations in parameter space and identify optimal combination voltages. As representative example, this applied case dot array, described terms Hubbard model. Here, we first potentially relevant regions multidimensional boundaries between charge stability regions, determined within semiclassical approach. Then, quantitatively characterize such means Altogether, provides procedure for optimizing discrimination different particle numbers and/or total spins.