Negative differential capacitance of quantum dots

The dependence of charges accumulated on a quantum dot under an external voltage bias is studied. The charge is sensitive to the changes of number of filled levels and the number of conducting levels ~channels!. We clarify that there are two possible outcomes of applying a bias. ~a! The number of conducting channels increases, but the number of filled levels decreases. ~b! The number of filled levels increases or does not change while the number of conducting channels ~levels! increases with the bias. In case ~b!, charges are generally expected to increase monotonically with the applied bias. We show, however, that this expectation may not materialize when the electron transmission coefficients depend on bias. Numerical evidences and a theoretical explanation of this negative differential capacitance, i.e., charges accumulated on a quantum dot decrease with applied bias, are presented.