Coulomb staircase and total spin in quantum dots

The dependence of the Coulomb staircase on the total spin of a quantum dot is calculated at a current step corresponding to a transition between the ground states of two successive electron numbers. The ratio of the step heights for the positive and negative bias is simply the ratio of the spin degeneracies of the ground states, when tunneling rates across the two barriers are strongly asymmetric. This can be used for determining experimentally the total spin and therefore identifying the spin blockade. The in-plane magnetic-field dependence of the Coulomb staircase is also calculated, and it is shown that the relative height of spin-split steps can be used alternatively to determine the total spin.