Positive cross-correlations due to dynamical channel blockade in a three-terminal quantum dot

We investigate current fluctuations in a three-terminal quantum dot in the sequential tunneling regime. In the voltage-bias configuration chosen here, the circuit is operated as a beam splitter, i.e., one lead is used as an input and the other two as outputs. In the limit where a double occupancy of the dot is not possible, a super-Poissonian Fano factor of the current in the input lead and positive cross correlations between the current fluctuations in the two output leads can be obtained, due to dynamical channel blockade. When a single orbital of the dot transports current, these effects can be obtained by lifting the spin degeneracy of the circuit with ferromagnetic leads or with a magnetic field. When several orbitals participate in the electronic conduction, lifting spin degeneracy is not necessary. In all cases, we show that a super-Poissonian Fano factor for the input current is not equivalent to positive cross correlations between the outputs. We identify the conditions for obtaining these two effects and discuss possible experimental realizations.