  We construct a theoretical model to study the orbital Kondo effect in a
parallel double quantum dot (DQD). Recently, pseudospin-resolved transport
spectroscopy of the orbital Kondo effect in a DQD has been experimentally
reported. The experiment revealed that when interdot tunneling is ignored,
there exist two and one Kondo peaks in the conductance-bias curve for the
pseudospin-non-resolved and pseudospin-resolved cases, respectively. Our
theoretical studies reproduce this experimental result. We also investigate the
situation of all lead voltages being non-equal (the complete
pseudospin-resolved case), and find that there are four Kondo peaks at most in
the curve of the conductance versus the pseudospin splitting energy. When the
interdot tunneling is introduced, some new Kondo peaks and dips can emerge.
Besides, the pseudospin transport and the pseudospin flipping current are also
studied in the DQD system. Since the pseudospin transport is much easier to be
controlled and measured than the real spin transport, it can be used to study
the physical phenomenon related to the spin transport.
