  We study the local antisymmetric spin-orbit (ASO) coupling effect on spin,
orbital, and charge degrees of freedom for the Kondo effect in a triangular
triple quantum dot (TTQD). Here, one of the three QDs is coupled to a metallic
lead through electron tunneling, and a local electric polarization is induced
by the Kondo effect. The ASO interaction is introduced in the other two coupled
QDs on the opposite side of the lead. Generally, the ASO coupling effect is
very weak and not easily detectable, but it essentially causes spin and charge
reconfigurations in the TTQD through the Kondo effect. Using an extended
Anderson model for the TTQD Kondo system, we elucidate that the ASO coupling
gives rise to a considerable reduction of the emergent electric polarization,
as a consequence of the parity mixing of molecular orbitals in the triangular
loop as well as the spin-up and spin-down coupling of local electrons. The
latter leads to a local diamagnetic susceptibility owing to the ASO coupled
spins. We also show that the Kondo-induced electric polarization can be
controlled by the ASO coupling as well as by the magnetic flux penetrating
through the TTQD.
