  We present a theory of tunneling spectroscopy of spin-selective Aharonov-Bohm
oscillations in a lateral triple quantum dot molecule. The theory combines
exact treatment of an isolated many-body system with the rate equation approach
when the quantum dot molecule is weakly connected to the leads subject to
arbitrary source-drain bias. The tunneling spectroscopy of the many-body
complex is analyzed using the spectral functions of the system and applied to
holes in a quantum dot molecule. Negative differential conductance is predicted
and explained as a result of the redistribution of the spectral weight between
transport channels. It is shown that different interference effects on singlet
and triplet hole states in a magnetic field lead to spin-selective
Aharonov-Bohm oscillations.
