Gate-controlled transitions in triple dots with interdot repulsion and magnetic field

We study the quantum phase transition (QPT) and electronic transport in triple quantum dots for a wide range of the gate voltage ϵ. We focus on the effect of the interdot repulsion V and the magnetic field B. In the case of particle-hole (p-h) symmetry and B = 0, we find the local quadruplet-doublet transition of first order when V increases to a critical point Vc ≈ U, where U is the on-site repulsion. Beyond the p-h symmetry, the sequence of the QPTs depends on ϵ. For small ϵ, a first order doublet-singlet transition is observed. For middle ϵ, we find the quadruplet-triplet transition of first order at Vc1 and the triplet-singlet transition of the Kosterlitz-Thouless type at Vc2. For large ϵ, there are two kinds of first order QPT with phase sequence quadruplet-triplet-doublet. The magnetic field B compensates for the effect of V. For V > U, as B increases we find a first order or second order QPT from a low-spin state to a high-spin state. The restoring of the Kondo effect and a perfect spin filtering is realized in the appropriate regime of the magnetic field.