Analysis of low-energy response and possible emergent SU(4) Kondo state in a double quantum dot

We examine the low-energy behavior of a double quantum dot in a regime where spin and pseudospin excitations are degenerate. The individual quantum dots are described by Anderson impurity models with an on-site interaction U which are capacitively coupled by an interdot interaction U-12 < U. The low-energy response functions are expressed in terms of renormalized parameters, which can be deduced from an analysis of the fixed point in a numerical renormalization group calculation. At the point where the spin and pseudospin degrees of freedom become degenerate, the free quasiparticle excitations have a phase shift of pi/4 and a 4-fold degeneracy. We find, however, when the quasiparticle interactions are included, that the low-energy effective model has SU(4) symmetry only in the special case U-12 = U unless both U and U-12 are greater than D, the half bandwidth of the conduction electron bath. We show that the gate voltage dependence of the temperature-dependent differential conductance observed in recent experiments can be described by a quasiparticle density of states with temperature-dependent renormalized parameters.