Thermopower of an SU(4) Kondo resonance under an SU(2) symmetry-breaking field

We calculate the thermopower of a quantum dot described by two doublets hybridized with two degenerate bands of two conducting leads, conserving orbital (band) and spin quantum numbers, as a function of the temperature T and a splitting delta of the quantum dot levels that breaks the SU(4) symmetry. The splitting can be regarded as a Zeeman (spin) or valley (orbital) splitting. We use the noncrossing approximation (NCA), the slave bosons in the mean-field approximation (SBMFA), and also the numerical renormalization group (NRG) for large delta . The model describes transport through clean C nanotubes and in Si fin-type field-effect transistors, under an applied magnetic field. The thermopower as a function of temperature S(T) displays two dips that correspond to the energy scales given by the Kondo temperature T sub(K) and delta and one peak when k sub(B)T reaches the charge-transfer energy. These features are much more pronounced than the corresponding ones in the conductance, indicating that the thermopower is a more sensitive probe of the electronic structure at intermediate or high energies. At low temperatures (T [Lt] T sub(K)), T sub(K)S(T)/T is a constant that increases strongly near the degeneracy point delta = 0. We find that the SBMFA fails to provide an accurate description of the thermopower for large delta . Instead, a combination of Fermi liquid relations with the quantum-dot occupations calculated within the NCA gives reliable results for T [Lt] T sub(K).