Zero-energy modes in serially coupled double quantum dots

We investigate symmetrically coupled double quantum dots via the hierarchical equations of motion method and propose a novel zero-energy mode (ZEM) at a temperature above the spin singlet-triplet transition temperature. Owing to the resonance of electron quasi-particle and hole quasi-particle, ZEM has a peak at ω=0 in the spectral density function. We further examine the effect of the magnetic field on the ZEM, where an entanglement of spin and charge has been determined; therefore, the magnetic field can split the ZEM in the spectra.