We report capacitive coupling induced Kondo–Fano (K–F) interference in a double quantum dot (DQD) by systematically investigating its low-temperature properties on the basis of hierarchical equations of motion evaluations. We show that the interdot capacitive coupling U 12 splits the singly-occupied (S-O) state in quantum dot 1 (QD1) into three quasi-particle substates: the unshifted S-O0 substate, and elevated S-O1 and S-O2. As U 12 increases, S-O2 and S-O1 successively cross through the Kondo resonance state at the Fermi level (ω = 0), resulting in the so-called Kondo-I (KI), K–F, and Kondo-II (KII) regimes. While both the KI and KII regimes have the conventional Kondo resonance properties, remarkable Kondo–Fano interference features are shown in the K–F regime. In the view of scattering, we propose that the phase shift η(ω) is suitable for analysis of the Kondo–Fano interference. We present a general approach for calculating η(ω) and applying it to the DQD in the K–F regime where the two maxima of η(ω = 0) characterize the interferences between the Kondo resonance state and S-O2 and S-O1 substates, respectively.
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.
We investigate low-temperature spin and charge (orbital) Kondo effect of capacitively hierarchical equations of motion. In a charge stability diagram at finite interdot Coulomb repulsion, a line between triple points (LBTP) serves as the degeneracy of charge configuration states. With one electron difference on each dot, these charge configuration states can be regarded as pseudospins. It is shown that charge can also screen its counterpart through the high-order process using tunnelling-coupled reservoirs. In the charge configuration regime , in addition to the spin Kondo effect, the degeneracy and detuning of charge configuration states and may also cause a charge Kondo resonance that agrees with the experiments on triple-peak structures with differential conductance.
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