Linear and non-linear transport properties of quantum-dot devices - Guessi, Luiz Henrique Bugatti (2021)
This thesis investigates (i) the correlation effects in the emergence of bound states in the continuum (BIC); and (ii) non-equilibrium effects of the asymmetric two-channel Kondo problem. BICs are discrete states embedded in the continuum. They have localized wave-function and are originated by the quantum interference effects. In the first project of this thesis, we investigate the correlation effects in the emergence of a BIC in a two identical quantum dot device coupled to a quantum wire. This device was modeled by the two-impurity Anderson Hamiltonian and diagonalized via the Numerical Renormalization Group method. Given the symmetry between the quantum dots, the system was projected on the bonding and antibonding orbital representation resulting from the symmetric and antisymmetric combinations of the quantum dots, respectively. In the non-interacting regime, the antibonding orbital is a Friedrich-Wintgen BIC. As the Coulomb interaction grows, the antibonding orbital is indirectly coupled to the continuum via spin-spin and isospin-isospin interactions with the bonding orbital. In addition, at zero-temperature, the Coulomb interaction triggers a quantum phase transition between a magnetic and a non-magnetic phase. The magnetic phase is associated to the emergence of a bound spin state in the continuum (spin-BIC). The phase transition results from competition between a singlet isospin state, formed by the isospin-isospin interaction, and a triplet spin state, formed by the spin-spin interaction, between the two orbitals. The two phases are due to the conservation of the spin of the antibonding orbital. At low temperature, the spin-BIC interacts ferromagnetically with the conduction band, and the interaction renormalizes to zero as T → 0. In the second project of this thesis, motivated by a recent experiment [Z. Iftikhar et al., Nature 526, 233 (2015)], we investigate the transport properties of a macroscopic metallic island coupled to two leads. In the low-energy regime, only two charging states of the island are energetically accessible, which mimic a pseudospin-1/2. The charge fluctuations on the island emulate a spin-flip mechanism. Therefore, the low- energy physics of this device is well described by the anisotropic two-channel Kondo model. To explore the non-linear electronic transport, the system is driven out of equilibrium by the sudden application of a bias voltage between the leads. Time-dependent Density Matrix Renormalization Group computations follow the time evolution of the electrical current for times longer than the transient regime, although not long enough to reach the steady state. In the symmetric-coupling regime, the time-dependent current and differential conductance measurements show the universal behavior of the two-channel Kondo effect. In this limit, the differential conductance scales with the square root of the Kondo temperature and vary with the square of the bias voltage. In the presence of asymmetry, the transient behavior can be explained via energy-time uncertainty principle. As a function of the bias voltage, the conductance displays the expected crossover from non-Fermi liquid to Fermi-liquid behavior.