Electrically and thermally driven transport in interacting quantum dot structures

The main goal of this thesis is to study the quantum transport of quantum dot systems driven by voltage and thermal biases. Particularly, we study interacting single and double quantum dots yielding Coulomb blockade and Kondo effects giving an special emphasis at the thermally- driven response.

The first part of the thesis gives a general introduction of the main concepts of this thesis. Ch. 1 explains the fundamentals of a quantum dot and gives an overview of the most relevant experimental and theoretical works. Ch. 2 focuses on the Kondo effect, a paradigmatic many- body phenomenon which may appear in quantum dots at low temperatures. Ch. 3 summarizes the basic concepts of thermoelectrics including a discussion of state of the art involving quantum dots in the thermoelectric transport.

The models and theoretical techniques are discussed in the second part. Particularly, Ch. 4 introduces the nonequilibrium Green’s function formalism which will be used in the following chapters. Ch. 5 defines the Anderson Hamiltonian and transforms it into the slave-boson and Kondo Hamiltonians. In addition, we discuss the equation of motion technique for obtaining the retarded Green’s functions at several regimes and the slave-boson mean-field theory. In Ch. 6 we determine the current expressions required for the numerical calculations of the results.

Finally, the third part reveals the quantum transport results obtained for several quantum dot structures. Ch. 7 focuses on single quantum dots. First, we consider the transport across a quantum dot in the Coulomb blockade regime obtaining nonlinear thermoelectric effects such as nontrivial zeros in the thermocurrent or heat current asymmetries. Second, the Coulomb blockade theory is used to fit the results of a molecular junction experiment and, comparing with a noninteracting model, we propose the application of a magnetic field to distinguish between interacting and noninteracting molecules. The third work studies the thermally-driven response of a Kondo impurity using three different approaches covering different temperature regimes. We find that the Kondo resonance is quenched at large thermal biases implying nonlinear effects in the thermoelectric transport.

The works concerning double dot structures are explained in Ch. 8. First, the transport across a parallel-coupled double quantum dot with intradot Coulomb interactions is studied taking into account the formation of bound states in the continuum. We investigate how to detect such states using the electric and thermoelectric conductances. Second, we analyze the Coulomb drag effect in the Green’s function formalism obtaining the conditions to obtain drag currents. Finally, we focus on the nonlinear transport driven by thermal biases for a two-impurity system in the Fermi liquid regime. We observe different regimes depending on the coupling between impurities. Remarkably, the system decouples at large thermal bias since one Kondo resonance vanishes.

Ch. 9 contains the general conclusions of this thesis with a discussion about the limitations of the models used and suggesting further extensions.