• Coulomb blockade
• heat rectification
• quantum dot

Nanodevices are attracting a lot of attention also for their thermoelectric properties, that are key to a more sustainable and efficient energy system.
Quantum dots (QDs) offer interesting possibilities for nanodevices thanks to their discrete energy spectrum, that allows only the electrons with the resonant energies to enter the QD.
Furthermore, if the capacitance of the QD is small, Coulomb interaction gives rise to a finite charging energy (E_C) that has to be overcome by an extra incoming electron in order to enter in the QD.
When E_C is large with respect to the thermal energy and chemical potential of the system, a single electron in the QD can prevent other electrons from entering, giving rise to the so-called Coulomb blockade.
This interaction between the electrons in the QD introduces nonlinearities in the thermoelectric properties.
One of the nanodevices that exploit such interaction is the thermal diode, a device that ”rectifies” heat allowing it to flow only in one direction, as the regular diode does with electrical current.
In this thesis we study the heat rectification in a QD that is connected to two metallic leads kept at different temperatures and chemical potentials.
First, we show some general properties of charge and heat current in the device and we define the rectification parameter R=|(J^++J^-)/(J^+-J^-)|, where J^+ is forward heat current, calculated when the left lead is hotter than the right lead, and J^- is the backward heat current, obtained when the right lead is hotter than the left lead, i.e. by reversing the temperatures of the two leads.
The rectification parameter R is 0 when J^+ and J^- have the same modulus but opposite sign, therefore there is no rectification.
Under the condition that the power generated by the QD is zero, R is bounded to be lower than 1, and reaches this value only when one of the currents J^+ and J^- is zero, i.e. for ideal rectification.
Then, we study the transport in the sequential tunneling regime, that accounts solely for the first order tunneling processes, which consist of single electrons hopping between the QD and the leads.
We calculate the heat currents and the rectification for a QD with two degenerate levels, two non-degenerate levels, and two N-degenerate levels.
We find that the rectification for the degenerate QD cannot exceed 1/5, while the rectification for the non-degenerate case can reach 1, which corresponds to perfect rectification.
However, at high values of R, the heat currents become exponentially small.
For the QD with two N-degenerate levels of different energies, we find that the currents increase with N, while the effects of the degeneracy on the rectification depend on the configuration of the system.
At last, we study the cotunneling processes, which are the second-order tunneling processes and become important when the sequential contribution to the transport is negligible.
We calculate the cotunneling contributions to the currents and we evaluate the rectification with the cotunneling contributions.
For the degenerate QD, we find that the cotunneling increases the maximum of the rectification when the temperature bias ΔT is smaller than 1.7T, where T is the average leads' temperature, while it decreases the maximum for ΔT>1.7T.
For the QD with two non-degenerate levels, the cotunneling decreases the maximum of the rectification.
However, we show that the cotunneling can increase the rectification near the peaks of the heat currents.
The increase of the degeneracy N of the QD levels increases the maximum of the rectification with respect to the sequential tunneling regime, but this maximum is obtained when the heat currents are near their minimum.