The density of states of proximitized normal nanowires interrupting superconducting rings can be tuned by the magnetic flux piercing the loop. Using these as the contacts of a single-electron transistor allows to control the energetic mirror asymmetry of the conductor, this way introducing rectification properties. In particular, we show that the system works as a diode that rectifies both charge and heat currents and whose polarity can be reversed by the magnetic field and a gate voltage. We emphasize the role of dissipation at the island. The coupling to substrate phonons enhances the effect and furthermore introduces a channel for phase tunable conversion of heat exchanged with the environment into electrical current.Nanometric electronic devices demand on-chip components that are driven by temperature gradients or that manage thermal flows. Indeed, nanoscale conductors are interesting in this sense because of their intrinsic nonlinearities, strong spectral features and tunability 1,2 . However, progress in this direction has been slow due to difficulties in the precise experimental detection of heat currents. Only very recently, great advances have been achieved in various mesoscopic configurations [3][4][5][6][7][8] . They open the way to realize theoretical proposals of heat to current converters 9-17 , refrigerators 18-26 , thermal transistors 27,28 and diodes 29-32 , and valves 33 in the lab.A thermal rectifier is a system that responds to reversed temperature gradients with currents of different magnitude 34 . For it to work as a thermal diode, forward and backward flows must be of different orders of magnitude. In electronic systems, this is the case for two terminal mesoscopic junctions with strong non-linearities due to Coulomb interactions 29,[35][36][37][38] or coupled to an additional thermal bath with which it exchanges energy but no charge [39][40][41][42][43] . The performance of the device is then controlled by an external parameter, typically a gate voltage. A requirement is the absence of mirror symmetry, which can also be introduced in the spectral properties of the contacts [30][31][32]44,45 .At low temperatures, hybrid metallic-superconducting junctions are interesting candidates as one can make use of the properties of single-electron tunneling in strongly interacting islands 46 and of the energy filtering introduced by the gap of the superconducting contacts. Here we investigate a superconducting quantum interference single-electron transistor (SQUISET), sketched in Fig. 1(a). Similar setups have recently been proposed 47 and implemented 48 as single-particle sources and heat valves 49 . It consists on a normal metal island in the strong Coulomb blockade regime such that its occupation fluctuates between n=0,1 extra electrons. It can be controlled by the voltage V g of a plunger gate coupled to it via a capacitance C g . The island is tunnel-coupled to two short wires that close two respective superconducting rings serving as contacts. Due to the proximity effect, the wires acquire a min...

We report on the results of an ab initio study of the thermodynamics of intrinsic point defects in the thermoelectric oxychalcogenide BiCuSeO. By using phase boundary mapping, we build a thermodynamic stability diagram that enables identification of several thermodynamic conditions that could be targeted experimentally in order to control the concentration of defects by tuning the chemical potential of the elements. In these conditions, the formation energies of selected intrinsic defects in their different possible charged states have been calculated. It shows that if the copper vacancy dominates the other defects over the whole energy band gap, V Bi vacancy as well as Cu Se substitution can also play a role in certain thermodynamic limits. Last, calculations of the equilibrium Fermi energy and defect concentrations show that native copper vacancies are responsible for the p-type conductivity in pristine BiCuSeO. They also give possible directions to achieve n-type conductivity in this system and to optimize the carrier concentrations in the p-type regime.