We formulate a general theory to study the time-dependent charge and energy transport of an adiabatically driven interacting quantum dot in contact to a reservoir for arbitrary amplitudes of the driving potential. We study within this framework the Anderson impurity model with a local ac gate voltage. We show that the exact adiabatic quantum dynamics of this system is fully determined by the behavior of the charge susceptibility of the frozen problem. At T = 0, we evaluate the dynamic response functions with the numerical renormalization group (NRG). The time-resolved heat production exhibits a pronounced feature described by an instantaneous Joule law characterized by an universal resistance quantum R 0 = h/(2e 2 ) for each spin channel. We show that this law holds in non-interacting as well as in the interacting system and also when the system is spin-polarized. In addition, in the presence of a static magnetic field, the interplay between many-body interactions and spin polarization leads to a non-trivial energy exchange between electrons with different spin components.
We study single-electron transport in a three-ion molecule with strong uniaxial anisotropy and in the presence of a transverse magnetic field. Two magnetic ions are connected to each other through a third, nonmagnetic ion. The magnetic ions are coupled to ideal metallic leads and a back gate voltage is applied to the molecule, forming a field-effect transistor. The microscopic Hamiltonian describing this system includes inter-ion hopping, on-site repulsions and magnetic anisotropies. For a range of values of the parameters of the Hamiltonian, we obtain an energy spectrum similar to that of single-molecule magnets in the giant spin approximation where the two states with maximum spin projection along the uniaxial anisotropy axis are well separated from other states. In addition, upon applying an external in-plane magnetic field, the energy gap between the ground and first excited states of the molecule oscillates, going to zero at certain special values of the field, analogous to the diabolical points resulting from Berry phase interference in the giant spin model. Thus, our microscopic model provides the same phenomenological behavior expected from the giant spin model of a single-molecule magnet but with direct access to the internal structure of the molecule, thus making it more appropriate for realistic electronic transport studies. To illustrate this point, the nonlinear electronic transport in the sequential tunneling regime is evaluated for values of the field near these degeneracy points. We show that the existence of these points has a clear signature in the I-V characteristics of the molecule, most notably the modulation of excitation lines in the differential conductance.
We study the adiabatic dynamics of the charge, spin and energy of a quantum dot with a Coulomb interaction under two-parameter driving, associated to time-dependent gate voltage and magnetic field. The quantum dot is coupled to a single reservoir at temperature T = 0 and the dynamical Onsager matrix is fully symmetric, hence, the net energy dynamics is fully dissipative. However, in the presence of many-body interactions, other interesting mechanisms take place, like the net exchange of work between the two types of forces and the nonequilibrium accumulation of charge with different spin orientations. The latter has a geometric nature. The dissipation takes place in the form of an instantaneous Joule law with the universal resistance R 0 = h/2e 2 . We show the relation between this Joule law and instantaneous fluctuation-dissipation relations. The latter lead to generalized Korringa-Shiba relations, valid in the Fermi-liquid regime.
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