Exchange fields and relaxation times in quantum dot
Final Report Abstract
In this project we have further developed a theoretical (density-operator) method for the calculation of transport properties of quantum dot systems. We have discovered a very general relation that strongly restricts the form of the time-evolution of such fermionic open systems. It is surprising that this has been overlooked so far since it originates from a fundamental principle of quantum physics which forbids superpositions of states with different fermion-number parity. Roughly speaking, the discovered ’duality’ relation maps the time-evolution problem of the open system to that of a (fictitious) dual open system with inverted energies. As a consequence, the measurable properties of a system of interest with repulsive interactions shows clear signatures of resonances of its dual ’partner’ system which has attractive interaction. We have demonstrated that this duality is already important for a quantum dot weakly coupled to a single electrode subjected to a sudden change in the gate-voltage (’quench’): the amplitudes of two components of the time-dependent heat-current show a sharp change when the gate voltage after the switch hits a pair-tunneling resonance of the dual quantum dot with attractive interaction, even though the actual system is repulsive. Importantly, the duality applies much more generally than this example, including strong coupling, low temperature and strong nonequilibrium conditions, as long as the energy-dependence of the coupling is weak (wide-band limit). It thus covers a wide range of problems of current interest in the physics of transport spectroscopy, quantum thermodynamics, open systems and quantum information. For example, relevant applications to thermoelectric response of quantum dots have already been found. The duality is not an isolated result, but underlies a complete reorganization of the description of how an open system interacts with its environment (superfermion perturbation theory). A second key result of this project is that we have shown that this approach allows for a drastic simplification of stationary heatcurrent calculations that go beyond the weak-coupling limit. It not only provides a large numerical speed up, but also allows the heat current to be decomposed into natural contributions, even though there is no conservation law for local energy transfer due to the system-reservoir coupling energy. This translates into an explicit contribution to the heat current that accounts for the Heisenberg energy uncertainty, in stark contrast to the charge current where no such explicit uncertainty term appears. Finally, the superfermion approach was shown to be useful in studying spintransport of noncollinear exchange biased quantum dots and a first connection to other techniques, such as nonequilibrium Green’s functions was established.
Publications
- Fermion-parity duality and energy relaxation in interacting open systems. Phys. Rev. B 93, 081411 (2016)
Schulenborg, J., Saptsov, R. B., Haupt, F., Splettstoesser, J. & Wegewijs, M. R.
(See online at https://doi.org/10.1103/PhysRevB.93.081411) - Relaxation of quantum dots in a magnetic field at finite bias charge, spin, and heat currents. physica status solidi (b) 254, 1600614 (2017)
Vanherck, J., Schulenborg, J., Saptsov, R. B., Splettstoesser, J. & Wegewijs, M. R.
(See online at https://doi.org/10.1002/pssb.201600614) - Transport and topological states in strongly correlated nanostructures (2017). (PhD thesis) Utrecht University
Gergs, N.
