Relaxation of quantum dots in a magnetic field at finite bias -- charge, spin and heat currents

Abstract

We perform a detailed study of the effect of finite bias and magnetic field on the tunneling-induced decay of the state of a quantum dot by applying a recently discovered general duality [PRB 93, 81411 (2016)]. This duality provides deep physical insight into the decay dynamics of electronic open quantum systems with strong Coulomb interaction. It associates the amplitudes of decay eigenmodes of the actual system to the eigenmodes of a so-called dual system with attractive interaction. Thereby, it predicts many surprising features in the transient transport and its dependence on experimental control parameters: the attractive interaction of the dual model shows up as sharp features in the amplitudes of measurable time-dependent currents through the actual repulsive system. In particular, for interacting quantum dots, the time-dependent heat current exhibits a decay mode that dissipates the interaction energy and that is tied to the fermion parity of the system. We show that its decay amplitude has an unexpected gate-voltage dependence that is robust up to sizable bias voltages and then bifurcates, reflecting that the Coulomb blockade is lifted in the dual system. Furthermore, combining our duality relation with the known Iche-duality, we derive new symmetry properties of the decay rates as a function of magnetic field and gate voltage. Finally, we quantify charge- and spin-mode mixing due to the magnetic field using a single mixing parameter.

14 pages, 6 figures

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• Role of electron-electron interaction in the Mpemba effect in quantum dots
• Thermovoltage in quantum dots with attractive interaction
• Spectroscopy of hot-electron pair emission from a driven quantum dot
• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor
• Fermionic duality: General symmetry of open systems with strong dissipation and memory