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

TL;DR

This paper investigates how finite bias and magnetic fields influence the decay dynamics of quantum dot states, revealing duality-based insights into charge, spin, and heat transport with novel symmetry and decay features.

Contribution

It introduces a duality approach to analyze decay modes in quantum dots under bias and magnetic field, uncovering unexpected gate-voltage dependence and symmetry properties.

Findings

Decay modes linked to fermion parity show robust gate-voltage dependence.

Duality predicts sharp features in transient currents due to attractive interactions.

Magnetic field induces charge-spin mode mixing quantified by a single parameter.

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.