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.

arXiv comment14 pages, 6 figures

References in corpus (24)

• An On-Demand Coherent Single Electron Source
• Spontaneous Emission Spectrum in Double Quantum Dot Devices
• Single-electron current sources: towards a refined definition of ampere
• Mesoscopic quantum transport: Resonant tunneling in the presence of strong Coulomb interaction
• Resonant tunneling through ultrasmall quantum dots: zero-bias anomalies, magnetic field dependence, and boson-assisted transport
• Foundations and Measures of Quantum Non-Markovianity
• Tunneling through molecules and quantum dots: master-equation approaches
• A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
• Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model
• Clock-controlled emission of single-electron wavepackets in a solid-state circuit
• Fast electron thermometry towards ultra-sensitive calorimetric detection
• Partitioning of on-demand electron pairs
• Fast spin information transfer between distant quantum dots using individual electrons
• A two-atom electron pump
• Fermionic superoperators for zero-temperature non-linear transport: real-time perturbation theory and renormalization group for Anderson quantum dots
• Time scales in the dynamics of an interacting quantum dot
• Charge and spin dynamics in interacting quantum dots
• Real-time renormalization group in frequency space: A 2-loop analysis of the nonequilibrium anisotropic Kondo model at finite magnetic field
• Measurement and control of electron wave packets from a single-electron source
• Nonequilibrium charge-Kondo transport through negative-U molecules
• Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states
• Fermion-parity duality and energy relaxation in interacting open systems
• Time local master equation connecting the Born and Markov approximations
• Detection of the relaxation rates of an interacting quantum dot by a capacitively coupled sensor dot

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• The Interacting Mesoscopic Capacitor Out of Equilibrium
• Geometric energy transport and refrigeration with driven quantum dots
• Inverse counting statistics based on generalized factorial cumulants
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• Role of electron-electron interaction in the Mpemba effect in quantum dots
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• 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