[Paper Review] Non-linear regime for enhanced performance of an Aharonov-Bohm heat engine

Géraldine Haack, Francesco Giazotto|arXiv (Cornell University)|Jul 28, 2021

Quantum and electron transport phenomena26 references10 citations

TL;DR

This paper demonstrates that an Aharonov-Bohm (AB) interferometer operating as a quantum heat engine achieves significantly enhanced performance in the non-linear regime, with thermopower up to 50 times larger than in the linear regime and thermodynamic efficiency reaching ~40% of the Carnot limit. Using a scattering-matrix approach, the authors show tunable control via magnetic flux and gate voltage, enabling high power and efficiency simultaneously through optimal load resistance selection at cryogenic temperatures (Th = 2 K, Tc = 0.05 K).

ABSTRACT

Thermal transport and quantum thermodynamics at the nanoscale is nowadays garnering an increasing attention, in particular in the context of quantum technologies. Experiments relevant for quantum technology are expected to be performed in the non-linear regime. In this work, we build on previous results derived in the linear response regime for the performance of an Aharonov-Bohm (AB) interferometer operated as heat engine. In the non-linear regime, we demonstrate the tunability, large efficiency and thermopower that this mesoscopic quantum machine can achieve, confirming the exciting perspectives that this AB ring offers for developing efficient thermal machines in the fully quantum regime.

Motivation & Objective

• To investigate the performance of an Aharonov-Bohm interferometer as a quantum heat engine beyond the linear response regime.
• To explore the tunability of thermoelectric properties—thermovoltage, thermopower, and efficiency—via magnetic flux and gate voltage in the non-linear regime.
• To determine optimal operating conditions for maximizing both power output and thermodynamic efficiency in a phase-coherent mesoscopic system.
• To assess the relevance of electron-electron interactions and non-linear effects in quantum thermoelectric devices.

Proposed method

• Employed a scattering-matrix formalism to compute charge and heat currents in the AB ring under non-linear temperature bias.
• Calculated the differential Seebeck coefficient (thermopower) and thermovoltage in open-circuit configuration to characterize non-linear thermoelectric response.
• Modeled the AB ring transmission probability TAB(E, Vg, ϕ) as a function of energy, gate voltage Vg, and normalized magnetic flux ϕ = 2πΦAB/Φ0, incorporating dynamical and geometric phases.
• Analyzed closed-circuit operation by connecting the AB ring to a load resistor RL via superconducting lines to simulate real heat engine operation.
• Derived expressions for heat current Jh, output power P = (Vth^cl)^2 / RL, and efficiency η = P / Jh, and optimized RL for maximum P + η.
• Used numerical simulations with fixed parameters: Th = 2 K, Tc = 0.05 K, ε = 0.1, δτ = 0.3, and Rq = h/(2e^2) ≈ 6.45 kΩ.

Experimental results

Research questions

• RQ1 Can the thermoelectric performance of an AB interferometer be significantly enhanced in the non-linear response regime compared to the linear regime?
• RQ2 How does the differential Seebeck coefficient (thermopower) scale with magnetic flux and gate voltage in the non-linear regime?
• RQ3 What is the optimal load resistance RL that maximizes both power and efficiency in a non-linear AB heat engine?
• RQ4 To what extent can magnetic flux and gate voltage independently tune the thermoelectric response and efficiency of the device?
• RQ5 What is the achievable thermodynamic efficiency relative to the Carnot limit under non-linear conditions?

Key findings

• The differential Seebeck coefficient (thermopower) in the non-linear regime is approximately 50 times larger than in the linear regime, indicating a dramatic enhancement in thermoelectric response.
• The heat engine achieves a maximum efficiency of ~40% of the Carnot efficiency under optimal conditions, demonstrating high thermodynamic performance in the quantum regime.
• Power output exhibits strong non-linear dependence on magnetic flux ϕ and gate voltage Vg, with peak values observed at specific combinations of ϕ = π and Vg ≈ 1.4 mV.
• The optimal load resistance RL for maximizing both power and efficiency varies with gate voltage, with values ranging from 15Rq to 40Rq depending on Vg, indicating high tunability.
• Heat current Jh shows strong modulation with magnetic flux and gate voltage, peaking at ϕ = π and Vg ≈ 1.4 mV, consistent with power and efficiency trends.
• The system remains robust under realistic cryogenic conditions (Th = 2 K, Tc = 0.05 K), with tunable performance across a wide range of parameters, confirming feasibility for experimental realization.