Transport and Fluctuations in the Quantum Dot Heat Engine

Abstract

Quantum effects at the nanoscale offer significant potential for future device technologies. A quantum dot heat engine, for instance, is able to convert heat into electrical current. This thesis investigates the transport properties and current fluctuations in a single-level quantum dot heat engine operating in the sequential tunneling regime. Based on the existing experimental data, both the current and its noise characteristics are analyzed and interpreted. Electron transport is modelled with rate equations, and analytical expressions for the fluctuations are derived with full counting statistics. Theoretical models are fitted to experimental thermocurrent measurements to extract key parameters such as tunneling rates and reservoir temperatures. However, a difference is observed between measured and calculated current noise, with a factor of approximately 100. Further analysis attributes this deviation to the energy-level fluctuations induced by gate voltage instability, evidenced by 1/f-like noise in the power spectral density. These findings reveal that, in the experiment, gate voltage fluctuations dominate the overall noise characteristics, while the contribution from intrinsic electron transport is comparatively minor. The methods and models developed provide a framework for analyzing similar nanoscale heat engine systems and contribute to the broader understanding of fluctuation phenomena in nanoscale thermoelectric devices.

Popular Abstract

Imagine a tiny machine at the nanoscale that can generate an electric current from just a small amount of heat–that is a quantum dot heat engine! This thesis develops theoretical models to calculate how large and how steady the current is in such an engine. These quantities help us understand how the engine behaves and are also essential for designing future devices that can be both powerful and super-efficient. A quantum dot (QD) is ”quantum” because of its quantized energy levels, like the rungs of a ladder. It confines electron movement in all directions. Each rung in the QD ladder represents an energy level. Two electrons with opposite spin can occupy the same rung, which acts as a bridge connecting two electron reservoirs on both sides. A gate voltage can control which rung is accessible. The interesting part about QDs is that only one electron with the same ”height” (energy) as the rung can pass through. Since electrons can move in both directions, if the same number travel right as left, no net current exists. However, by introducing a temperature difference between the two reservoirs, the electron distribution varies and a current emerges Looking at the right side of the engine for example, the net flow of electrons is simply the number of electrons leaving the QD minus those entering from the right. These electrons shifting around can change the electron number on the rung at any moment. But eventually, the chance of finding 0, 1, or 2 electrons in the dot settles down. Under this steady-state condition, we can calculate the average current of the engine. To see how stable the current is over time, we look at its fluctuations around the average. We fully count the number of electrons crossing the QD to the right over a given time period. For easier analysis, we transform our perspective from the time domain to the frequency domain, allowing us to identify the patterns and find the noise sources. When we compared our calculations with the experimental measurements, the current formula did a good job of capturing the general behaviour (Fig.2). Small differences appeared, which we attributed to the approximations in our assumptions about electron hopping rates. Interestingly, the noise calculation from our model was surprisingly off by a factor of around 100 compared to the measurement (Fig.3). What caused this huge gap? We dug deeper, modelling the gate voltage fluctuations, which matched the measurement well! It turns out the gate voltage ”jiggles” are the dominant source of noise, hiding the more fundamentally interesting noise directly from temperature-induced electron transport. These findings offer valuable insights and practical guidance for improving experimental setups and future studies.

• author: Wu, Jiayang
• supervisor: Peter Samuelsson; Adam Burke
• organization: Mathematical Physics; Department of Physics
• course: PHYM03 20251
• year: 2025
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• language: English
• id: 9207540
• date added to LUP: 2025-07-07 09:49:11
• date last changed: 2025-07-07 09:49:11