Testing Quantum Thermodynamics with local Probes – TQT

In our work we both applied existing theoretical methods, as well as developed new ones. On the one hand, we applied such well-established methods as Landauer scattering theory, heat transport equation, fluctuational electrodynamics, etc. On the other hand, in a common work of the two groups we developed a novel approach to describe spatially resolved dissipation in nanoscale transport: we combined a Boltzmann equation with the Landauer scattering theory and devised a numerical scheme to handle this problem. We have also developed a novel neural-network-based approach to reconstruct the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy.

Within the collaboration of the two partner teams at the IPCMS and the LPMMC, we have worked on the theory of spatially resolved energy dissipation in electronic quantum transport. As a first step towards a general theory describing coupled charge and heat flows, we have studied a model of electrons in two semi-infinite one-dimensional wires subject to a driving electric field and connected by a local elastic scatterer. The dissipation in the wires is taken into account in the framework of the Boltzmann equation within the relaxation-time approximation, and the scatterer leads to matching conditions between the electron distribution functions at the connection between the two wires.

While the voltage drop occurs in the vicinity of the scatterer, it turns out that the features of the spatial heating/cooling profile extend on distances of the order of the mean free path. Non-monotonic behaviour with heat spots and cool spots can occur depending on the energy-dependence of the transmission of the scatterer. In particular, we find cases where the heating/cooling behaviour differs qualitatively from expectations based on the Landauer scattering theory. Those findings are explained in detail in a paper [Leumer et al., arXiv:2407.10192] that has been written jointly by all members of the consortium.

The dependence of heat and charge transport on the energy-dependence of the transmission within the Landauer approach to scattering was studied by the IPCMS partner for the particular and experimentally relevant case of a model quantum point contact in a two-dimensional electron gas (2DEG) [Blaas-Anselmi et al., SciPost Phys. 12, 105 (2022)]. The relevance of transmission changes with energy for an asymmetric energy dissipation was confirmed. In parallel, a method was developed to extract the disorder potential seen by the electrons in a 2DEG from Scanning gate microscopy data [Percebois et al., SciPost Phys. 15, 242 (2023)].

The partner at the LPMMC has performed a study of the local heating provided by microwave radiation from a local tip on a superconductor [Karki et al., PRB 106, 155419 (2022)]. Interestingly, a bi-stability occurs in the balance between the conductivity-dependent heating and the phonon cooling, leading to stationary solutions at different temperatures. It was found that a small normal region can be induced under the tip, with a sharp domain wall, thereby providing a new way to locally probe the properties of superconducting samples. In parallel, a study of the possible performance of hot-carrier solar cells was performed [Tesser et al., PRApplied 19, 044038 (2023)]. It could be shown that such devices can possibly improve the output power and the efficiency.

With the understanding of the spatially resolved heating and cooling within a one-dimensional model with a local scatterer, it might become possible to study the more generic situation of two-dimensional systems scanned by a Scanning Thermal Microscope as it is the case in experiments, with the goal to better understand local heating and cooling in quantum transport that could then be exploited in experiments and in devices for applications.

The proposed local heating probe to investigate and manipulate superconducting materials also deserves more attention as it could become a new tool to probe the local properties of superconducting devices.

In one sentence, this project is about developing theories that explore how and where dissipation occurs in quantum transport through nanostructures, when such quantum transport is known to be "non-local". It is extremely timely because recent experimental breakthroughs in local probes have given unprecedented spatial resolution on where such dissipation occurs, and require quantitative theoretical analysis.

This theoretical project will use modelling of local probes of nanoscale systems to address fundamental questions in the field of quantum thermodynamics. Quantum thermodynamics is the study of heating, dissipation, and heat-to-work conversion in quantum systems which exhibit quantization, interference effects, entanglement, or other correlations between individual quantum particles. When applied to quantum transport in nanostructures, much of this physics is non-local. For example, it has long been known that interference effects are the result of an electron following multiple paths though a nanostructure, while correlations (including entanglement) between individual electrons occur at long range as a result of Coulomb interactions. However, exciting recent experiments by Zeldov and co-workers have confirmed in the starkest possible way the dissipation is also non-local. They did this using a SQUID-on-tip thermometer to achieve unprecedented spatial resolution of the heat dissipated in a nanoscale device, and showed that Joule heating occurs a significant distance away from the voltage drop (the resistance) that induces the Joule heating.

This project's objectives are twofold.
First, we will develop models of coupled charge and heat transport, and use them to describe the local thermal distribution in the vicinity of different nanoscale devices like quantum point contacts and quantum dots. The theory will be compared to the SQUID-on-tip thermometry experiments of Zeldov and co-workers, in which local temperature changes are detected by scanning a SQUID on a sharp tip (50nm in diameter) over the sample. This comparison will allow us to determine parameters and to validate the theoretical approach. We will then apply our theory to model cases of nanoscale thermal machines, including thermoelectric energy harvesters, heat-to-work conversion in quantum heat engines, and proposed devices that can act as Maxwell demons. For those systems that are potentially interesting for applications as quantum technology devices, we will explore the possibilities of using nanoscale thermometry to locate and understand undesired dissipation, with the aim of improving such thermal machines and other devices.
Second, we propose a new operation mode, a sort of thermal equivalent of a scanning gate microscope, for which we will develop the theory. We propose heating the tip (or an ac driving of the tip) to use it to heat/excite electrons locally in the sample being studied, and to measure its effect on the current flow in the device. This will have one big advantage over the conventional scanning gate microscope (which measures the effect of a charged tip on a samples' current flow); heat from a tip is not screened out by the electrons in the sample being studied (unlike the tip's charge). So this new probe should give us spatial information on current flow in metal and superconductor nanostructures, which have too much screening for scanning gate microscopy to be possible. This part of the project is to develop a quantitative theory for the information that this probe can extract.