Thermodynamic investigations of mesoscopic 2D systems – THERMES-2D

The measurement method adopted, based on AC calorimetry (2ω method), is particularly suited to mesoscopic systems at very low temperatures. It offers high sensitivity and overcomes certain limitations of more traditional approaches, such as relaxation or adiabatic methods. The work is based on several instrumental developments. It includes the manufacture of ultra-sensitive thermometers based on thin-film niobium nitride, optimised for low resistivity, high thermal sensitivity and compatibility with the system's micrometric environment. Their thermal and magnetoresistive behaviour has been studied in detail to enable their calibration and proper functioning under extreme conditions (T ~ 70 mK and up to B = 35 T). This study has identified the physical laws governing the magnetoresistance of Mott insulators, opening up new prospects for thermometry in magnetic fields and at low temperatures.

Significant effort has also been devoted to the fabrication of samples, including the production of mechanically suspended 2D gas membranes serving as calorimetric platforms. The basis for these samples are GaAs/AlGaAs heterostructures grown by molecular beam epitaxy (MBE). They incorporate a 2DEG and a micrometer thick sacrificial AlGaAs layer with high Al content. By selectively etching this layer, it has been possible to suspend the resulting 2DEG membrane without any degradation of the carrier mobility of the 2DEG. This work demonstrated that the quality of 2D gas is maintained after suspension and that thermal leaks can be limited to reduce the frequency of the adiabatic plateau required for specific heat measurement.

A comprehensive experimental setup has been designed to implement these measures. It incorporates electrical and thermal measurement chains, a suitable cryogenic architecture, and compatibility with intense magnetic fields. It allows the extreme conditions required to optimise the study of 2D gases in quantum Hall regime to be achieved. Its proper functioning has been validated experimentally, in particular by thermalising 2D gas wires smaller than the membranes to 14 mK. A protocol for researching and optimising the thermal signal was implemented on the samples, followed by a frequency scan to identify the adiabatic regimes of each one. This protocol also made it possible to quantify the thermal leaks in the membranes. Experimental signatures of the adiabatic plateau were observed on certain samples, thus validating the relevance of the approach and the device's ability to achieve the target regime under the defined experimental conditions. These results led to the definition of optimal experimental parameters and precise manufacturing criteria necessary to obtain reliable measurements. This work represents a significant advance in the development of thermodynamic techniques suitable for the study of low-temperature quantum electronic systems, and paves the way for direct experimental exploration of phase transitions in 2DEGs in the quantum regime.

Beyond the initial experimental results obtained, the work as a whole represents a significant step forward in the development of a calorimetric measurement platform suitable for nanometric electronic systems. It lays the foundations for future exploration of subtle thermodynamic phenomena in 2DEGs, such as phase transitions in the quantum Hall regimes, and more broadly, paves the way for the study of new quantum states of matter in two-dimensional nano- and microscopic systems. The behaviour under magnetic field was studied at a frequency of 65 kHz in order to approach the quasi-adiabatic regime while limiting capacitive couplings. Although the measurements carried out did not allow a conclusion to be drawn as to whether or not there were oscillating structures in the heat capacity as a function of the magnetic field, they represent a significant step forward in the implementation of the experiment. These results highlight the complexity of this work and the areas for improvement to be considered for the next steps in the study: reduction of noise signals, averaging over a large number of scans, extension of measurements to lower temperatures, and optimisation of membrane suspension conditions. This work also provides a solid basis for optimising thermometry by exploiting the properties of Mott-Anderson insulators at low temperatures and under magnetic fields, thus opening up prospects for the development of other measurement devices adapted to extreme experimental conditions.

Studies of electronic transport in GaAs/AlGaAs two-dimensional electron gases (2 DEGs.) have resulted in great advances in our understanding of mesoscopic and correlated physics. In particular, the exploration of the quantum Hall regime (QHR) has shown itself very advantageous, with its abundant physics of electron correlations, as well as the possibility to make use of the chiral transport in one-dimensional channels. In contrast, only recently have experiments shown the importance of thermodynamic investigations of low-dimensional and mesoscopic systems. With the THERMES-2D project we wish to develop novel, thermodynamic tools for the experimental study of mesoscopic, 2DEG-based systems, focusing on the specific heat cp, a bulk property with contributions from all degrees of freedom of a given thermodynamic system. The electron contribution to cp is a probe sensitive to quantum phase changes, excess of entropy, the electron density of states, and to the electronic effective mass. Within the frame of this project we will search for a better understanding of the correlated physics in the (fractional and integer) QHR
The THERMES-2D consortium exhibit an indispensible synergy for this purpose: the world-leading expertise in high sensitive specific heat measurements of the NEEL team, the capability of the C2N team to furnish the very special membrane samples needed, and the expertise in quantum Hall measurements at low temperatures and high magnetic fields of the LNCMI team. The concept is to study 2DEGs on sub-micrometer thin membranes using the unique NEEL nanocalometry setup, which allows us to measure extremely small specific heat variations at low temperature. In such samples the specific heat contribution from the GaAs substrate is limited, making it feasible to study the cp of the dilute electron gas. Combining the skills of the partners makes the project perfectly suited for exploring the rich 2D physics in high magnetic fields.
The electrons of a 2DEG condense into a sequence of distinct quantum phases, which makes the system an ideal test bed for specific heat studies of correlated physics. The competition between disorder, interaction and/or spin leads to a number of many-body quantum phases, such as fractional quantum Hall states, Wigner crystals, and ferromagnetic states. Through our cp measurements we will search for signatures of spin collective excitations (skyrmions), specific temperature-dependent features at the various phase boundaries, and the existence of new phase transitions between the quantum Hall states. In addition, the evaluation of the entropy of a 2DEG can provide important physical information. Though entropy is a fundamental thermodynamic quantity, its absolute value cannot be directly measured; only changes in entropy or relative values are physically relevant. The ideal way to gain access to this crucial thermodynamic quantity is by specific heat measurements versus temperature. An excess of entropy is predicted in various 2DEG states; it may be the signature of non-abelian anyon statistics or linked to quantum criticality at a quantum phase transition.
There is also a strong experimental motivation for pursuing the thermodynamic measurements on 2DEGs in this project. Following the demands of the compelling physics that we will encounter, we will push to extend this expertise even further, in terms of improvements in measurements at low temperature and low noise, in innovative thermometry, and in sample realisation.