Periodic Reporting for period 4 - QUAHQ (PROBING EXOTIC QUANTUM HALL STATES WITH HEAT QUANTUM TRANSPORT)
Reporting period: 2023-08-01 to 2025-01-31
In extreme environmental conditions, such as very low temperatures and/or very high magnetic field, interactions between electrons in an otherwise electrically conducting material can cause this material to become in insulator. Understanding the physics that underlies those so called "correlated insulators" is one of the major challenges of condensed matter research. Indeed, making theoretical predictions on a system comprising a huge number of interacting particles is, to begin with, extremely difficult; furthermore, experimentally probing an electrically insulating system evidently rules out the use of electrical measurements.
The goal of the project QUAHQ is to tackle this experimental issue on a material that has driven a very large amount of novel research in the past decade, due to the many promises it holds both for fundamental and applied electronics. Under high magnetic field and at cryogenics temperatures, graphene can host electrically insulating, strongly correlated electronic states. These states are expected to host a number of charge neutral collective modes which can carry heat across the sample, and that directly reflect the intrinsic microscopic nature of the correlated states.
To probe these collective modes, we perform heat transport measurements in ultra-high quality graphene samples, cooled down to extremely low temperatures, and immersed in high magnetic fields. We are focusing our efforts on two classes of correlated states in graphene: the so-called "nu=0" state of the quantum Hall effect, which arises in a very peculiar point of the band structure of graphene where its valence and conduction bands touch one another; and fractional quantum Hall states, where interactions become dominant and give rise to excitations on the edge of the sample which have fractional charges.
The results of our investigations have shown that in contradiction to theoretical predictions, the nu=0 state is both an electrical and thermal insulator (Nat. Phys. 20, 1927 (2024))). Its thermal conduction properties were thought to arise from a spectrum of collective excitations carrying magnetic textures that remained ungapped; our results suggest that this spectrum actually has a significant gap, requiring further theoretical and experimental investigations. We also have demonstrated, again through heat transport, that neutral modes carrying heat in the direction opposite to that of the chiral charge carrying channels circulating along the edges of the sample in the fractional quantum Hall effect can exchange energy with the charged edge channel, regardless of the type of excitation the latter carry: fractional charge with anyonic quantum statistics, or integer charges with fermionic statistics. This result answers questions central to the community, and shows how one can control the electrostatics at the edge of a graphene sample (Phys. Rev. Lett. 129, 116803 (2022)).
These main results, as well as the rest of the work performed during the project, highlight the importance of heat transport measurements as a tool to investigate strongly correlated phases of matter.
The goal of the project QUAHQ is to tackle this experimental issue on a material that has driven a very large amount of novel research in the past decade, due to the many promises it holds both for fundamental and applied electronics. Under high magnetic field and at cryogenics temperatures, graphene can host electrically insulating, strongly correlated electronic states. These states are expected to host a number of charge neutral collective modes which can carry heat across the sample, and that directly reflect the intrinsic microscopic nature of the correlated states.
To probe these collective modes, we perform heat transport measurements in ultra-high quality graphene samples, cooled down to extremely low temperatures, and immersed in high magnetic fields. We are focusing our efforts on two classes of correlated states in graphene: the so-called "nu=0" state of the quantum Hall effect, which arises in a very peculiar point of the band structure of graphene where its valence and conduction bands touch one another; and fractional quantum Hall states, where interactions become dominant and give rise to excitations on the edge of the sample which have fractional charges.
The results of our investigations have shown that in contradiction to theoretical predictions, the nu=0 state is both an electrical and thermal insulator (Nat. Phys. 20, 1927 (2024))). Its thermal conduction properties were thought to arise from a spectrum of collective excitations carrying magnetic textures that remained ungapped; our results suggest that this spectrum actually has a significant gap, requiring further theoretical and experimental investigations. We also have demonstrated, again through heat transport, that neutral modes carrying heat in the direction opposite to that of the chiral charge carrying channels circulating along the edges of the sample in the fractional quantum Hall effect can exchange energy with the charged edge channel, regardless of the type of excitation the latter carry: fractional charge with anyonic quantum statistics, or integer charges with fermionic statistics. This result answers questions central to the community, and shows how one can control the electrostatics at the edge of a graphene sample (Phys. Rev. Lett. 129, 116803 (2022)).
These main results, as well as the rest of the work performed during the project, highlight the importance of heat transport measurements as a tool to investigate strongly correlated phases of matter.
During the first period of the project, we have set up our heat transport measurement platform, and developed and optimized our fabrication process. The measurement platform consists in a cryogen-free dilution refrigerator equipped with a large superconducting magnet, and wired to perform electrical and heat transport measurements down to extremely low temperatures. In particular, a major experimental challenge of the project QUAHQ is the ability to perform ultra-high sensitivity noise measurements so as to resolve local temperature changes of a fraction of milliKelvin (mK), from a base electronic temperature of about 10 mK. These changes are measured on micrometer-sized metallic islands electrically connected to the graphene crystal. We have optimized the fabrication process to enhance the connectivity of these islands while minimizing their size to suppress spurious heat transport due to crystalline phonons.
We now routinely measure the thermal conductance of chiral edge channels of the quantum Hall effect, for fully filled Landau levels, for partially filled Landau levels where spin and valley symmetries are broken, as well as , since very recently for fractional quantum Hall states. The obtained base electronic temperature (11 mK) is very close to the base temperature of the refrigerator, and among the lowest obtained in a cryogen free system under high magnetic field. This places us in a very competitive position with respect to other groups performing heat transport measurement in graphene.
The experiments performed during the second part of the project have directly addressed the questions central to the two WPs of the project. WP1 was focused on the thermal properties of the nu=0 state of graphene, which was thought to be a thermal conductor despite being an electric insulator. Surprisingly, we found out that it does not carry heat. We performed several check experiments, using complementary geometries and different device configuration, to assure the validity of our observations. This led to new technological developments of graphene heterostructures encompassing many different and independent functional layers. WP2 was focused on the neutral edge modes arising in the fractional quantum Hall effect, the central question around which is whether they carry energy ballistically, or lose energy to the charge carrying edge channels along their propagation. We managed to fully tune the coupling between the neutral modes and the charged edge channels, observing the transition from ballistic heat conduction by the neutral mode to its full suppression. Both results have been published in high impact scientific journals (Nature Physics at Physical Review Letters, respectively), and have been the subject of invited talks at international conferences, seminars, as well as internal communication. Our technological developmements led as well to the investigation of the electronic coherence properties of highly doped graphene under high magnetic field, whose result was published in Physical Review B.
We also investigated subjects closely related to the physics at the heart of the proposal: we observed an important increase in the shot noise generated in a graphene quantum point contact in the quantum Hall regime, highlighted the role of disorder in the temperature dependence of quantum Hall states of graphene, and realized an experimental simulator of a quantum Hall edge hosting strongly coupled counter-propagating edge channel. All three topics are the subject of articles currently being written, to be submitted in March-April 2025.
We now routinely measure the thermal conductance of chiral edge channels of the quantum Hall effect, for fully filled Landau levels, for partially filled Landau levels where spin and valley symmetries are broken, as well as , since very recently for fractional quantum Hall states. The obtained base electronic temperature (11 mK) is very close to the base temperature of the refrigerator, and among the lowest obtained in a cryogen free system under high magnetic field. This places us in a very competitive position with respect to other groups performing heat transport measurement in graphene.
The experiments performed during the second part of the project have directly addressed the questions central to the two WPs of the project. WP1 was focused on the thermal properties of the nu=0 state of graphene, which was thought to be a thermal conductor despite being an electric insulator. Surprisingly, we found out that it does not carry heat. We performed several check experiments, using complementary geometries and different device configuration, to assure the validity of our observations. This led to new technological developments of graphene heterostructures encompassing many different and independent functional layers. WP2 was focused on the neutral edge modes arising in the fractional quantum Hall effect, the central question around which is whether they carry energy ballistically, or lose energy to the charge carrying edge channels along their propagation. We managed to fully tune the coupling between the neutral modes and the charged edge channels, observing the transition from ballistic heat conduction by the neutral mode to its full suppression. Both results have been published in high impact scientific journals (Nature Physics at Physical Review Letters, respectively), and have been the subject of invited talks at international conferences, seminars, as well as internal communication. Our technological developmements led as well to the investigation of the electronic coherence properties of highly doped graphene under high magnetic field, whose result was published in Physical Review B.
We also investigated subjects closely related to the physics at the heart of the proposal: we observed an important increase in the shot noise generated in a graphene quantum point contact in the quantum Hall regime, highlighted the role of disorder in the temperature dependence of quantum Hall states of graphene, and realized an experimental simulator of a quantum Hall edge hosting strongly coupled counter-propagating edge channel. All three topics are the subject of articles currently being written, to be submitted in March-April 2025.
During the project, we have demonstrated the ability to perform heat transport measurement in graphene at the lowest electronic temperature in high complexity devices, largely advancing the state of the art. We have also demonstrated the ability to perform quantum transport measurements over more than three orders of magnitude of temperature range (10 mK-50 K) without having at fixed high magnetic field, up to 14 T. We have observed novel quantum Hall phases of graphene underhigh magnetic field which will require further confirmation and investigation.