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Heat equilibration of integer and fractional quantum Hall edge modes in graphene
Heat equilibration of integer and fractional quantum Hall edge modes in graphene
Neutral modes of the fractional quantum Hall effect have been shown to exchange energy with their fractionally charged counterparts, but it remains unknown whether they do so with the nearby integer quantum Hall edge channels. In our manuscript, we describe a heat transport experiment in graphene answering this question. By controlling the electrostatics of the edges, we observed a maximal suppression of the thermal conductance in the fractional quantum Hall regime, a clear signature of energy exchanges between integer edge channels and the neutral modes. Our work identifies a crucial issue for future quantum circuits in the quantum Hall regime.
The fractional quantum Hall effect is one of the most intriguing phenomena of condensed matter physics, where electronic interactions in a two-dimension electron gas subjected to a strong magnetic field lead to the emergence of highly exotic states with highly unusual properties. Among these, the existence of neutral edge modes, carrying only energy along the edges of the sample in a direction upstream to that of charge transport, has driven more than three decades of research. Their charge neutral nature has made them singularly challenging to probe, such that they were only first observed in 2010. Since then, many works have addressed the thermal transport properties of neutral modes, in particular whether they exchange energy with their neighboring counterpropagating charged edge modes. Significant progress was recently made on this topic, but an important question remained unanswered: can upstream neutral modes exchange energy and thermalize with integer¬-charged edge modes located up to several hundreds of nanometers away from them? This question is far from trivial, as it can profoundly change our understanding of the quantum Hall effect in terms of independent transport channels, and affect the realization of future experiments seeking to explore and exploit the remarkable properties of fractional quantum Hall states.
To address this question, we have performed heat transport measurements in a high quality graphene sample embedded in a van der Waals heterostructures. We measures the heat flow carried along the edge of the sample at very low temperatures and strong magnetic field. In the quantum Hall regime, the edge heat flow is quantized, generally reflecting the total number of ballistic integer and fractional edge modes flowing along the edge. Heat exchanges between the upstream neutral modes and the downstream charged modes decreases the edge heat flow: if all modes are fully thermalized, the heat flow reaches a quantized value given by the difference between the number of upstream and downstream modes. Importantly, if those two numbers are the same, the heat exchange are expected to take place over very large length, and can be essentially neglected.
Charged and neutral edge modes of the quantum Hall effect.
Charged and neutral edge modes of the quantum Hall effect.
Edge structure of the ν=8/3 state of the quantum Hall effect. The thick red arrows represent the two integer-charged edge modes, the thin red arrow the fractional-charged edge mode, and the blue dashed arrow the neutral mode. Electrical conductances of each mode are given on the right side.
We focused our investigation on the filling factor ν=8/3 of the fractional quantum Hall effect, the edge structure of which comprises two integer-charged downstream modes, one fractionally charged downstream mode and one upstream neutral mode. If the latter does not exchange energy with the integer modes, we expect to measure the equivalent quantized heat flow of 4 independent ballistic channels; if, on the contrary, if the neutral mode fully thermalizes with the integer mode, the heat flow is quantized to the equivalent of 2 ballistic channels.
Our results show that upon changing the edge electrostatics of our graphene sample, we were able to efficiently couple the neutral mode to the integer mode. This resulted in the observation of a transition from a non-equilibrated regime with a 4-channels quantized heat flow, to a fully equilibrated regime with a reduced 2-channels quantized heat flow.
Edge modes equilibration.
Edge modes equilibration.
Quantized heat flow at ν=8/3 measured as a function of the temperature. The non-equilibrated case is shown as dark red circles, and the equilibrated case as purple circles. The straight lines are the theoretical predictions for 4 and 2 channels quantized heat flow. The two cartoons illustrate the couplings between edge modes.
This work not only brings a clear answer on the energy exchanges between fractional and integer quantum Hall edge modes, but also stresses the central importance of edge electrostatics in the quantum Hall effect.
Heat Equilibration of Integer and Fractional Quantum Hall Edge Modes in Graphene
Heat Equilibration of Integer and Fractional Quantum Hall Edge Modes in Graphene
G. Le Breton, R. Delagrange, Y. Hong, M. Garg, K. Watanabe, T. Taniguchi, R. Ribeiro-Palau, P. Roulleau, P. Roche, and F. D. Parmentier
G. Le Breton, R. Delagrange, Y. Hong, M. Garg, K. Watanabe, T. Taniguchi, R. Ribeiro-Palau, P. Roulleau, P. Roche, and F. D. Parmentier
Physical Review Letters 129, 116803 (2022) (Editor's Suggestion)
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.116803
Vanishing bulk heat flow in the ν = 0 quantum Hall ferromagnet in monolayer graphene
Vanishing bulk heat flow in the ν = 0 quantum Hall ferromagnet in monolayer graphene
Graphene is a gapless semiconductor, meaning that it always conducts electricity, even at low temperature. However, under high magnetic field, it becomes an insulator, and its nature is still far from being fully understood. We have probed the thermal transport properties of this peculiar insulating state at low temperature and high magnetic field, and foundit is also a thermal insulator, in contradiction with recent theoretical predictions.
Under high magnetic field and at low temperature, graphene exhibits an unusual insulating state called ν=0, which stems from the interplay between electronic interactions and the intrinsic spin and valley symmetries of graphene. Despite almost two decades of intense theoretical and experimental work, the nature of ν=0 still remains a highly active and fascinating research domain. In particular, the various candidate ground states of ν=0 are quantum Hall ferromagnets with different spin and valley polarizations, providing a rich phase diagram with several experimentally accessible knobs. While most experiments probing ν=0 to date are based on electron transport, several recent theoretical works have suggested turning to thermal transport.
Indeed, not only is it quite evident to use thermal transport to probe an electrically insulating system, but, more fundamentally, the ferromagnetic nature of nu=0 endows its candidate ground states with a low energy excitation spectrum involving collective spin and valley waves which do not carry charge, but carry heat. Thus, the low temperature thermal transport properties of ν=0 directly reflect its ground state; particularly, the two most likely candidates have gapless spin/valley waves spectra, yielding a finite thermal conductance even at very low temperature.
Phase diagram of the ν=0 state.
The four possible ground states of ν=0, shown as two spins (red and blue arrows) distributed on the honeycomb lattice of graphene. Yellow: antiferromagnetic phase: the two opposite spins reside on a separate sublattice. Purple: ferromagnetic phase: the two spins are aligned, each on its sublattice. Orange: Kekule distorsion phase: the two opposite spins live on a superposition of the two sublattices. Cyan: sublattice polarized phase: the two opposite spins live on the same sublattice. The central cartoon depicts the principle of the experiment, where heat is carried for a hot electrode (red) to a cold one (purple) across ν=0. Only the antiferromagnetic and Kekule distorsion phase are thermal conductors at low temperature.
To probe the thermal conductance of ν=0, we have used a technique implemented at SPEC to measure thermal transport in graphene in the quantum Hall effect regime. It relies on the fact that Joule power is only dissipated in the electrodes of a sample in the quantum Hall regime, allowing to define hot electron reservoirs which exchange heat across a ν=0 region of a monolayer graphene sample. We have adapted this technique to several samples in complementary geometries allowing to probe both charge and thermal transport at ν=0.
ν=0 thermal transport samples.
Left: sketch of the “two-terminal” thermal transport geometry, allowing to measure the thermal flow between the source (red brick) and detector (purple brick) electrodes. The external parts of the sample allow controlling a measuring the source and detector temperature TS and TD. Right: optical micrograph of one of the devices fabricated to implement this geometry, along with the schematized experimental wiring.
Surprisingly, our experiment showed that no matter the sample geometry, magnetic field, and accessible temperatures, there was no significant thermal flow through ν=0, suggesting that it is both an electrical and thermal insulator. While this would point to one of the two thermally insulating ground states, the inconsistencies with previous experiments and the theoretical predictions hint that none of the candidate ground states may actually be thermal conductors, thereby calling for further experimental and theoretical investigations.
Typical results of the experiment. Left: temperatures of the source (red) and detector (purple) versus source heating current. As the source heats up, the detector stays at low temperature, heralding an absence of heating. Right: reverse situation with the detector being heated up, also leading to an absence of heating in the source.
Our results are published simultaneously with those obtained by a team at IISC Bengaluru (India), also demonstrating demonstrating a negligible heat flow for ν =0 in bilayer graphene, where the same physics is at play.
Vanishing bulk heat flow in the ν = 0 quantum Hall ferromagnet in monolayer graphene
R. Delagrange, M. Garg, G. Le Breton, A. Zhang, Q. Dong, Y. Jin, K. Watanabe, T. Taniguchi, P. Roulleau, O. Maillet, P. Roche, and F. D. Parmentier
Vanishing bulk heat flow in the ν = 0 quantum Hall ferromagnet in monolayer graphene
R. Delagrange, M. Garg, G. Le Breton, A. Zhang, Q. Dong, Y. Jin, K. Watanabe, T. Taniguchi, P. Roulleau, O. Maillet, P. Roche, and F. D. Parmentier
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