François D. Parmentier

Graphene, through the coexistence of large cyclotron gaps and small spin and valley gaps, offers the possibility to study the breakdown of the quantum Hall effect (QHE) across a wide range of energy scales. In this Letter, we investigate the breakdown of the QHE in high-mobility graphene Corbino devices under broadband excitation ranging from dc up to 10 GHz. We find that the conductance is consistently described by variable range hopping (VRH) and extract the hopping energies from both temperature- and field-driven measurements. Using VRH thermometry, we can distinguish between non-Ohmic and Ohmic regimes of bulk conduction, which are dominated by electric-field-assisted VRH and Joule heating, respectively. Our results demonstrate that the breakdown in the quantum Hall regime of graphene is governed by a crossover from non-Ohmic, field-driven VRH to Ohmic, Joule-heating-dominated transport.

Heat flow in the Chern Insulator states of the Hofstadter butterfly is obtained in a graphene/hBN moir\'e for the first time.

Coulomb interactions deeply affect quantum transport in simple ballistic systems, but their impact on scaled up ballistic structures remains underexplored. Here, we theoretically consider a chain of small metallic dots with frozen charge dynamics connected by ballistic channels. We identify a neutral mode of transport that is specific to a chain with at least two islands and entwines local diffusion by neutral excitations with long-range correlations between the islands' charge states. We show, as an experimentally measurable signature of this many-body behavior, that the Wiedemann-Franz law is violated with a Lorenz ratio scaling as the square root of the chain's length.

Exotic quantum Hall systems hosting counterpropagating edge states can show seemingly nonuniversal transport regimes, usually depending on the size of the sample. We experimentally probe transport in a quantum Hall sample engineered to host a tunable number of counterpropagating edge states. The latter are coupled by Landauer reservoirs, which force charge equilibration over a tunable effective length. We show that charge transport is determined by the balance of up- and downstream channels, with a ballistic regime emerging for unequal numbers of channels. For equal numbers, we observe a transition to a critical diffusive regime, characterized by a diverging equilibration length. Our approach allows simulating the equilibration of hole-conjugate states and other exotic quantum Hall effects with fully controlled parameters using well-understood quantum Hall states.

Recent low-temperature electron transport experiments in high-quality graphene rely on a technique of doped graphene leads, where the coupling between the graphene flake and its metallic contacts is increased by locally tuning graphene to high doping near the contacts. While this technique is widely used and has demonstrated its usefulness numerous times, little is known about the actual transport properties of the doped graphene leads. Here, we present an experiment probing those properties in the quantum Hall regime at low temperature and high magnetic field, showing that electronic phase coherence and transport chirality are preserved, despite the significant charge equilibration occurring at the edges of the leads. Our work yields a finer understanding of the properties of the doped graphene leads, allowing for improvements of the contact quality that can be applied to other two-dimensional materials.

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states, e.g. , snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach–Zender and Fabry–Perot interferometers.

Flying qubits encode quantum information in propagating modes instead of stationary discrete states. Although photonic flying qubits are available, the weak interaction between photons limits the efficiency of conditional quantum gates. Conversely, electronic flying qubits can use Coulomb interactions, but the weaker quantum coherence in conventional semiconductors has hindered their realization. In this work, we engineered on-demand injection of a single electronic flying qubit state and its manipulation over the Bloch sphere. The flying qubit is a Leviton propagating in quantum Hall edge channels of a high-mobility graphene monolayer. Although single-shot qubit readout and two-qubit operations are still needed for a viable manipulation of flying qubits, the coherent manipulation of an itinerant electronic state at the single-electron level presents a highly promising alternative to conventional qubits.

Over the past 20 years, many efforts have been made to understand and control decoherence in 2D electron systems. In particular, several types of electronic interferometers have been considered in GaAs heterostructures, in order to protect the interfering electrons from decoherence. Nevertheless, it is now understood that several intrinsic decoherence sources fundamentally limit more advanced quantum manipulations. Here, we show that graphene offers a unique possibility to reach a regime where the decoherence is frozen and to study unexplored regimes of electron interferometry. We probe the decoherence of electron channels in a graphene quantum Hall PN junction, forming a Mach-Zehnder interferometer^1,2, and unveil a scaling behavior of decay of the interference visibility with the temperature scaled by the interferometer length. It exhibits a remarkable crossover from an exponential decay at higher temperature to an algebraic decay at lower temperature where almost no decoherence occurs, a regime previously unobserved in GaAs interferometers.