Herve Courtois

In this Perspective, we discuss thermal imbalance and the associated electron-mediated thermal transport in quantum electronic devices at very low temperatures. We first present the theoretical approaches describing heat transport in nanoscale conductors at low temperatures, in which quantum confinement and interactions play an important role. We then discuss the experimental techniques for generating and measuring heat currents and temperature gradients on the nanoscale. Eventually, we review the most important quantum effects on heat transport and discuss implications for quantum technologies and future directions in the field.

Hybridizing superconductivity with the quantum Hall (QH) effect has notable potential for designing circuits capable of inducing and manipulating non-Abelian states for topological quantum computation^1,2,3. However, despite recent experimental progress towards this hybridization^{4,5,6,7,8,9,10,11,12,13,14,15}, concrete evidence for a chiral QH Josephson junction¹⁶—the elemental building block for coherent superconducting QH circuits—is still lacking. Its expected signature is an unusual chiral supercurrent flowing in QH edge channels, which oscillates with a specific 2ϕ₀ magnetic flux periodicity^16,17,18,19 (ϕ₀ = h/2e is the superconducting flux quantum, where h is the Planck constant and e is the electron charge). Here we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit a chiral supercurrent, visible up to 8 T and carried by the spin-degenerate edge channel of the QH plateau of resistance h/2e² ≈ 12.9 kΩ. We observe reproducible 2ϕ₀-periodic oscillations of the supercurrent, which emerge at a constant filling factor when the area of the loop formed by the QH edge channel is constant, within a magnetic-length correction that we resolve in the data. Furthermore, by varying the junction geometry, we show that reducing the superconductor/normal interface length is crucial in obtaining a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface^19,20,21,22. Our findings are important for the exploration of correlated and fractional QH-based superconducting devices that host non-Abelian Majorana and parafermion zero modes^{23,24,25,26,27,28,29,30,31,32}.

Quantum Hall (QH) edge channels propagating along the periphery of two-dimensional (2D) electron gases under perpendicular magnetic field are a major paradigm in physics. However, groundbreaking experiments that could use them in graphene are hampered by the conjecture that QH edge channels undergo a reconstruction with additional nontopological upstream modes. By performing scanning tunneling spectroscopy up to the edge of a graphene flake on hexagonal boron nitride, we show that QH edge channels are confined to a few magnetic lengths at the crystal edges. This implies that they are ideal 1D chiral channels defined by boundary conditions of vanishing electronic wave functions at the crystal edges, hence free of electrostatic reconstruction. We further evidence a uniform charge carrier density at the edges, incompatible with the existence of upstream modes. This work has profound implications for electron and heat transport experiments in graphene-based systems and other 2D crystalline materials.

When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy^1,2,3,4,5. The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders^{6,7,8,9,10,11}. Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy¹² or by dielectric screening of the Coulomb interaction¹³. However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders¹⁴. Here we image three distinct broken-symmetry phases in graphene using scanning tunnelling spectroscopy. We explore the phase diagram by tuning the screening of the Coulomb interaction by a low- or high-dielectric-constant environment, and with a magnetic field. In the unscreened case, we find a Kekulé bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz–Thouless transition^15,16. Under dielectric screening, a sublattice-unpolarized ground state¹³ emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions^6,7,8,9,10. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

In a Josephson junction, which is the central element in superconducting quantum technology, irreversibility arises from abrupt slips of the gauge-invariant quantum phase difference across the contact. A quantum phase slip (QPS) is often visualized as the tunneling of a flux quantum in the transverse direction to the superconducting weak link, which produces dissipation. Here, we detect the instantaneous heat release caused by a QPS in a Josephson junction using time-resolved electron thermometry on a nanocalorimeter, signaled by an abrupt increase of the local electronic temperature in the weak link and subsequent relaxation back to equilibrium. Beyond providing a cornerstone in experimental quantum thermodynamics in form of observation of heat in an elementary quantum process, this result sets the ground for experimentally addressing the ubiquity of dissipation, including that in superconducting quantum sensors and qubits.

The Wiedemann–Franz law states that the charge conductance and the electronic contribution to the heat conductance are proportional. This sets stringent constraints on efficiency bounds for thermoelectric applications, which seek a large charge conduction in response to a small heat flow. We present experiments based on a quantum dot formed inside a semiconducting InAs nanowire transistor, in which the heat conduction can be tuned significantly below the Wiedemann–Franz prediction. Comparison with scattering theory shows that this is caused by quantum confinement and the resulting energy-selective transport properties of the quantum dot. Our results open up perspectives for tailoring independently the heat and electrical conduction properties in semiconductor nanostructures.