Imaging work and dissipation in the quantum Hall state in graphene.

Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations1,2. Dissipationless topologically protected states are therefore of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often susceptible to various dissipative mechanisms, which are difficult to study directly because of their microscopic origins. Here we use scanning nanothermometry3 to visualize and investigate the microscopic mechanisms that undermine dissipationless transport in the quantum Hall state in graphene. Simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries as a result of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work-generating process that we image directly, which involves elastic tunnelling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. By contrast, the heat and entropy generation process-which we visualize independently-occurs nonlocally upon resonant inelastic scattering from single atomic defects at graphene edges, and does not affect transport. Our findings provide an insight into the mechanisms that conceal the true topological protection, and suggest routes towards engineering more robust quantum states for device applications.

Publisher Correction: Imaging work and dissipation in the quantum Hall state in graphene.

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

Nanoscale thermal imaging of dissipation in quantum systems.

Energy dissipation is a fundamental process governing the dynamics of physical, chemical and biological systems. It is also one of the main characteristics that distinguish quantum from classical phenomena. In particular, in condensed matter physics, scattering mechanisms, loss of quantum information or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Yet the microscopic behaviour of a system is usually not formulated in terms of dissipation because energy dissipation is not a readily measurable quantity on the micrometre scale. Although nanoscale thermometry has gained much recent interest, existing thermal imaging methods are not sensitive enough for the study of quantum systems and are also unsuitable for the low-temperature operation that is required. Here we report a nano-thermometer based on a superconducting quantum interference device with a diameter of less than 50 nanometres that resides at the apex of a sharp pipette: it provides scanning cryogenic thermal sensing that is four orders of magnitude more sensitive than previous devices-below 1 µK Hz-1/2. This non-contact, non-invasive thermometry allows thermal imaging of very low intensity, nanoscale energy dissipation down to the fundamental Landauer limit of 40 femtowatts for continuous readout of a single qubit at one gigahertz at 4.2 kelvin. These advances enable the observation of changes in dissipation due to single-electron charging of individual quantum dots in carbon nanotubes. They also reveal a dissipation mechanism attributable to resonant localized states in graphene encapsulated within hexagonal boron nitride, opening the door to direct thermal imaging of nanoscale dissipation processes in quantum matter.

Hyperbolic enhancement of photocurrent patterns in minimally twisted bilayer graphene.

Quasi-periodic moiré patterns and their effect on electronic properties of twisted bilayer graphene have been intensely studied. At small twist angle θ, due to atomic reconstruction, the moiré superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride substrate is optically hyperbolic. Our results illustrate the capabilities of the nano-photocurrent technique for probing nanoscale electronic inhomogeneities in two-dimensional materials.

Nanoscale lattice dynamics in hexagonal boron nitride moiré superlattices.

Twisted two-dimensional van der Waals (vdW) heterostructures have unlocked a new means for manipulating the properties of quantum materials. The resulting mesoscopic moiré superlattices are accessible to a wide variety of scanning probes. To date, spatially-resolved techniques have prioritized electronic structure visualization, with lattice response experiments only in their infancy. Here, we therefore investigate lattice dynamics in twisted layers of hexagonal boron nitride (hBN), formed by a minute twist angle between two hBN monolayers assembled on a graphite substrate. Nano-infrared (nano-IR) spectroscopy reveals systematic variations of the in-plane optical phonon frequencies amongst the triangular domains and domain walls in the hBN moiré superlattices. Our first-principles calculations unveil a local and stacking-dependent interaction with the underlying graphite, prompting symmetry-breaking between the otherwise identical neighboring moiré domains of twisted hBN.

Probing dynamics and pinning of single vortices in superconductors at nanometer scales.

The dynamics of quantized magnetic vortices and their pinning by materials defects determine electromagnetic properties of superconductors, particularly their ability to carry non-dissipative currents. Despite recent advances in the understanding of the complex physics of vortex matter, the behavior of vortices driven by current through a multi-scale potential of the actual materials defects is still not well understood, mostly due to the scarcity of appropriate experimental tools capable of tracing vortex trajectories on nanometer scales. Using a novel scanning superconducting quantum interference microscope we report here an investigation of controlled dynamics of vortices in lead films with sub-Angstrom spatial resolution and unprecedented sensitivity. We measured, for the first time, the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized, including striking spring softening and broken-spring depinning, as well as spontaneous hysteretic switching between cellular vortex trajectories. Our results indicate the importance of thermal fluctuations even at 4.2 K and of the vital role of ripples in the pinning potential, giving new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors.