Heat conductance of the quantum Hall bulk.

The quantum Hall effect is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions and disorder1-9. The disorder enables the formation of localized states in the bulk that stabilize the quantum Hall states with respect to the magnetic field and carrier density3. Still, the details of the localized states and their contribution to transport remain beyond the reach of most experimental techniques10-31. Here we describe an extensive study of the bulk's heat conductance. Using a novel 'multiterminal' short device (on a scale of 10 µm), we separate the longitudinal thermal conductance, [Formula: see text] (owing to the bulk's contribution), from the topological transverse value [Formula: see text] by eliminating the contribution of the edge modes24. When the magnetic field is tuned away from the conductance plateau centre, the localized states in the bulk conduct heat efficiently ([Formula: see text]), whereas the bulk remains electrically insulating. Fractional states in the first excited Landau level, such as the [Formula: see text] and [Formula: see text], conduct heat throughout the plateau with a finite [Formula: see text]. We propose a theoretical model that identifies the localized states as the cause of the finite heat conductance, agreeing qualitatively with our experimental findings.

Integrating data types to estimate spatial patterns of avian migration across the Western Hemisphere.

For many avian species, spatial migration patterns remain largely undescribed, especially across hemispheric extents. Recent advancements in tracking technologies and high-resolution species distribution models (i.e., eBird Status and Trends products) provide new insights into migratory bird movements and offer a promising opportunity for integrating independent data sources to describe avian migration. Here, we present a three-stage modeling framework for estimating spatial patterns of avian migration. First, we integrate tracking and band re-encounter data to quantify migratory connectivity, defined as the relative proportions of individuals migrating between breeding and nonbreeding regions. Next, we use estimated connectivity proportions along with eBird occurrence probabilities to produce probabilistic least-cost path (LCP) indices. In a final step, we use generalized additive mixed models (GAMMs) both to evaluate the ability of LCP indices to accurately predict (i.e., as a covariate) observed locations derived from tracking and band re-encounter data sets versus pseudo-absence locations during migratory periods and to create a fully integrated (i.e., eBird occurrence, LCP, and tracking/band re-encounter data) spatial prediction index for mapping species-specific seasonal migrations. To illustrate this approach, we apply this framework to describe seasonal migrations of 12 bird species across the Western Hemisphere during pre- and postbreeding migratory periods (i.e., spring and fall, respectively). We found that including LCP indices with eBird occurrence in GAMMs generally improved the ability to accurately predict observed migratory locations compared to models with eBird occurrence alone. Using three performance metrics, the eBird + LCP model demonstrated equivalent or superior fit relative to the eBird-only model for 22 of 24 species-season GAMMs. In particular, the integrated index filled in spatial gaps for species with over-water movements and those that migrated over land where there were few eBird sightings and, thus, low predictive ability of eBird occurrence probabilities (e.g., Amazonian rainforest in South America). This methodology of combining individual-based seasonal movement data with temporally dynamic species distribution models provides a comprehensive approach to integrating multiple data types to describe broad-scale spatial patterns of animal movement. Further development and customization of this approach will continue to advance knowledge about the full annual cycle and conservation of migratory birds.

Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale.

Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream propagating edge modes, which leads to complex transport behavior. Here, we combine two measurement techniques, local noise thermometry and thermal conductance, to study thermal properties of states with counter-propagating edge modes. We find that, while charge equilibration between counter-propagating edge modes is very fast, the equilibration of heat is extremely inefficient, leading to an almost ballistic heat transport over macroscopic distances. Moreover, we observe an emergent quantization of the heat conductance associated with a strong interaction fixed point of the edge modes. Such understanding of the thermal equilibration on edges with counter-propagating modes is a natural route towards extracting the topological order of the exotic 5/2 state.

Distinguishing between non-abelian topological orders in a quantum Hall system.

Quantum Hall states can harbor exotic quantum phases. The nature of these states is reflected in the gapless edge modes owing to "bulk-edge" correspondence. The most studied putative non-abelian state is the spin-polarized filling factor (ν) = 5/2, which permits different topological orders that can be abelian or non-abelian. We developed a method that interfaces the studied quantum state with another state and used it to identify the topological order of ν = 5/2 state. The interface between two half-planes, one hosting the ν = 5/2 state and the other an integer ν = 3 state, supports a fractional ν = 1/2 charge mode and a neutral Majorana mode. The counterpropagating chirality of the Majorana mode, probed by measuring partition noise, is consistent with the particle-hole Pfaffian (PH-Pf) topological order and rules out the anti-Pfaffian order.