Oscillations of conductance observed in strong magnetic fields are a striking manifestation of the quantum dynamics of charge carriers in solids. The large charge carrier density in typical metals sets the scale of oscillations in both electrical and thermal conductivity, which characterize the Fermi surface. In semimetals, thermal transport at low-charge carrier density is expected to be phonon dominated, yet several experiments observe giant quantum oscillations in thermal transport. This raises the question of whether there is an overarching mechanism leading to sizable oscillations that survives in phonon-dominated semimetals. In this work, we show that such a mechanism exists. It relies on the peculiar phase-space allowed for phonon scattering by electrons when only a few Landau levels are filled. Our measurements on the Dirac semimetal ZrTe5 support this counter-intuitive mechanism through observation of pronounced thermal quantum oscillations, since they occur in similar magnitude and phase in directions parallel and transverse to the magnetic field. Our phase-space argument applies to all low-density semimetals, topological or not, including graphene and bismuth. Our work illustrates that phonon absorption can be leveraged to reveal degrees of freedom through their imprint on longitudinal thermal transport.

We analyze the transport properties of curved, three-dimensional graphite samples in strong magnetic fields. Focusing on a millimeter-scale graphite cylinder as a prototypical curved object, we perform longitudinal and Hall voltage measurements while applying quantizing magnetic fields. These measurements are investigated as a function of field strength and angles. Most importantly, we find that angle-dependent Shubnikov-de Hass oscillations are superimposed with angle-independent features. Reproducing the experimental observations, we introduce a network model that accounts for the cylindrical geometry effect by conceptualizing the cylinder as composed of strips of planar graphite in an effectively inhomogeneous magnetic field. Our work highlights how the interplay between geometric curvature and quantizing magnetic fields can be leveraged to engineer tunable spatial current densities within solid-state systems, and paves the way for understanding transport properties of curved and bent three-dimensional samples more generally.

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin-momentum locked metallic edge states-both helical and chiral-surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps-up to a few hundred meV-promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.

Surface polaritons comprise a wealth of light–matter interactions with deep sub-wavelength scale confinement of electromagnetic modes. However, their nanoscale localized dissipation and thermalization processes are not readily accessible experimentally. Here, we introduce photothermal force microscopy to image surface plasmon polaritons (SPPs) in monolayer graphene through their non-radiative SiO2 substrate dissipation. We demonstrate the real-space SPP imaging via photo-induced atomic force detection, and from comparison with scattering-type scanning near-field optical microscopy imaging attribute the force response to substrate dissipation-enhanced thermal expansion. This work illustrates that nano-optical tip–sample induced dissipative forces facilitate a direct mechanical detection of surface polariton interactions with monolayer sensitivity.

Using scanning thermal microscopy, we have mapped the spatial distribution of temperatures in an operating nanoscale device formed from a magnetic injector, an Ag connecting wire, and a magnetic detector. An analytical model explained the thermal diffusion over the measured temperature range (2-300 K) and injector-detector separation (400-3000 nm). The characteristic diffusion lengths of the Peltier and Joule heat differ remarkably below 60 K, a fact that can be explained by the onset of ballistic phonon heat transfer in the substrate.

ZusammenfassungIn den letzten Jahren wurden in elektrischen Leitern Anzeichen von hydrodynamischem Ladungstransport beobachtet. Dazu gehören die starke Abhängigkeit des Widerstands von der Leiterbreite, Verwirbelungen oder das Brechen des Wiedemann‐Franz‐Gesetzes. Die Messung dieser schon lange vorhergesagten Eigenschaften erlaubt neue Einblicke in das Elektronensystem. Zum Teil lässt sich die Viskosität der Elektronenfluide direkt mit Stoßprozessen zwischen Ladungsträgern erklären. In Wolframphosphid ist die Energiedissipation durch Stoßvorgänge durch das sogenannte Planksche Dissipationslimit begrenzt, das Ähnlichkeit mit der quantenmechanischen Energie‐Zeit‐Unschärfe hat. Aktuell wird an einem möglichen technischen Einsatz von hydrodynamischen Ladungstransport geforscht, in Form neuartiger elektronischer Bauteile.

We report heat transport measurements on suspended single-layer graphene disks with radius of 150-1600 nm using a high-vacuum scanning thermal microscope. The results of this study revealed a radius-dependent thermal contact resistance between tip and graphene, with values between 1.15 and 1.52 x 10(8) KW-1. The observed scaling of thermal resistance with radius is interpreted in terms of ballistic phonon transport in suspended graphene discs with radius smaller than 775 nm. In larger suspended graphene discs (radius > 775 nm), the thermal resistance increases with radius, which is attributed to in-plane heat transport being limited by phonon-phonon resistive scattering processes, which resulted in a transition from ballistic to diffusive thermal transport. In addition, by simultaneously mapping topography and steady-state heat flux signals between a self-heated scanning probe sensor and graphene with 17 nm thermal spatial resolution, we demonstrated that the surface quality of the suspended graphene and its connectivity with the Si/SiO2 substrate play a determining role in thermal transport. Our approach allows the investigation of heat transport in suspended graphene at sub-micrometre length scales and overcomes major limitations of conventional experimental methods usually caused by extrinsic thermal contact resistances, assumptions on the value of the graphene's optical absorbance and limited thermal spatial resolution.

We present further development and application examples of a thermometry approach capable of producing real-space temperature maps of operating nanoscale devices with sub-10nm resolution. The technique relies on scanning thermal microscopy with a resistive element coupled to a cantilevered tip. The resistive element acts both as integrated heater and as sensing element. A modulated temperature field is generated in the sample by exciting the device under investigation with an electrical AC bias. A map of the sample's temperature response due to different physical effects, such as Joule heating and thermoelectric effects, can be inferred from the demodulated sensor signal. As application examples, we demonstrate the investigation of thermoelectric heating/cooling at crystal phase heterostructures in InAs nanowires and Joule self-heating of individual multi-walled carbon nanotubes.

As electronic devices are downsized, physical processes at the interface to electrodes may dominate and limit device performance. A crucial step towards device optimization is being able to separate such contact effects from intrinsic device properties. Likewise, an increased local temperature due to Joule heating at contacts and the formation of hot spots may put limits on device integration. Therefore, being able to observe profiles of both electronic and thermal device properties at the nanoscale is important. Here, we show measurements by scanning thermal and Kelvin probe force microscopy of the same 60 nm diameter indium arsenide nanowire in operation. The observed temperature along the wire is substantially elevated near the contacts and deviates from the bell-shaped temperature profile one would expect from homogeneous heating. Voltage profiles acquired by Kelvin probe force microscopy not only allow us to determine the electrical nanowire conductivity, but also to identify and quantify sizable and non-linear contact resistances at the buried nanowire–electrode interfaces. Complementing these data with thermal measurements, we obtain a device model further permitting separate extraction of the local thermal nanowire and interface conductivities.

In stark contrast to ordinary metals, in materials in which electrons strongly interact with each other or with phonons, electron transport is thought to resemble the flow of viscous fluids. Despite their differences, it is predicted that transport in both conventional and correlated materials is fundamentally limited by the uncertainty principle applied to energy dissipation. Here we report the observation of experimental signatures of hydrodynamic electron flow in the Weyl semimetal tungsten diphosphide. Using thermal and magneto-electric transport experiments, we find indications of the transition from a conventional metallic state at higher temperatures to a hydrodynamic electron fluid below 20 K. The hydrodynamic regime is characterized by a viscosity-induced dependence of the electrical resistivity on the sample width and by a strong violation of the Wiedemann-Franz law. Following the uncertainty principle, both electrical and thermal transport are bound by the quantum indeterminacy, independent of the underlying transport regime.

Control of photoinduced forces allows nano particle manipulation, atom trapping, and fundamental studies of light-matter interactions. Scanning probe microscopy enables the local detection of photoinduced effects with nano-optical imaging and spectroscopy modalities being used for chemical analysis and the study of physical effects. Recently, the development of a novel scanning probe technique has been reported with local chemical sensitivity attributed to the localization and detection of the optical gradient force between a probe tip and sample surface via infrared vibrationally resonant coupling. However, the magnitude and spectral line shape of the observed signals disagree with theoretical predictions of optical gradient forces. Here, we clarify this controversy by resolving and analyzing the interplay of several photoinduced effects between scanning probe tips and infrared resonant materials through spectral and spatial force measurements. Force spectra obtained on IR-active vibrational modes of polymer thin films are symmetric and match the material absorption spectra in contrast to the dispersive spectral line shape expected for the optical gradient force response. Sample thickness dependence shows continuous increase in force signal beyond the thickness where the optical dipole force would saturate. Our results illustrate that photoinduced force interactions between scanning probe tips and infrared-resonant materials are dominated by short-range thermal expansion and possibly long-range thermally induced photoacoustic effects. At the same time, we provide a guideline to detect and discriminate optical gradient forces from other photoinduced effects, which opens a new perspective for the development of new scanning probe modalities exploiting ultrastrong opto-mechanical coupling effects in tip-sample cavities.

Metallic atomic junctions pose the ultimate limit to the scaling of electrical contacts. They serve as model systems to probe electrical and thermal transport down to the atomic level as well as quantum effects occurring in one-dimensional systems. Charge transport in atomic junctions has been studied intensively in the last two decades. However, heat transport remains poorly characterized because of significant experimental challenges. Specifically the combination of high sensitivity to small heat fluxes and the formation of stable atomic contacts has been a major hurdle for the development of this field. Here we report on the realization of heat transfer measurements through atomic junctions and analyze the thermal conductance of single atomic gold contacts at room temperature. Simultaneous measurements of charge and heat transport reveal the proportionality of electrical and thermal conductance, quantized with the respective conductance quanta. This constitutes an atomic scale verification of the well-known Wiedemann-Franz law. We anticipate that our findings will be a major advance in enabling the investigation of heat transport properties in molecular junctions, with meaningful implications towards the manipulation of heat at the nanoscale

Materials with strongly-correlated electrons exhibit interesting phenomena such as metal-insulator transitions and high-temperature superconductivity. In stark contrast to ordinary metals, electron transport in these materials is thought to resemble the flow of viscous fluids. Despite their differences, it is predicted that transport in both, conventional and correlated materials, is fundamentally limited by the uncertainty principle applied to energy dissipation. Here we discover hydrodynamic electron flow in the Weyl-semimetal tungsten phosphide (WP2). Using thermal and magneto-electric transport experiments, we observe the transition from a conventional metallic state, at higher temperatures, to a hydrodynamic electron fluid below 20 K. The hydrodynamic regime is characterized by a viscosity-induced dependence of the electrical resistivity on the square of the channel width, and by the observation of a strong violation of the Wiedemann-Franz law. From magneto-hydrodynamic experiments and complementary Hall measurements, the relaxation times for momentum and thermal energy dissipating processes are extracted. Following the uncertainty principle, both are limited by the Planckian bound of dissipation, independent of the underlying transport regime.

Weyl semimetals are materials where electrons behave effectively as a kind of massless relativistic particles known asWeyl fermions. These particles occur in two flavours, or chiralities, and are subject to quantum anomalies, the breaking of a conservation law by quantum fluctuations. For instance, the number of Weyl fermions of each chirality is not independently conserved in parallel electric and magnetic field, a phenomenon known as the chiral anomaly. In addition, an underlying curved spacetime provides a distinct contribution to a chiral imbalance, an effect known as the mixed axial-gravitational anomaly, which remains experimentally elusive. However, the presence of a mixed gauge-gravitational anomaly has recently been tied to thermoelectrical transport in a magnetic field, even in flat spacetime, opening the door to experimentally probe such type of anomalies in Weyl semimetals. Using a temperature gradient, we experimentally observe a positive longitudinal magnetothermoelectric conductance (PMTC) in the Weyl semimetal NbP for collinear temperature gradients and magnetic fields (DT || B) that vanishes in the ultra quantum limit. This observation is consistent with the presence of a mixed axial-gravitational anomaly. Our work provides clear experimental evidence for the existence of a mixed axial-gravitational anomaly of Weyl fermions, an outstanding theoretical concept that has so far eluded experimental detection.