The conventional description of transport through the interface between a normal conductor and a superconductor reduces the system to a one-dimensional problem treating Andreev reflection based on a zero-dimensional Sharvin-type point-contact model, and effectively neglects all considerations of device geometry. While this has been successful in systems where conductance in the normal material is in the diffusive transport regime, such an oversimplification of the problem fails in other transport regimes. In particular, when transport is ballistic as in a typical semiconductor-superconductor hybrid structure, geometrical effects are inherently important, and a proper description must consider a one-dimensional contact injecting into a two-dimensional ballistic cavity. We present a study of this regime and explore the bias-voltage dependence of Andreev transport in a cavity-type device comprised of a high-mobility HgTe quantum well side-contacted by one superconducting and one normal contact, each creating a one-dimensional interface. The enhanced conductance from Andreev transport features two finite-bias conductance peaks, observed at energies within the energy gap of the superconductor. Interestingly, these two peaks respond differently to the application of a perpendicular-to-plane magnetic field. Using a semiclassical model for the quantum transport within the cavity, we are able to attribute each peak to a different class of ballistic trajectories. One class is dominated by normal reflection, and its interference condition is independent of magnetic field, whereas the other one contains retroreflected Andreev processes at the superconductor interface. These create closed trajectories that are strongly suppressed by magnetic field due to Aharonov-Bohm and Doppler shift effects.

Nonlinear transport in narrow band-gap materials has recently attracted significant attention, being commonly recognized as a useful tool to study a variety of complex physical effects related to Berry phase. Here we demonstrate that a mundane, commonly overlooked mechanism stemming from tunneling between charge puddles, can drive substantial nonlinearities in these narrow band gap materials. As a test bed, we use an epitaxial topological HgTe layer, underscoring that even good crystalline quality materials suffer from this issue. Indeed, we show that signatures of electrical transport through a network of charge puddles are not limited to the linear planar magnetoresistance, but also dominate nonlinear transport. Our findings highlight the need for utmost caution when interpreting nonlinear electrical transport phenomena, as harmonic distortion of the electrical signal, caused by charge puddles, is unavoidable in any realistic narrow-gap system, complicating the identification of other proposed effects related to the Berry phase.

An exceptional trait of the quantum Hall effect is quantum adiabatic transport, dissipationless quantized edge transport that is robust to bias voltages multiple orders of magnitude larger than any known relevant energy scale. This enables stable and highly sensitive measurements in quantum metrology at temperatures above 1 K. In contrast, prior experiments have shown that an electrical bias of the same order applied to the quantum anomalous Hall edge modes in magnetic topological insulators causes a breakdown of quantization, resulting from material limitations (electric field activates bulk transport). In this paper, to mitigate the effects of this electric field and study edge transport at a large electrical bias, we utilize electrochemical potential balancing. We find that electrical transport along the edge of a quantum anomalous Hall insulator is ubiquitously of dissipationless quantum adiabatic nature. In fact, we can verify that the adiabaticity holds at least up to an applied bias voltage of some 600 mV at 4.2 K, multiple orders of magnitude larger than any known energy scale associated with the quantum anomalous Hall state. This is a level of robustness on par with the conventional quantum Hall modes used in mainstream metrology.

The quantum anomalous Hall effect has been observed in several magnetically doped topological insulators, where its robustness and macroscopic magnetization properties have been taken to suggest the presence of long-range ferromagnetic order. However, experiments in such systems have found evidence for both long- and short-range order, leaving the precise nature of the magnetism in these systems unclear. Here, we use scanning superconducting quantum interference device microscopy to study magnetic domains in V-doped (Bi,Sb)_2Te_3 exhibiting a quantum anomalous Hall effect with precise quantization. By imaging stray magnetic fields as a function of applied field, we map the formation and evolution of domains through magnetic reversal. We reconstruct the magnetization configuration underlying the measured stray field and find that magnetic domains and crystallographic grains are of similar size. Moreover, magnetic reversal is found to occur through domain expansion, typical of ferromagnets, rather than through nucleation at random sites. Our measurements thus reveal a coexistence of both local magnetic interactions within crystallographic grains and long-range ferromagnetic coupling between grains. This behavior in V-doped (Bi,Sb)_2Te_3 is markedly distinct from that previously reported for Cr-doped (Bi,Sb)_2Te_3.

Quantum Hall Effect (QHE) is the basis of the realisation of the SI unit of electrical resistance, the ohm. Present QHE devices require low temperatures and high magnetic fields to operate. The Quantum Anomalous Hall effect (QAHE) in topological insulators is a good candidate to simplify the realisation of the resistance unit and the development of a ‘quantum electrical metrology toolbox’ for universal adoption of quantum electrical SI standards, beyond just the NMIs. The Joint Research Project QuAHMET — Quantum anomalous Hall effect materials and devices for metrology of the European Partnership on Metrology . European Partnerships are a key implementation tool of the European Commission’s Horizon Europe. The aim of the project is to investigate and implement novel technologies for the development of QAHE devices and measurement systems for metrology, by performing traceable measurement and characterisation of QAHE materials as devices and primary resistance standard candidates. The project is exploring, understanding, and implementing a scientifically grounded methodology for developing metrology grade QAHE devices, by focussing on the improvement of the growth techniques of magnetically doped topological insulator (TI) optimising the material properties for the QAHE, the investigation of electronic, structural, magnetic, and magneto-electronic properties of the samples, and of the limitation conditions of QAHE (expecially temperature and current), by employing also scanning probes and magnetometry techniques at low temperatures. The NMIs involved will be in charge of the development and application of accurate measurement techniques to perform a detailed metrological assessment of the optimised QAHE devices at low-to-zero applied magnetic field. The consortium consists of 14 partners and gathers 7 leading European national metrology institutes (NMIs), a Japanese NMI for metrology, complemented by 6 globally recognized institutes from academia and applied research. The project aims to connect with and impact on NMIs and calibration centers, academia, T&M industry and end users interested in applications, such as spintronics and topological quantum computing and advance the research and progress in the field of TIs. The project started in June 2024 and the poster will report on its advancements and results. The project is open to collaborations and interest from stakeholders. You can connect to the project via its website (sites.google.com/inrim.it/quahmet/home), LinkedIn group (www.linkedin.com/groups/8824119/) and YouTube channel (www.youtube.com/channel/UCaHuyb8YzrjPnLUz7nSiauA). Acknowledgement: The project 23FUN07 QuAHMET has received funding from the European Partnership on Metrology, co-financed from the European Union’s Horizon Europe Research and Innovation Programme and by the Participating States.

We study ultrafast photocurrents in thin films of a model ferromagnetic metal with broken bulk inversion symmetry, the half-metallic Heusler compound NiMnSb, following excitation with an optical pump pulse with photon energy 1.55 eV. Remarkably, in terms of the direction of the sample magnetization M, all photocurrents are found to be a superposition of a component with Rashba- and Dresselhaus-type symmetry. We explain the Dresselhaus bulk photocurrent as follows: Pump-induced electron heating induces an excess of spin μ_s||M, which transfers spin angular momentum into states with Dresselhaus-type spin-momentum locking. The resulting charge current relaxes on a time scale of 10 fs by momentum relaxation and, thus, follows μ_s quasi-instantaneously. The relaxation of μ_s is governed by the cooling of the electrons and not by the significantly slower spin-lattice relaxation of half-metals. Our findings add the Dresselhaus spin-galvanic effect (SGE) to the set of ultrafast spin-charge-conversion phenomena. They indicate a route to more efficient spintronic terahertz emitters and detectors based on the volume scaling of the bulk SGE.

The fractional AC Josephson effect is a discerning property of topological superconductivity in hybrid Josephson junctions. Recent experimental observations of missing odd Shapiro steps and half Josephson frequency emission in various materials have sparked significant debate regarding their potential origin in the effect. In this study, we present microwave emission measurements on a resistively shunted Josephson junction based on a HgTe quantum well. We demonstrate that, with significant spurious inductance in the shunt wiring, the experiment operates in a nonlinear dynamic regime characterized by period-doubling. This leads to additional microwave emission peaks at half of the Josephson frequency, f_J/2, which can mimic the 4π-periodicity of topological Andreev states. The observed current-voltage characteristics and emission spectra are well-described by a simple RCLSJ model. Furthermore, we show that the nonlinear dynamics of the junction can be controlled using gate voltage, magnetic field, and temperature, with our model accurately reproducing these effects without incorporating any topological attributes. Our observations urge caution in interpreting emission at f_J/2 as evidence for gapless Andreev bound states in topological junctions and suggest the appropriate parameter range for future experiments.

The quantum anomalous Hall effect (QAHE) in magnetic topological insulators offers great potential to revolutionize quantum electrical metrology by establishing primary resistance standards operating at zero external magnetic field and realizing a universal “quantum electrical metrology toolbox” that can perform quantum resistance, voltage, and current metrology in a single instrument. To realize such promise, significant progress is still required to address materials and metrological challenges—among which, one main challenge is to make the bulk of the topological insulator sufficiently insulating to improve the robustness of resistance quantization. In this Perspective, we present an overview of the QAHE; discuss the aspects of topological material growth and characterization; and present a path toward a QAHE resistance standard realized in magnetically doped (Bi,Sb)2Te3 systems. We also present guidelines and methodologies for QAHE resistance metrology, its main limitations and challenges, as well as modern strategies to overcome them.

QuAHMET - Quantum anomalous Hall effect materials and devices for metrology is a Joint Research Project of the European Metrology Partnership. The project focus is on the traceable measurement and characterisation of quantum anomalous Hall effect (QAHE) materials as devices and primary resistance standard candidates.

The quantum anomalous Hall effect holds promise as a disruptive innovation in condensed matter physics and metrology, as it gives access to Hall resistance quantization in terms of the von-Klitzing constant RK = h/e2 at zero external magnetic field. In this work, we study the accuracy of Hall resistance quantization in a device based on the magnetic topological insulator material (V,Bi,Sb)2Te3. We show that the relative deviation of the Hall resistance from RK at zero external magnetic field is (4.4 +/- 8.7) nohm/ohm when extrapolated to zero measurement current, and (8.6 +/- 6.7) nohm/ohm when extrapolated to zero longitudinal resistivity (each with combined standard uncertainty, k = 1), which sets a new benchmark for the quantization accuracy in topological matter. This precision and accuracy at the nohm/ohm level (or 10-9 of relative uncertainty) achieve the thresholds for relevant metrological applications and establish a zero external magnetic field quantum standard of resistance - an important step towards the integration of quantum-based voltage and resistance standards into a single universal quantum electrical reference.

The quantum anomalous Hall effect in magnetic topological insulators has been recognized as a promising platform for applications in quantum metrology. The primary reason for this is the electronic conductance quantization at zero external magnetic field, which allows to combine it with the quantum standard of voltage. Here we demonstrate a measurement scheme that increases the robustness of the zero magnetic field quantum anomalous Hall resistor, allowing for higher operational currents. This is achieved by simultaneous current injection into the two disconnected perimeters of a multi-terminal Corbino device to balance the electrochemical potential between the edges, screening the electric field that drives back-scattering through the bulk, and thus improving the stability of the quantization at increased currents. This approach is not only applicable to devices based on the quantum anomalous Hall effect, but more generally can also be applied to existing quantum resistance standards that rely on the integer quantum Hall effect.

High-resolution transmission electron microscopy and superconducting quantum interference device magnetometry shows that epitaxial CuMnSb films exhibit a coexistence of two magnetic phases, coherently intertwined in nanometric scales. The dominant alpha phase is half-Heusler cubic antiferromagnet with the N & eacute;el temperature of 62 K, the equilibrium structure of bulk CuMnSb. The secondary phase is its ferromagnetic tetragonal 9 polymorph with the Curie temperature of about 100 K. First principles calculations provide a consistent interpretation of experiment, since (i) total energy of 9-CuMnSb is higher than that of alpha-CuMnSb only by 0.12 eV per formula unit, which allows for epitaxial stabilization of this phase, (ii) the metallic character of 9-CuMnSb favors the Ruderman-Kittel-Kasuya-Yoshida ferromagnetic coupling, and (iii) the calculated effective Curie-Weiss magnetic moment of Mn ions in both phases is about 5.5 mu B, favorably close to the measured value. Calculated properties of all point native defects indicate that the most likely to occur are MnCuantisites. They affect magnetic properties of epilayers, but they cannot induce the ferromagnetic order in CuMnSb. Combined, the findings highlight a practical route towards fabrication of functional materials in which coexisting polymorphs provide complementing functionalities in one host.

A superconductor, when exposed to a spin-exchange field, can exhibit spatial modulation of its order parameter, commonly referred to as the Fulde-Ferrell-Larkin-Ovchinnikov state. Such a state can be induced by controlling the spin-splitting field in Josephson junction devices, allowing access to a wide range of the phase diagram. Here we demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov state can be induced in Josephson junctions based on the two-dimensional dilute magnetic topological insulator (Hg,Mn)Te. We do this by observing the dependence of the critical current on the magnetic field and temperature. The substitution of Mn dopants induces an enhanced Zeeman effect, which can be controlled with high precision by using a small external magnetic field. We observe multiple re-entrant behaviours of the critical current as a response to an in-plane magnetic field, which we assign to transitions between ground states with a phase shifted by pi. This will enable the study of the Fulde-Ferrell-Larkin-Ovchinnikov state in much more accessible experimental conditions. Despite their potential device applications, experimental realizations of proximity-induced Fulde-Ferrell-Larkin-Ovchinnikov states are rare. Now Josephson junctions based on a dilute magnetic topological insulator provide evidence of such a state.

This study explores the quantum anomalous Hall effect (QAHE) in V-doped (BiSb)(2)Te-3, a magnetically-doped topological insulators. We use a precision resistance bridge based on a cryogenic current comparator to measure the QAHE at a zero magnetic field with unprecedented uncertainty (Delta R-xy/R-K = 12 n Omega/Omega). Measurement results obtained at currents between 40 and 300 nA demonstrate the potential of this technology for quantum metrology, offering a path to a primary electrical resistance standard without external magnetic fields.

The quantum anomalous Hall effect holds promise for quantum resistance metrology, but has been limited to low operating currents. A measurement scheme that increases the effect's operational current is now demonstrated - a scheme that could also be used more generally to improve the performance of existing primary quantum standards of resistance based on the conventional quantum Hall effect.

Fluctuationsin planar magnetotransport are ubiquitousin topologicalHgTe structures, in both tensile (topological insulator) and compressivelystrained layers (Weyl semimetal phase). We show that the common reasonfor the fluctuations is the presence of tilted Dirac cones combinedwith the formation of charge puddles. The origin of the tilted Diraccones is the mix of the Zeeman term due to the in-plane magnetic fieldand quadratic contributions to the dispersion relation. We developa network model that mimics the transport of tilted Dirac fermionsin the landscape of charge puddles. The model captures the essentialfeatures of the experimental data. It should be relevant for the interpretationof planar magnetotransport in a variety of topological and small bandgap materials.

HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular due to coupling of the Te 5p-derived valence electrons to Hg 5d core states at shallow binding energy. We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg 5d states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its non-trivial band topology.

Macroscopic Quantum Tunneling The profound question of how the laws of quantum mechanics merge into those governing classical physics at macroscopic sizes remains largely unexplored. In article number 2303165 by Kajetan M. Fijalkowski, Charles Gould, Laurens W. Molenkamp, and co‐workers, quantum tunneling of the magnetization, a phenomenon quantum by nature, is studied in a magnetic object that is, without any doubt, macroscopic.

Nonlinear planar magnetotransport is ubiquitous in topological HgTe structures, both in tensile (topological insulator) or compressively strained layers (Weyl semimetal phase). We show that the common reason for the nonlinear planar magnetotransport is the presence of tilted Dirac cones combined with the formation of charge puddles. The origin of the tilted Dirac cones is the mix of the Zeeman term due to the in-plane magnetic field and quadratic contributions to the dispersion relation. We develop a network model that mimics transport of tilted Dirac fermions in the landscape of charge puddles. The model captures the essential features of the experimental data. It should be relevant for nonlinear planar magnetotransport in a variety of topological and small band gap materials.

The search for topological superconductivity has motivated investigations into materials that combine topological and superconducting properties. The half-Heusler compound YPtBi appears to be such a material, however experiments have thus far been limited to bulk single crystals, drastically limiting the scope of available experiments. This has made it impossible to investigate the potential topological nature of the superconductivity in this material. Experiments to access details about the superconducting state require sophisticated lithographic structures, typically based on thin films. Here we report on the establishment of high crystalline quality epitaxial thin films of YPtBi(111), grown using molecular beam epitaxy on Al2O3(0001) substrates. A robust superconducting state is observed, with both critical temperature and critical field consistent with that previously reported for bulk crystals. Moreover we find that AlOx capping sufficiently protects the sample surface from degradation to allow for proper lithography. Our results pave a path towards the development of advanced lithographic structures, that will allow the exploration of the potentially topological nature of superconductivity in YPtBi.