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Semiconductor nanowires with superconducting leads are considered promising for quantum computation. The current–phase relation is systematically explored in gate-tunable InAs Josephson junctions, and is shown to provide a clean handle for characterizing the transport properties of these structures. Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation 1 , 2 , 3 and as model systems for mesoscopic Josephson junctions 4 , 5 . The supercurrent, I , versus the phase, φ , across the junction is called the current–phase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating few-mode junctions with high transmissions. In a gate-tunable junction, we found that the CPR varied with gate voltage: near the onset of supercurrent, we observed behaviour consistent with resonant tunnelling through a single, highly transmitting mode. The gate dependence is consistent with modelled subband structure that includes an effective tunnelling barrier due to an abrupt change in the Fermi level at the boundary of the gate-tuned region. These measurements of skewed, tunable, few-mode CPRs are promising both for applications that require anharmonic junctions 6 , 7 and for Majorana readout proposals 8 .

Achieving spin-pinning at the interface of hetero-bilayer ferromagnet/antiferromagnet structures in conventional exchange bias systems can be challenging due to difficulties in interface control and the weakening of spin-pinning caused by poor interface quality. In this work, we propose an alternative approach to stabilize the exchange interaction at the interface of an uncompensated antiferromagnet by utilizing a gradient of interlayer exchange coupling. We demonstrate this exchange interaction through a designed field training protocol in the odd-layer topological antiferromagnet MnBi 2 Te 4 . Our results reveal a remarkable field-trained exchange bias of up to ~ 400 mT, which exhibits high repeatability and can be easily reset by a large training field. Notably, this field-trained exchange bias effect persists even with zero-field initialization, presenting a stark contrast to the traditional field-cooled exchange bias. The highly tunable exchange bias observed in this single antiferromagnet compound, without the need for an additional magnetic layer, provides valuable insight into the exchange interaction mechanism. These findings pave the way for the systematic design of topological antiferromagnetic spintronics. Exchange bias occurs in a variety of magnetic materials and heterostructures. The quintessential example occurs in antiferromagnetic/ferromagnetic heterostructures and has been employed extensively in magnetic memory devices. Here, via a specific field training protocol, the authors demonstrate an exchange bias of up to 400mT in odd layered MnBi2Te4.

We present transport and scanning SQUID measurements on InAs/GaSb double quantum wells, a system predicted to be a two-dimensional topological insulator. Top and back gates allow independent control of density and band offset, allowing tuning from the trivial to the topological regime. In the trivial regime, bulk conductivity is quenched but transport persists along the edges, superficially resembling the predicted helical edge-channels in the topological regime. We characterize edge conduction in the trivial regime in a wide variety of sample geometries and measurement configurations, as a function of temperature, magnetic field, and edge length. Despite similarities to studies claiming measurements of helical edge channels, our characterization points to a non-topological origin for these observations.

The ability to wiggle and stretch individual superconducting vortices with nanoscale precision enables unprecedented insight into their dynamics and the properties of the superconductor that supports them. Superconductors often contain quantized microscopic whirlpools of electrons, called vortices, that can be modelled as one-dimensional elastic objects 1 . Vortices are a diverse area of study for condensed matter because of the interplay between thermal fluctuations, vortex–vortex interactions and the interaction of the vortex core with the three-dimensional disorder landscape 2 , 3 , 4 , 5 . Although vortex matter has been studied extensively 1 , 6 , 7 , the static and dynamic properties of an individual vortex have not. Here, we use magnetic force microscopy (MFM) to image and manipulate individual vortices in a detwinned YBa 2 Cu 3 O 6.991 single crystal, directly measuring the interaction of a moving vortex with the local disorder potential. We find an unexpected and marked enhancement of the response of a vortex to pulling when we wiggle it transversely. In addition, we find enhanced vortex pinning anisotropy that suggests clustering of oxygen vacancies in our sample and demonstrates the power of MFM to probe vortex structure and microscopic defects that cause pinning.

Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry simultaneously images the local magnetic fields and susceptibilities above a sample with sub-micron spatial resolution. Further development of this technique requires a thorough understanding of the current, voltage, and flux ( I V Φ ) characteristics of scanning SQUID susceptometers. These sensors often have striking anomalies in their current–voltage characteristics, which we believe to be due to electromagnetic resonances. The effect of these resonances on the performance of these SQUIDs is unknown. To explore the origin and impact of the resonances, we develop a model that qualitatively reproduces the experimentally-determined I V Φ characteristics of our scanning SQUID susceptometers. We use this model to calculate the noise characteristics of SQUIDs of different designs. We find that the calculated ultimate flux noise is better in susceptometers with damping resistors that diminish the resonances than in susceptometers without damping resistors. Such calculations will enable the optimization of the signal-to-noise characteristics of scanning SQUID susceptometers.

Fluctuations are important near phase transitions, where they can be difficult to describe quantitatively. Superconductivity in mesoscopic rings is particularly intriguing because the critical temperature is an oscillatory function of magnetic field. There is an exact theory for thermal fluctuations in one-dimensional superconducting rings, which are therefore expected to be an excellent model system. We measured the susceptibility of many rings, one ring at a time, by using a scanning superconducting quantum interference device that can isolate magnetic signals that are seven orders of magnitude smaller than applied flux. We find that the fluctuation theory describes the results and that a single parameter characterizes the ways in which the fluctuations are especially important at magnetic fields where the critical temperature is suppressed.

When the insulators lanthanum aluminate and strontium titanate are brought together, the interface between them forms a two-dimensional superconductor. Moreover, magnetic imaging of this interface shows that superconductivity and ferromagnetism coexist in separated nanoscale domains. LaAlO 3 and SrTiO 3 are insulating, non-magnetic oxides, yet the interface between them exhibits a two-dimensional electron system with high electron mobility 1 , superconductivity at low temperatures 2 , 3 , 4 , 5 , 6 and electric-field-tuned metal–insulator and superconductor–insulator phase transitions 3 , 6 , 7 , 8 . Bulk magnetization and magnetoresistance measurements also indicate some form of magnetism depending on preparation conditions 5 , 9 , 10 , 11 and a tendency towards nanoscale electronic phase separation 10 . Here we use local imaging of the magnetization and magnetic susceptibility to directly observe a landscape of ferromagnetism, paramagnetism and superconductivity. We find submicrometre patches of ferromagnetism in a uniform background of paramagnetism, with a non-uniform, weak diamagnetic superconducting susceptibility at low temperature. These results demonstrate the existence of nanoscale phase separation as indicated by theoretical predictions based on nearly degenerate interface sub-bands associated with the Ti orbitals 12 , 13 . The magnitude and temperature dependence of the paramagnetic response indicate that the vast majority of the electrons at the interface are localized 14 , and do not contribute to transport measurements 3 , 6 , 7 . In addition to the implications for magnetism, the existence of a two-dimensional superconductor at an interface with highly broken inversion symmetry and a ferromagnetic landscape in the background indicates the potential for exotic superconducting phenomena.

Quantum wells based on mercury telluride are an experimental realization of a two-dimensional topological insulator. By using a scanning superconducting quantum interference device (SQUID) technique, the magnetic fields flowing through HgTe/CdTe heterostructures are imaged both in the quantum spin Hall and the trivial regimes, revealing the edge states associated with the quantum spin Hall state. The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels 1 , 2 , 3 , 4 , 5 . The QSH state was predicted 6 and experimentally demonstrated 7 to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices 7 , 8 , 9 . Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems 10 , 11 , 12 , 13 .

The emergence of conductivity at the {001} interface of LaAlO 3 and SrTiO 3 is one of the more celebrated examples of interface engineering. Using a microscopy approach based on a sensitive magnetometry probe, it is now shown that narrow paths of enhanced conductivity occur along the crystallographic axes of the oxide structures. The ability to control materials properties through interface engineering is demonstrated by the appearance of conductivity at the interface of certain insulators, most famously the {001} interface of the band insulators LaAlO 3 and TiO 2 -terminated SrTiO 3 (STO; refs  1 , 2 ). Transport and other measurements in this system show a plethora of diverse physical phenomena 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 . To better understand the interface conductivity, we used scanning superconducting quantum interference device microscopy to image the magnetic field locally generated by current in an interface. At low temperature, we found that the current flowed in conductive narrow paths oriented along the crystallographic axes, embedded in a less conductive background. The configuration of these paths changed on thermal cycling above the STO cubic-to-tetragonal structural transition temperature, implying that the local conductivity is strongly modified by the STO tetragonal domain structure. The interplay between substrate domains and the interface provides an additional mechanism for understanding and controlling the behaviour of heterostructures.

In LaAlO 3 /SrTiO 3 heterointerfaces, charge carriers migrate from the LaAlO 3 to the interface in an electronic reconstruction. Magnetism has been observed in LaAlO 3 /SrTiO 3 , but its relationship to the interface conductivity is unknown. Here we show that reconstruction is necessary, but not sufficient, for the formation of magnetism. Using scanning superconducting quantum interference device microscopy we find that magnetism appears only above a critical LaAlO 3 thickness, similar to the conductivity. We observe no change in ferromagnetism with gate voltage, and detect ferromagnetism in a non-conducting p -type sample. These observations indicate that the carriers at the interface do not need to be itinerant to generate magnetism. The ferromagnetism appears in isolated patches whose density varies greatly between samples. This inhomogeneity strongly suggests that disorder or local strain generates magnetism in a population of the interface carriers. The interface within heterostructures consisting of LaAlO 3 and SrTiO 3 has been reported to give rise to magnetism, in addition to a two-dimensional electron gas. Kalisky et al . observe that magnetism can occur only above a critical thickness, and that it occurs in heterogeneous patches.