Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry

Gate- and flux-tunable sin(2φ) Josephson element with planar-Ge junctions

Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as Josephson junctions with gate-tunable critical current. Additionally, they can feature a non-sinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase difference, a so-far underutilized property. Here we exploit this multi-harmonicity to create a Josephson circuit element with an almost perfectly π-periodic CPR, indicative of a largely dominant charge-4e supercurrent transport. We realize such a Josephson element, recently proposed as building block of a protected superconducting qubit, using a superconducting quantum interference device (SQUID) with low-inductance aluminum arms and two nominally identical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure embedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages and finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve a regime where the sin ( 2 φ ) component accounts for more than 95% of the total supercurrent. This result demonstrates a new promising route towards parity-protected superconducting qubits.

Voltage-Controlled Synthesis of Higher Harmonics in Hybrid Josephson Junction Circuits

We report measurements of the current-phase relation of two voltage-controlled semiconductor-superconductor hybrid Josephson junctions (JJs) in series. The two hybrid junctions behave similar to a single-mode JJ with effective transparency determined by the ratio of Josephson coupling strengths of the two junctions. Gate-voltage control of Josephson coupling (measured from switching currents) allows tuning of the harmonic content from sinusoidal, for asymmetric tuning, to highly nonsinusoidal, for symmetric tuning. The experimentally observed tunable harmonic content agrees with a model based on two conventional (sinusoidal) JJs in series.

Long-range phase coherence and tunable second order φ 0-Josephson effect in a Dirac semimetal 1T-PtTe2

Superconducting diode effects have recently attracted much attention for their potential applications in superconducting logic circuits. Several pathways have been proposed to give rise to non-reciprocal critical currents in various superconductors and Josephson junctions. In this work, we establish the presence of a large Josephson diode effect in a type-II Dirac semimetal 1T-PtTe2 facilitated by its helical spin-momentum locking and distinguish it from extrinsic geometric effects. The magnitude of the Josephson diode effect is shown to be directly correlated to the large second-harmonic component of the supercurrent. We denote such junctions, where the relative phase between the two harmonics can be tuned by a magnetic field, as 'tunable second order φ 0-junctions'. The direct correspondence between the second harmonic supercurrents and the diode effect in 1T-PtTe2 junctions at relatively low magnetic fields makes it an ideal platform to study the Josephson diode effect and Cooper quartet transport in Josephson junctions.

Interfering Josephson diode effect in Ta2Pd3Te5 asymmetric edge interferometer

Edge states in topological systems have attracted great interest due to their robustness and linear dispersions. Here a superconducting-proximitized edge interferometer is engineered on a topological insulator Ta2Pd3Te5 with asymmetric edges to realize the interfering Josephson diode effect (JDE), which hosts many advantages, such as the high efficiency as much as 73% at tiny applied magnetic fields with an ultra-low switching power around picowatt. As an important element to induce such JDE, the second-order harmonic in the current-phase relation is also experimentally confirmed by half-integer Shapiro steps. The interfering JDE is also accompanied by the antisymmetric second harmonic transport, which indicates the corresponding asymmetry in the interferometer, as well as the polarity of JDE. This edge interferometer offers an effective method to enhance the performance of JDE, and boosts great potential applications for future superconducting quantum devices.

Direct Measurement of a sin(2φ) Current Phase Relation in a Graphene Superconducting Quantum Interference Device

In a Josephson junction, the current phase relation relates the phase variation of the superconducting order parameter φ, between the two superconducting leads connected through a weak link, to the dissipationless current. This relation is the fingerprint of the junction. It is usually dominated by a sin(φ) harmonic, however, its precise knowledge is necessary to design superconducting quantum circuits with tailored properties. Here, we directly measure the current phase relation of a superconducting quantum interference device made with gate-tunable graphene Josephson junctions and we show that it can behave as a sin(2φ) Josephson element, free of the traditionally dominant sin(φ) harmonic. Such element will be instrumental for the development of superconducting quantum bits protected from decoherence.

One-dimensional proximity superconductivity in the quantum Hall regime

Extensive efforts have been undertaken to combine superconductivity and the quantum Hall effect so that Cooper-pair transport between superconducting electrodes in Josephson junctions is mediated by one-dimensional edge states1-6. This interest has been motivated by prospects of finding new physics, including topologically protected quasiparticles7-9, but also extends into metrology and device applications10-13. So far it has proven challenging to achieve detectable supercurrents through quantum Hall conductors2,3,6. Here we show that domain walls in minimally twisted bilayer graphene14-18 support exceptionally robust proximity superconductivity in the quantum Hall regime, allowing Josephson junctions to operate in fields close to the upper critical field of superconducting electrodes. The critical current is found to be non-oscillatory and practically unchanging over the entire range of quantizing fields, with its value being limited by the quantum conductance of ballistic, strictly one-dimensional, electronic channels residing within the domain walls. The system described is unique in its ability to support Andreev bound states at quantizing fields and offers many interesting directions for further exploration.

Asymmetric edge supercurrents in MoTe2 Josephson junctions

To investigate the higher order topology in MoTe2, the supercurrent interference phenomena in Nb/MoTe2/Nb planar Josephson junctions have been systematically studied. By analyzing the obtained interference pattern of the critical supercurrents and performing a comparative study of the edge-touched and untouched junctions, it's found that the supercurrent is dominated by the edges, rather than the bulk or surfaces of MoTe2. An asymmetric Josephson effect with a field-tunable sign is also observed, indicating the nontrivial origin of the edge states. These results not only provide initial evidence for the hinge states in the higher order topological insulator MoTe2, but also demonstrate the potential applications of MoTe2-based Josephson junctions in rectifying the supercurrent.

Broad and colossal edge supercurrent in Dirac semimetal Cd3As2 Josephson junctions

Edge supercurrent has attracted great interest recently due to its crucial role in achieving and manipulating topological superconducting states. Proximity-induced superconductivity has been realized in quantum Hall and quantum spin Hall edge states, as well as in higher-order topological hinge states. Non-Hermitian skin effect, the aggregation of non-Bloch eigenstates at open boundaries, promises an abnormal edge channel. Here we report the observation of broad edge supercurrent in Dirac semimetal Cd3As2-based Josephson junctions. The as-grown Cd3As2 nanoplates are electron-doped by intrinsic defects, which enhance the non-Hermitian perturbations. The superconducting quantum interference indicates edge supercurrent with a width of ~1.6 μm and a magnitude of ~1 μA at 10 mK. The wide and large edge supercurrent is inaccessible for a conventional edge system and suggests the presence of non-Hermitian skin effect. A supercurrent nonlocality is also observed. The interplay between band topology and non-Hermiticity is beneficial for exploiting exotic topological matter.

Zeeman- and Orbital-Driven Phase Shifts in Planar Josephson Junctions

We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to φ0 = 0.5π, which are consistent with a Zeeman field coupling to highly transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit, and orbital effects in InAs/Al JJs, giving improved understanding of phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics.

Limitations of the Current-Phase Relation Measurements by an Asymmetric dc-SQUID

Exotic quantum transport phenomena established in Josephson junctions (JJs) are reflected by a nonsinusoidal current-phase relation (CPR). The solidified approach to measuring the CPR is via an asymmetric dc-SQUID with a reference JJ that has a high critical current. We probed this method by measuring CPRs of hybrid JJs based on the 3D topological insulator (TI) Bi₂Te₂Se with a nanobridge acting as a reference JJ. We captured both highly skewed and sinusoidal critical current oscillations within single devices which contradict the uniqueness of the CPR. This implies that the widely used method provides inaccurate CPR measurement and leads to misinterpretation. It was shown that the accuracy of the CPR measurement is mediated by the asymmetry in derivatives of the CPRs but not in critical currents, as was previously thought. Finally, we provided considerations for an accurate CPR measurement via the most commonly used reference JJs.

Current-Phase Relation of a WTe2 Josephson Junction

When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4π-periodic current-phase relation. Here, we report the measurement of a 4π-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe₂. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTe_x inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the 1.5 μm long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.

Topologically Localized Insulators

We show that fully localized, three-dimensional, time-reversal-symmetry-broken insulators do not belong to a single phase of matter but can realize topologically distinct phases that are labeled by integers. The phase transition occurs only when the system becomes conducting at some filling. We find that these novel topological phases are fundamentally distinct from insulators without disorder: they are guaranteed to host delocalized boundary states giving rise to the quantized boundary Hall conductance, whose value is equal to the bulk topological invariant.

Transition metal dichalcogenide magnetic atomic chains

Reducing the dimensions of a material to the atomic scale endows them with novel properties that are significantly different from their bulk counterparts. A family of stoichiometric transition metal dichalcogenide (TMD) MX₂ (M = Ti to Mn, and X = S to Te) atomic chains is proposed. The results reveal that the MX₂ atomic chains, the smallest possible nanostructure of a TMD, are lattice-dynamically stable, as confirmed from their phonon spectra and ab initio molecular dynamics simulations. In contrast to their bulk and two-dimensional (2D) counterparts, the TiX₂ atomic chains are nonmagnetic semiconductors, while the VX₂, CrX₂, and MnX₂ chains are unipolar magnetic, bipolar magnetic, and antiferromagnetic semiconductors, respectively. In addition, the VX₂, CrX₂, and MnX₂ chains can be converted via carrier doping from magnetic semiconductors to half metals with reversible spin-polarization orientation at the Fermi level. Of these chains, the MnX₂ chains exhibit either ferromagnetic or antiferromagnetic half metallicity depending on the injected carrier type and concentration. The diverse and tunable electronic and magnetic properties in the MX₂ chains originate, based on crystal field theory, from the occupation of the metal d orbitals and the exchange interaction between the tetrahedrally coordinated metal atoms in the atomic chain. The calculated interaction between the carbon nanotubes and the MX₂ chains implies that armchair (7,7) or armchair (8,8) carbon nanotubes are appropriate sheaths for growing MX₂ atomic single-chains in a confined channel. This study reveals the diverse magnetic properties of MX₂ atomic single-chains and provides a promising building block for nanoscale electronic and spintronic devices.

Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al-MoTe2-Al junctions

When an electron is incident on a superconductor from a metal, it is reflected as a hole in a process called Andreev reflection. If the metal N is sandwiched between two superconductors S in an SNS junction, multiple Andreev reflections (MARs) occur. We have found that, in SNS junctions with high transparency ([Formula: see text]) based on the Dirac semimetal MoTe2, the MAR features are observed with exceptional resolution. By tuning the phase difference [Formula: see text] between the bracketing Al superconductors, we establish that the MARs coexist with a Josephson supercurrent [Formula: see text]. As we vary the junction voltage V, the supercurrent amplitude [Formula: see text] varies in step with the MAR order n, revealing a direct relation between them. Two successive Andreev reflections serve to shuttle a Cooper pair across the junction. If the pair is shuttled coherently, it contributes to [Formula: see text]. The experiment measures the fraction of pairs shuttled coherently vs. V. Surprisingly, superconductivity in MoTe2 does not affect the MAR features.

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Superconducting Materials and Devices Grown by Focused Ion and Electron Beam Induced Deposition

Since its discovery in 1911, superconductivity has represented an equally inciting and fascinating field of study in several areas of physics and materials science, ranging from its most fundamental theoretical understanding, to its practical application in different areas of engineering. The fabrication of superconducting materials can be downsized to the nanoscale by means of Focused Ion/Electron Beam Induced Deposition: nanopatterning techniques that make use of a focused beam of ions or electrons to decompose a gaseous precursor in a single step. Overcoming the need to use a resist, these approaches allow for targeted, highly-flexible nanopatterning of nanostructures with lateral resolution in the range of 10 nm to 30 nm. In this review, the fundamentals of these nanofabrication techniques are presented, followed by a literature revision on the published work that makes use of them to grow superconducting materials, the most remarkable of which are based on tungsten, niobium, molybdenum, carbon, and lead. Several examples of the application of these materials to functional devices are presented, related to the superconducting proximity effect, vortex dynamics, electric-field effect, and to the nanofabrication of Josephson junctions and nanoSQUIDs. Owing to the patterning flexibility they offer, both of these techniques represent a powerful and convenient approach towards both fundamental and applied research in superconductivity.

Superconducting Triplet Rim Currents in a Spin-Textured Ferromagnetic Disk

Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge in highly localized (sub-80 nm) channels at the rim of the ferromagnet, despite its trivial band structure. We show that these robust rim currents arise from the magnetization texture acting as an effective spin-orbit coupling, which results in spin accumulation at the bilayer-vacuum boundary. Lastly, we demonstrate that by altering the spin texture of a single ferromagnet, both 0 and π channels can be realized in the same device.

Andreev Interference in the Surface Accumulation Layer of Half-Shell InAsSb/Al Hybrid Nanowires

Understanding the spatial distribution of charge carriers in III-V nanowires proximity coupled to superconductors is important for the design and interpretation of experiments based on hybrid quantum devices. In this letter, the gate-dependent surface accumulation layer of half-shell InAsSb/Al nanowires is studied by means of Andreev interference in a parallel magnetic field. Both uniform hybrid nanowires and devices featuring a short Josephson junction fabricated by shadow lithography, exhibit periodic modulation of the switching current. The period corresponds to a flux quantum through the nanowire diameter and is consistent with Andreev bound states occupying a cylindrical surface accumulation layer. The spatial distribution is tunable by a gate potential as expected from electrostatic models.

Boundary conductance in macroscopic bismuth crystals

The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary between the three-dimensional crystal and vacuum. The effect is absent in antimony, which has an identical crystal symmetry, a similar Fermi surface structure and equally ballistic carriers, but an inverted band symmetry and a topological invariant of opposite sign. Our observation confirms that the boundary interrupting the cyclotron orbits remains metallic in bismuth, which is in agreement with what was predicted by Azbel decades ago. However, the absence of the effect in antimony indicates an intimate link between band symmetry and this boundary conductance.

The topology of the surface states of a bismuth crystal remains an ongoing debate. Here, the authors observe surface electric conductivity with a magnetic field parallel to the two-dimensional boundary between the three-dimensional bismuth crystal and vacuum, but this effect is absent in antimony crystals indicating a link between band symmetry and boundary conductance.

Surface Modification and Subsequent Fermi Density Enhancement of Bi(111)

Defects introduced to the surface of Bi(111) break the translational symmetry and modify the surface states locally. We present a theoretical and experimental study of the 2D defects on the surface of Bi(111) and the states that they induce. Bi crystals cleaved in ultrahigh vacuum (UHV) at low temperature (110 K) and the resulting ion-etched surface are investigated by low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy (UPS), and scanning tunneling microscopy (STM) as well as spectroscopy (STS) techniques in combination with density functional theory (DFT) calculations. STS measurements of cleaved Bi(111) reveal that a commonly observed bilayer step edge has a lower density of states (DOS) around the Fermi level as compared to the atomic-flat terrace. Following ion bombardment, the Bi(111) surface reveals anomalous behavior at both 110 and 300 K: Surface periodicity is observed by LEED, and a significant increase in the number of bilayer step edges and energetically unfavorable monolayer steps is observed by STM. It is suggested that the newly exposed monolayer steps and the type A bilayer step edges result in an increase to the surface Fermi density as evidenced by UPS measurements and the Kohn-Sham DOS. These states appear to be thermodynamically stable under UHV conditions.

Josephson Inductance as a Probe for Highly Ballistic Semiconductor-Superconductor Weak Links

We present simultaneous measurements of Josephson inductance and dc transport characteristics of ballistic Josephson junctions based upon an epitaxial Al-InAs heterostructure. The Josephson inductance at finite current bias directly reveals the current-phase relation. The proximity-induced gap, the critical current and the average value of the transparency τ[over ¯] are extracted without need for phase bias, demonstrating, e.g., a near-unity value of τ[over ¯]=0.94. Our method allows us to probe the devices deeply in the nondissipative regime, where ordinary transport measurements are featureless. In perpendicular magnetic field the junctions show a nearly perfect Fraunhofer pattern of the critical current, which is insensitive to the value of τ[over ¯]. In contrast, the signature of supercurrent interference in the inductance turns out to be extremely sensitive to τ[over ¯].

Phase Signature of Topological Transition in Josephson Junctions

Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable Al/InAs Josephson junctions in a loop geometry, we measure a π jump in the junction phase with an increasing in-plane magnetic field B_{∥}. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in B_{∥}. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states.

Observation of backscattering induced by magnetism in a topological edge state

The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer's pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

One-Dimensional Edge Transport in Few-Layer WTe2

WTe2 is a layered transitional-metal dichalcogenide (TMD) with a number of intriguing topological properties. Recently, WTe2 has been predicted to be a higher-order topological insulator (HOTI) with topologically protected hinge states along the edges. The gapless nature of WTe2 complicates the observation of one-dimensional (1D) topological states in transport due to their small contribution relative to the bulk. Here, we study the behavior of the Josephson effect in magnetic field to distinguish edge from bulk transport. The Josephson effect in few-layer WTe2 reveals 1D states residing on the edges and steps. Moreover, our data demonstrates a combination of Josephson transport properties observed solely in another HOTI-bismuth, including Josephson transport over micrometer distances, extreme robustness in a magnetic field, and nonsinusoidal current-phase relation (CPR). Our observations strongly suggest the topological origin of the 1D states and that few-layer WTe2 is a HOTI.

Reducing Electronic Transport Dimension to Topological Hinge States by Increasing Geometry Size of Dirac Semimetal Josephson Junctions

The notion of topological phases has been extended to higher-order and has been generalized to different dimensions. As a paradigm, Cd_{3}As_{2} is predicted to be a higher-order topological semimetal, possessing three-dimensional bulk Dirac fermions, two-dimensional Fermi arcs, and one-dimensional hinge states. These topological states have different characteristic length scales in electronic transport, allowing one to distinguish their properties when changing sample size. Here, we report an anomalous dimensional reduction of supercurrent transport by increasing the size of Dirac semimetal Cd_{3}As_{2}-based Josephson junctions. An evolution of the supercurrent quantum interferences from a standard Fraunhofer pattern to a superconducting quantum interference device (SQUID)-like one is observed when the junction channel length is increased. The SQUID-like interference pattern indicates the supercurrent flowing through the 1D hinges. The identification of 1D hinge states should be valuable for deeper understanding of the higher-order topological phase in a 3D Dirac semimetal.

Fermi-arc supercurrent oscillations in Dirac semimetal Josephson junctions

One prominent hallmark of topological semimetals is the existence of unusual topological surface states known as Fermi arcs. Nevertheless, the Fermi-arc superconductivity remains elusive. Here, we report the critical current oscillations from surface Fermi arcs in Nb-Dirac semimetal Cd₃As₂-Nb Josephson junctions. The supercurrent from bulk states are suppressed under an in-plane magnetic field ~0.1 T, while the supercurrent from the topological surface states survives up to 0.5 T. Contrary to the minimum normal-state conductance, the Fermi-arc carried supercurrent shows a maximum critical value near the Dirac point, which is consistent with the fact that the Fermi arcs have maximum density of state at the Dirac point. Moreover, the critical current exhibits periodic oscillations with a parallel magnetic field, which is well understood by considering the in-plane orbital effect from the surface states. Our results suggest the Dirac semimetal combined with superconductivity should be promising for topological quantum devices.

Gate controlled anomalous phase shift in Al/InAs Josephson junctions

In a standard Josephson junction the current is zero when the phase difference between superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin–orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect—the hallmark effect of superconducting spintronics—which can be characterized by the corresponding anomalous phase shift. Here we report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device. By gate controlling the density of InAs, we are able to tune the spin–orbit coupling in the Josephson junction. This gives us the ability to tune the anomalous phase, and opens new opportunities for superconducting spintronics, and new possibilities for realizing and characterizing topological superconductivity.

The anomalous Josephson effect can be regarded as the hall-mark effect of superconducting spintronics. Here, the authors report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device.

Resistive State of Superconductor-Ferromagnet-Superconductor Josephson Junctions in the Presence of Moving Domain Walls

We describe resistive states of the system combining two types of orderings-a superconducting and a ferromagnetic one. It is shown that in the presence of magnetization dynamics such systems become inherently dissipative and in principle cannot sustain any amount of the superconducting current because of the voltage generated by the magnetization dynamics. We calculate generic current-voltage characteristics of a superconductor-ferromagnet-superconductor Josephson junction with an unpinned domain wall and find the low-current resistance associated with the domain wall motion. We suggest the finite slope of Shapiro steps as the characteristic feature of the regime with domain wall oscillations driven by the ac external current flowing through the junction.

Splitting the Hinge Mode of Higher-Order Topological Insulators

The surface of a higher order topological insulator comprises a two-dimensional topological insulator (TI) with broken inversion symmetry, whose mass is determined by the microscopic details of the surface such as surface potentials and termination. It hosts a helical mode pinned to selected hinges where the surface gap changes its sign. We study the effect of perturbations that break time reversal and particle conservation on this helical mode, such as a Zeeman field and a proximate superconductor. We find that in contrast to the helical modes of inversion symmetric TIs, which are gapped by these couplings, the helical modes at the hinges can remain gapless and spatially split. When this happens, the Zeeman field splits the helical mode into a chiral mode surrounding the magnetized region, and a superconductor results in a helical Majorana mode surrounding the superconducting region. The combination of the two might lead to the gapping of one of the chiral Majorana modes, and leave a single one-dimensional chiral Majorana mode around the superconducting island. We propose that the different topological states can be measured in electrical transport.

Zeeman-Effect-Induced 0-π Transitions in Ballistic Dirac Semimetal Josephson Junctions

One of the consequences of Cooper pairs having a finite momentum in the interlayer of a Josephson junction is π-junction behavior. The finite momentum can either be due to an exchange field in ferromagnetic Josephson junctions, or due to the Zeeman effect. Here, we report the observation of Zeeman-effect-induced 0-π transitions in Bi_{1-x}Sb_{x}, three-dimensional Dirac semimetal-based Josephson junctions. The large in-plane g factor allows tuning of the Josephson junctions from 0 to π regimes. This is revealed by measuring a π phase shift in the current-phase relation measured with an asymmetric superconducting quantum interference device (SQUID). Additionally, we directly measure a nonsinusoidal current-phase relation in the asymmetric SQUID, consistent with models for ballistic Josephson transport.

Observation of a Majorana zero mode in a topologically protected edge channel

Superconducting proximity pairing in helical edge modes, such as those of topological insulators, is predicted to provide a unique platform for realizing Majorana zero modes (MZMs). We used scanning tunneling microscopy measurements to probe the influence of proximity-induced superconductivity and magnetism on the helical hinge states of bismuth(111) films grown on a superconducting niobium substrate and decorated with magnetic iron clusters. Consistent with model calculations, our measurements revealed the emergence of a localized MZM at the interface between the superconducting helical edge channel and the iron clusters, with a strong magnetization component along the edge. Our experiments also resolve the MZM’s spin signature, which distinguishes it from trivial in-gap states that may accidentally occur at zero energy in a superconductor.

Microwave Signature of Topological Andreev level Crossings in a Bismuth-based Josephson Junction

Demonstrating the topological protection of Andreev states in Josephson junctions is an experimental challenge. In particular the telltale 4π periodicity expected for the current phase relation has remained elusive, because of fast parity breaking processes. It was predicted that low temperature ac susceptibility measurements could reveal the topological protection of quantum spin Hall edge states by probing their low energy Andreev spectrum at finite frequency. We have performed such a microwave probing of a phase-biased Josephson junction built around a bismuth nanowire, a predicted second order topological insulator, and which was previously shown to host one-dimensional ballistic edge states. We find absorption peaks at the Andreev level crossings, whose temperature and frequency dependencies point to protected topological crossings with an accuracy limited by the electronic temperature of our experiment.

Field-Tunable 0-π-Transitions in SnTe Topological Crystalline Insulator SQUIDs

The manifestation of spin-orbit interactions, long known to dramatically affect the band structure of heavy-element compounds, governs the physics in the surging class of topological matter. A particular example is found in the new family of topological crystalline insulators. In this systems transport occurs at the surfaces and spin-momentum locking yields crystal-symmetry protected spin-polarized transport. We investigated the current-phase relation of SnTe thin films connected to superconducting electrodes to form SQUID devices. Our results demonstrate that an assisting in-plane magnetic field component can induce 0-π-transitions. We attribute these findings to giant g-factors and large spin-orbit coupling of SnTe topological crystalline insulator, which provides a new platform for investigation of the interplay between spin-orbit physics and topological transport.

Majorana Kramers Pairs in Higher-Order Topological Insulators

We propose a tune-free scheme to realize Kramers pairs of Majorana bound states in recently discovered higher-order topological insulators (HOTIs). We show that, by bringing two hinges of a HOTI into the proximity of an s-wave superconductor, the competition between local and crossed Andreev pairing leads to the formation of Majorana Kramers pairs, when the latter pairing dominates over the former. We demonstrate that such a topological superconductivity is stabilized by moderate electron-electron interactions. The proposed setup avoids the application of a magnetic field or local voltage gates, and requires weaker interactions compared with nonhelical nanowires.

Signatures of van Hove Singularities Probed by the Supercurrent in a Graphene-hBN Superlattice

The band structure of graphene can be strongly modified if its lattice is aligned with the one of a boron nitride substrate. A moiré superlattice forms, which manifests itself by the appearance of new Dirac points, accompanied by van Hove singularities. In this work, we present supercurrent measurements in a Josephson junction made from such a graphene superlattice in the long and diffusive transport regime, where the critical current depends on the Thouless energy. We can then estimate the specific density of states of the graphene superlattice from the combined measurement of the critical current and the normal state resistance. The result matches with theoretical predictions and highlights the strong increase of the density of states at the van Hove singularities. By measuring the magnetic field dependence of the critical current, we find the presence of edge currents at these singularities. We explain it by the reduction of the Fermi velocity associated with the van Hove singularity, which suppresses the supercurrent in the bulk while the electrons at the edges remain less localized, resulting in an edge supercurrent. We attribute these different behaviors of the edges to defects or chemical doping.

Higher-Order Topology in Bismuth

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk-boundary correspondence. Here, we establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk-boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principle calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunneling spectroscopy, we probe the unique signatures of the rotational symmetry of the one-dimensional states located at step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.

Proximity coupling in superconductor-graphene heterostructures

This review discusses the electronic properties and the prospective research directions of superconductor-graphene heterostructures. The basic electronic properties of graphene are introduced to highlight the unique possibility of combining two seemingly unrelated physics, superconductivity and relativity. We then focus on graphene-based Josephson junctions, one of the most versatile superconducting quantum devices. The various theoretical methods that have been developed to describe graphene Josephson junctions are examined, together with their advantages and limitations, followed by a discussion on the advances in device fabrication and the relevant length scales. The phase-sensitive properties and phase-particle dynamics of graphene Josephson junctions are examined to provide an understanding of the underlying mechanisms of Josephson coupling via graphene. Thereafter, microscopic transport of correlated quasiparticles produced by Andreev reflections at superconducting interfaces and their phase-coherent behaviors are discussed. Quantum phase transitions studied with graphene as an electrostatically tunable 2D platform are reviewed. The interplay between proximity-induced superconductivity and the quantum-Hall phase is discussed as a possible route to study topological superconductivity and non-Abelian physics. Finally, a brief summary on the prospective future research directions is given.

Reflection-Symmetric Second-Order Topological Insulators and Superconductors

Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but with topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners (in two dimensions) or at crystal edges (in three dimensions) continue to exist if reflection symmetry is broken. A three-dimensional second-order topological insulator with broken time-reversal symmetry shows a Hall conductance quantized in units of e^{2}/h.