Edge superconductivity in multilayer WTe2 Josephson junction

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

Magnetic field filtering of the boundary supercurrent in unconventional metal NiTe2-based Josephson junctions

Topological materials with boundary (surface/edge/hinge) states have attracted tremendous research interest. Additionally, unconventional (obstructed atomic) materials have recently drawn lots of attention owing to their obstructed boundary states. Experimentally, Josephson junctions (JJs) constructed on materials with boundary states produce the peculiar boundary supercurrent, which was utilized as a powerful diagnostic approach. Here, we report the observations of boundary supercurrent in NiTe2-based JJs. Particularly, applying an in-plane magnetic field along the Josephson current can rapidly suppress the bulk supercurrent and retain the nearly pure boundary supercurrent, namely the magnetic field filtering of supercurrent. Further systematic comparative analysis and theoretical calculations demonstrate the existence of unconventional nature and obstructed hinge states in NiTe2, which could produce hinge supercurrent that accounts for the observation. Our results reveal the probable hinge states in unconventional metal NiTe2, and demonstrate in-plane magnetic field as an efficient method to filter out the bulk contributions and thereby to highlight the hinge states hidden in topological/unconventional materials.

Intrinsic supercurrent non-reciprocity coupled to the crystal structure of a van der Waals Josephson barrier

Non-reciprocal electronic transport in a spatially homogeneous system arises from the simultaneous breaking of inversion and time-reversal symmetries. Superconducting and Josephson diodes, a key ingredient for future non-dissipative quantum devices, have recently been realized. Only a few examples of a vertical superconducting diode effect have been reported and its mechanism, especially whether intrinsic or extrinsic, remains elusive. Here we demonstrate a substantial supercurrent non-reciprocity in a van der Waals vertical Josephson junction formed with a Td-WTe2 barrier and NbSe2 electrodes that clearly reflects the intrinsic crystal structure of Td-WTe2. The Josephson diode efficiency increases with the Td-WTe2 thickness up to critical thickness, and all junctions, irrespective of the barrier thickness, reveal magneto-chiral characteristics with respect to a mirror plane of Td-WTe2. Our results, together with the twist-angle-tuned magneto-chirality of a Td-WTe2 double-barrier junction, show that two-dimensional materials promise vertical Josephson diodes with high efficiency and tunability.

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.

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.

Positive Magnetoresistance and Chiral Anomaly in Exfoliated Type-II Weyl Semimetal Td-WTe2

Layered van der Waals semimetallic Td-WTe2, exhibiting intriguing properties which include non-saturating extreme positive magnetoresistance (MR) and tunable chiral anomaly, has emerged as a model topological type-II Weyl semimetal system. Here, ∼45 nm thick mechanically exfoliated flakes of Td-WTe2 are studied via atomic force microscopy, Raman spectroscopy, low-T/high-μ0H magnetotransport measurements and optical reflectivity. The contribution of anisotropy of the Fermi liquid state to the origin of the large positive transverse MR⊥ and the signature of chiral anomaly of the type-II Weyl Fermions are reported. The samples are found to be stable in air and no oxidation or degradation of the electronic properties is observed. A transverse MR⊥∼1200 % and an average carrier mobility of 5000 cm2V-1s-1 at T=5K for an applied perpendicular field μ0H⊥=7T are established. The system follows a Fermi liquid model for T≤50K and the anisotropy of the Fermi surface is concluded to be at the origin of the observed positive MR. Optical reflectivity measurements confirm the anisotropy of the electronic behaviour. The relative orientation of the crystal axes and of the applied electric and magnetic fields is proven to determine the observed chiral anomaly in the in-plane magnetotransport. The observed chiral anomaly in the WTe2 flakes is found to persist up to T=120K, a temperature at least four times higher than the ones reported to date.

Local Control of Supercurrent Density in Epitaxial Planar Josephson Junctions

The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density, and therefore the overall current distribution, can be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five minigates. We demonstrate that not only can the junction width be electrostatically defined but also the current profile can be locally adjusted to form superconducting quantum interference devices. Our studies show enhanced edge conduction in such long junctions, which can be eliminated by minigates to create a uniform current distribution.

Topological properties of bulk and bilayer 2M WS2: a first-principles study

Recently discovered 2M phase of bulk WS₂was observed to exhibit superconductivity with a critical temperature of 8.8 K, the highest reported among superconducting transition metal dichalcogenides. Also predicted to support protected surface states, it could be a potential topological superconductor. In the present study, we perform a detailed first-principles analysis of bulk and bilayer 2M WS₂. We report a comprehensive investigation of the bulk phase, comparing structural and electronic properties obtained from different exchange correlation functionals to the experimentally reported values. By calculation of theZ₂invariant and surface states, we give support for its non-trivial band nature. Based on the insights gained from the analysis of the bulk phase, we predict bilayer 2M WS₂as a new two-dimensional topological material. We demonstrate its dynamical stability from first-principles phonon computations and present its electronic properties, highlighting the band inversions between the Wdand Spstates. By means ofZ₂invariant computations and a calculation of the edge states, we show that bilayer 2M WS₂exhibits protected, robust edge states. The broken inversion symmetry in this newly proposed bilayer also leads to the presence of Berry curvature dipole and resulting non-linear responses. We compute the Berry curvature distribution and the dipole as a function of Fermi energy. We propose that Berry curvature dipole signals, which are absent in the centrosymmetric bulk 2M WS₂, can be signatures of the bilayer. We hope our predictions lead to the experimental realization of this as-yet-undiscovered two-dimensional topological material.

Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states

Td-WTe₂ (non-centrosymmetric and orthorhombic), a type-II Weyl semimetal, is expected to have higher-order topological phases with topologically protected, helical one-dimensional hinge states when its Weyl points are annihilated. However, the detection of these hinge states is difficult due to the semimetallic behaviour of the bulk. In this study, we have spatially resolved the hinge states by analysing the magnetic field interference of the supercurrent in Nb-WTe₂-Nb proximity Josephson junctions. The Josephson current along the a axis of the WTe₂ crystal, but not along the b axis, showed a sharp enhancement at the edges of the junction, and the amount of enhanced Josephson current was comparable to the upper limits of a single one-dimensional helical channel. Our experimental observations suggest a higher-order topological phase in WTe₂ and its corresponding anisotropic topological hinge states, in agreement with theoretical calculations. Our work paves the way for the study of hinge states in topological transition-metal dichalcogenides and analogous phases.