Nonlinear optical diode effect in a magnetic Weyl semimetal.

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light.

Giant nonlinear Hall effect in twisted bilayer WSe2.

The recently discovered nonlinear Hall effect (NHE) in a few non-interacting systems provides a novel mechanism for generating second-harmonic electrical Hall signals under time-reversal-symmetric conditions. Here, we introduce a new approach to engineering an NHE by using twisted moiré structures. We found that the twisted WSe2 bilayer exhibited an NHE when the Fermi level was tuned to the moiré flat bands. When the first moiré band was half-filled, the nonlinear Hall signal exhibited a sharp peak with a generation efficiency that was at least two orders of magnitude greater than those obtained in previous experiments. We discuss the possible origins of the diverging generation efficiency in twisted WSe2 based on resistivity measurements, such as moiré-interface-induced correlation effects and mass-diverging-type continuous Mott transition. This study demonstrates not only how interaction effects can combine with Berry curvature dipoles to produce novel quantum phenomena, but also the potential of NHE measurements as a new tool for studying quantum criticality.

Lattice reconstruction induced multiple ultra-flat bands in twisted bilayer WSe2.

Moiré superlattices in van der Waals heterostructures provide a tunable platform to study emergent properties that are absent in the natural crystal form. Twisted bilayer transition metal dichalcogenides (TB-TMDs) can host moiré flat bands over a wide range of twist angles. For twist angle close to 60°, it was predicted that TB-TMDs undergo a lattice reconstruction which causes the formation of ultra-flat bands. Here, by using scanning tunneling microscopy and spectroscopy, we show the emergence of multiple ultra-flat bands in twisted bilayer WSe2 when the twist angle is within 3° of 60°. The ultra-flat bands are manifested as narrow tunneling conductance peaks with estimated bandwidth less than 10 meV, which is only a fraction of the estimated on-site Coulomb repulsion energy. The number of these ultra-flat bands and spatial distribution of the wavefunctions match well with the theoretical predictions, strongly evidencing that the observed ultra-flat bands are induced by lattice reconstruction. Our work provides a foundation for further study of the exotic correlated phases in TB-TMDs.

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.

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

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Signature of a pair of Majorana zero modes in superconducting gold surface states.

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin-orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.

Spectroscopic fingerprint of chiral Majorana modes at the edge of a quantum anomalous Hall insulator/superconductor heterostructure.

With the recent discovery of the quantum anomalous Hall insulator (QAHI), which exhibits the conductive quantum Hall edge states without external magnetic field, it becomes possible to create a topological superconductor (SC) by introducing superconductivity into these edge states. In this case, 2 distinct topological superconducting phases with 1 or 2 chiral Majorana edge modes were theoretically predicted, characterized by Chern numbers (N) of 1 and 2, respectively. We present spectroscopic evidence from Andreev reflection experiments for the presence of chiral Majorana modes in an Nb/(Cr0.12Bi0.26Sb0.62)2Te3 heterostructure with distinct signatures attributed to 2 different topological superconducting phases. The results are in qualitatively good agreement with the theoretical predictions.

Proximity-induced surface superconductivity in Dirac semimetal Cd3As2.

Cd3As2 is a three-dimensional Dirac semimetal with separated Dirac points in momentum space. In spite of extensive transport and spectroscopic studies on its exotic properties, the evidence of superconductivity in its surface states remains elusive. Here, we report the observation of proximity-induced surface superconductivity in Nb/Cd3As2 hybrid structures. Our four-terminal transport measurement identifies a pronounced proximity-induced pairing gap (gap size comparable to Nb) on the surfaces, which exhibits a flat conductance plateau in differential conductance spectra, consistent with our theoretical simulations. The surface supercurrent from Nb/Cd3As2/Nb junctions is also achieved with a Fraunhofer/SQUID-like pattern under out-of-plane/in-plane magnetic fields, respectively. The resultant mapping shows a predominant distribution on the top and bottom surfaces as the bulk carriers are depleted, which can be regarded as a higher dimensional analog of edge supercurrent in two-dimensional quantum spin Hall insulators. Our study provides the evidence of surface superconductivity in Dirac semimetals.

Transport evidence of asymmetric spin-orbit coupling in few-layer superconducting 1Td-MoTe2.

Two-dimensional transition metal dichalcogenides MX2 (M = W, Mo, Nb, and X = Te, Se, S) with strong spin-orbit coupling possess plenty of novel physics including superconductivity. Due to the Ising spin-orbit coupling, monolayer NbSe2 and gated MoS2 of 2H structure can realize the Ising superconductivity, which manifests itself with in-plane upper critical field far exceeding Pauli paramagnetic limit. Surprisingly, we find that a few-layer 1Td structure MoTe2 also exhibits an in-plane upper critical field which goes beyond the Pauli paramagnetic limit. Importantly, the in-plane upper critical field shows an emergent two-fold symmetry which is different from the isotropic in-plane upper critical field in 2H transition metal dichalcogenides. We show that this is a result of an asymmetric spin-orbit coupling in 1Td transition metal dichalcogenides. Our work provides transport evidence of a new type of asymmetric spin-orbit coupling in transition metal dichalcogenides which may give rise to novel superconducting and spin transport properties.

Intrinsic valley Hall transport in atomically thin MoS2.

Electrons hopping in two-dimensional honeycomb lattices possess a valley degree of freedom in addition to charge and spin. In the absence of inversion symmetry, these systems were predicted to exhibit opposite Hall effects for electrons from different valleys. Such valley Hall effects have been achieved only by extrinsic means, such as substrate coupling, dual gating, and light illuminating. Here we report the first observation of intrinsic valley Hall transport without any extrinsic symmetry breaking in the non-centrosymmetric monolayer and trilayer MoS2, evidenced by considerable nonlocal resistance that scales cubically with local resistance. Such a hallmark survives even at room temperature with a valley diffusion length at micron scale. By contrast, no valley Hall signal is observed in the centrosymmetric bilayer MoS2. Our work elucidates the topological origin of valley Hall effects and marks a significant step towards the purely electrical control of valley degree of freedom in topological valleytronics.

Inducing Strong Superconductivity in WTe2 by a Proximity Effect.

The search for proximity-induced superconductivity in topological materials has generated widespread interest in the condensed matter physics community. The superconducting states inheriting nontrivial topology at interfaces are expected to exhibit exotic phenomena such as topological superconductivity and Majorana zero modes, which hold promise for applications in quantum computation. However, a practical realization of such hybrid structures based on topological semimetals and superconductors has hitherto been limited. Here, we report the strong proximity-induced superconductivity in type-II Weyl semimetal WTe2, in a van der Waals hybrid structure obtained by mechanically transferring NbSe2 onto various thicknesses of WTe2. When the WTe2 thickness ( tWTe2) reaches 21 nm, the superconducting transition occurs around the critical temperature ( Tc) of NbSe2 with a gap amplitude (Δp) of 0.38 meV and an unexpected ultralong proximity length ( lp) up to 7 µm. With the thicker 42 nm WTe2 layer, however, the proximity effect yields Tc ≈ 1.2 K, Δp = 0.07 meV, and a short lp of less than 1 µm. Our theoretical calculations, based on the Bogoliubov-de Gennes equations in the clean limit, predict that the induced superconducting gap is a sizable fraction of the NbSe2 superconducting one when tWTe2 is less than 30 nm and then decreases quickly as tWTe2 increases. This agrees qualitatively well with the experiments. Such observations form a basis in the search for superconducting phases in topological semimetals.

An unusual continuous paramagnetic-limited superconducting phase transition in 2D NbSe 2.

Time reversal and spatial inversion are two key symmetries for conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity 1 . Breaking inversion symmetry can lead to mixed-parity Cooper pairing and unconventional superconducting properties1-5. Two-dimensional (2D) NbSe2 has emerged as a new non-centrosymmetric superconductor with the unique out-of-plane or Ising spin-orbit coupling (SOC)6-9. Here we report the observation of an unusual continuous paramagnetic-limited superconductor-normal metal transition in 2D NbSe2. Using tunelling spectroscopy under high in-plane magnetic fields, we observe a continuous closing of the superconducting gap at the upper critical field at low temperatures, in stark contrast to the abrupt first-order transition observed in BCS thin-film superconductors10-12. The paramagnetic-limited continuous transition arises from a large spin susceptibility of the superconducting phase due to the Ising SOC. The result is further supported by self-consistent mean-field calculations based on the ab initio band structure of 2D NbSe2. Our findings establish 2D NbSe2 as a promising platform to explore novel spin-dependent superconducting phenomena and device concepts 1 , such as equal-spin Andreev reflection 13 and topological superconductivity14-16.

Two-dimensional superconductivity at the interface of a Bi2Te3/FeTe heterostructure.

The realization of superconductivity at the interface between a topological insulator and an iron-chalcogenide compound is highly attractive for exploring several recent theoretical predictions involving these two new classes of materials. Here we report transport measurements on a Bi2Te3/FeTe heterostructure fabricated via van der Waals epitaxy, which demonstrate superconductivity at the interface, which is induced by the Bi2Te3 epilayer with thickness even down to one quintuple layer, though there is no clear-cut evidence that the observed superconductivity is induced by the topological surface states. The two-dimensional nature of the observed superconductivity with the highest transition temperature around 12 K was verified by the existence of a Berezinsky-Kosterlitz-Thouless transition and the diverging ratio of in-plane to out-plane upper critical field on approaching the superconducting transition temperature. With the combination of interface superconductivity and Dirac surface states of Bi2Te3, the heterostructure studied in this work provides a novel platform for realizing Majorana fermions.

Surface reactivity enhancement on a Pd/Bi2Te3 heterostructure through robust topological surface states.

We present a study of the surface reactivity of a Pd/Bi2Te3 thin film heterostructure. The topological surface states from Bi2Te3, being delocalized and robust owing to their topological natures, were found to act as an effective electron bath that significantly enhances the surface reactivity of palladium in the presence of two oxidizing agents, oxygen and tellurium respectively, which is consistent with a theoretical calculation. The surface reactivity of the adsorbed tellurium on this heterostructure is also intensified possibly benefitted from the effective transfer of the bath electrons. A partially inserted iron ferromagnetic layer at the interface of this heterostructure was found to play two competing roles arising from the higher-lying d-band center of the Pd/Fe bilayer and the interaction between the ferromagnetism and the surface spin texture of Bi2Te3 on the surface reactivity and their characteristics also demonstrate that the electron bath effect is long-lasting against accumulated thickness of adsorbates.

Negative quantum capacitance induced by midgap states in single-layer graphene.

We demonstrate that single-layer graphene (SLG) decorated with a high density of Ag adatoms displays the unconventional phenomenon of negative quantum capacitance. The Ag adatoms act as resonant impurities and form nearly dispersionless resonant impurity bands near the charge neutrality point (CNP). Resonant impurities quench the kinetic energy and drive the electrons to the Coulomb energy dominated regime with negative compressibility. In the absence of a magnetic field, negative quantum capacitance is observed near the CNP. In the quantum Hall regime, negative quantum capacitance behavior at several Landau level positions is displayed, which is associated with the quenching of kinetic energy by the formation of Landau levels. The negative quantum capacitance effect near the CNP is further enhanced in the presence of Landau levels due to the magnetic-field-enhanced Coulomb interactions.