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The study of kagome materials has attracted much attention in the past few years due to the presence of many electron-electron interaction-driven phases in a single material.In this work, we report the discovery of intrinsic spin-polarized p-wave superconductivity in the thin-flake kagome material RbV$_3$Sb$_5$. Firstly, when an in-plane magnetic field is swept in opposite directions, we observe a unique form of hysteresis in magnetoresistance which is different from the hysteresis induced by extrinsic mechanisms such as flux-trapping or superheating and supercooling effects. The unconventional hysteresis indicates the emergence of an intrinsic time-reversal symmetry-breaking superconducting phase. Strikingly, at a fixed magnetic field, the finite-resistance state can be quenched to the zero-resistance state by applying a large current. Secondly, at temperatures around 400 mK, the re-entrance of superconductivity occurs during an in-plane field-sweeping process with a fixed sweeping direction. This kind of re-entrance is asymmetric about the zero field axis and observed in all field directions for a fixed current direction, which is different from the re-entrance observed in conventional superconductors. Moreover, the angle-dependent in-plane critical field measurements reveal a two-fold symmetry that deviates from the original, centrosymmetric D$_{6h}$ point group symmetry of the crystal. These findings put very strong constraints on the possible superconducting pairing symmetry of RbV$_3$Sb$_5$. We point out that the pairing symmetry, which is consistent with the crystal symmetry and all the observed novel properties, is a time-reversal symmetry-breaking, p-wave pairing with net spin polarization. Importantly, this p-wave pairing gives rise to a nodal topological superconducting state with Majorana flat bands on the sample edges., Comment: 21 pages, 4 figures

The intrinsic anomalous Hall effect (AHE) has been reported in numerous ferromagnetic (FM) Weyl semimetals. However, AHE in the antiferromagnetic (AFM) or paramagnetic (PM) state of Weyl semimetals has been rarely observed experimentally, and only in centrosymmetric materials. Different mechanisms have been proposed to establish the connection between the AHE and the type of magnetic order. In this paper, we report AHE in both the AFM and PM states of non-centrosymmetric compound SmAlSi. To account for the AHE in non-centrosymmetric Weyl semimetals without FM, we introduce a new mechanism based on magnetic field-induced Weyl nodes evolution. Angle-dependent quantum oscillations in SmAlSi provide evidence for the Weyl points and large AHE in both the PM and the AFM states. The proposed mechanism qualitatively explains the temperature dependence of the anomalous Hall conductivity (AHC), which displays unconventional power law behavior of the AHC in both AFM and PM states of SmAlSi.

Destructive interference between electron wavefunctions on the two-dimensional (2D) kagome lattice induces an electronic flat band, which could host a variety of interesting many-body quantum states. Key to realize these proposals is to demonstrate the real space localization of kagome flat band electrons. In particular, the extent to which the often more complex lattice structure and orbital composition of realistic materials counteract the localizing effect of destructive interference, described by the 2D kagome lattice model, is hitherto unknown. We used scanning tunneling microscopy (STM) to visualize the non-trivial Wannier states of a kagome flat band at the surface of CoSn, a kagome metal. We find that the local density of states associated with the flat bands of CoSn is localized at the center of the kagome lattice, consistent with theoretical expectations for their corresponding Wannier states. Our results show that these states exhibit an extremely small localization length of two to three angstroms concomitant with a strongly renormalized quasiparticle velocity, which is comparable to that of moir\'e superlattices. Hence, interaction effects in the flat bands of CoSn could be much more significant than previously thought. Our findings provide fundamental insight into the electronic properties of kagome metals and are a key step for future research on emergent many-body states in transition metal based kagome materials.

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 show 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., Comment: 20 pages, 4 figures, SI included

The study of quantum geometry effects in materials has been one of the most important research directions in recent decades. The quantum geometry of a material is characterized by the quantum geometry tensor of the Bloch states. The imaginary part of the quantum geometry tensor gives rise to the Berry curvature while the real part gives rise to the quantum metric. While Berry curvature has been well studied in the past decades, the experimental investigation on the quantum metric effects is only at its infancy stage. In this work, we measure the nonlinear transport of bulk MnBi${_2}$Te${_4}$, which is a topological anti-ferromagnet. We found that the second order nonlinear responses are negligible as required by inversion symmetry, the third-order nonlinear responses are finite. The measured third-harmonic longitudinal ($V_{xx}^{3{\omega}}$) and transverse ($V_{xy}^{3{\omega}}$) voltages with frequency 3w, driven by an a.c. current with frequency w, show an intimate connection with magnetic transitions of MnBi${_2}$Te${_4}$ flakes. Their magnitudes change abruptly as MnBi${_2}$Te${_4}$ flakes go through magnetic transitions from an AFM state to a canted AFM state and to a FM state. In addition, the measured $V_{xx}^{3{\omega}}$ is an even function of the applied magnetic field B while $V_{xy}^{3{\omega}}$ is odd in B. Amazingly, the field dependence of the third-order responses as a function of the magnetic field suggests that $V_{xx}^{3{\omega}}$ is induced by quantum metric quadrupole and $V_{xy}^{3{\omega}}$ is induced by Berry curvature quadrupole. Therefore, the quadrupoles of both the real and the imaginary part of the quantum geometry tensor of bulk MnBi${_2}$Te${_4}$ are revealed through the third order nonlinear transport measurements. This work greatly advanced our understanding on the connections between the higher order moments of quantum geometry and nonlinear transport.

Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may also enable future applications in energy harvesting and high-frequency technology. It was shown that a Berry curvature dipole can give rise to a 2nd order NLAHE in materials of low crystalline symmetry. Here, we demonstrate a fundamentally new mechanism for Berry curvature multipoles in antiferromagnets that are supported by the underlying magnetic symmetries. Carrying out electric transport measurements on the kagome antiferromagnet FeSn, we observe a 3rd order NLAHE, which appears as a transverse voltage response at the 3rd harmonic frequency when a longitudinal a.c. current drive is applied. Interestingly, this NLAHE is strongest at and above room temperature. We combine these measurements with a scaling law analysis, a symmetry analysis, model calculations, first-principle calculations, and magnetic Monte-Carlo simulations to show that the observed NLAHE is induced by a Berry curvature quadrupole appearing in the spin-canted state of FeSn. At a practical level, our study establishes NLAHE as a sensitive probe of antiferromagnetic phase transitions in other materials, such as moir\'e superlattices, two-dimensional van der Waal magnets, and quantum spin liquid candidates, that remain poorly understood to date. More broadly, Berry curvature multipole effects are predicted to exist for 90 magnetic point groups. Hence, our work opens a new research area to study a variety of topological magnetic materials through nonlinear measurement protocols.

In this work, ~100 nm wide quantum anomalous Hall insulator (QAHI) nanoribbons are etched from a two-dimensional QAHI film. One part of the nanoribbon is covered with superconducting Nb, while the other part is connected to an Au lead via two-dimensional QAHI regions. Andreev reflection spectroscopy measurements were performed, and multiple in-gap conductance peaks were observed in three different devices. In the presence of an increasing magnetic field perpendicular to the QAHI film, the multiple in-gap peak structure evolves into a single zero-bias conductance peak (ZBCP). Theoretical simulations suggest that the measurements are consistent with the scenario that the increasing magnetic field drives the nanoribbons from a multi-channel occupied regime to a single channel occupied regime, and that the ZBCP may be induced by zero energy Majorana modes as previously predicted [24]. Although further experiments are needed to clarify the nature of the ZBCP, we provide initial evidence that quasi-1D QAHI nanoribbon/superconductor heterostructures are new and promising platforms for realizing zero-energy Majorana modes.

Kramers nodal lines (KNLs) have recently been proposed theoretically as a special type of Weyl line degeneracy connecting time-reversal invariant momenta. KNLs are robust to spin orbit coupling and are inherent to all non-centrosymmetric achiral crystal structures, leading to unusual spin, magneto-electric, and optical properties. However, their existence in in real quantum materials has not been experimentally established. Here we gather the experimental evidence pointing at the presence of KNLs in SmAlSi, a non-centrosymmetric metal that develops incommensurate spin density wave order at low temperature. Using angle-resolved photoemission spectroscopy, density functional theory calculations, and magneto-transport methods, we provide evidence suggesting the presence of KNLs, together with observing Weyl fermions under the broken inversion symmetry in the paramagnetic phase of SmAlSi. We discuss the nesting possibilities regarding the emergent magnetic orders in SmAlSi. Our results provide a solid basis of experimental observations for exploring correlated topology in SmAlSi., Comment: 40 pages, 5 figures, 1 table

Moir\'e 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 moir\'e flat bands over a wide range of twist angles. For twist angle close to 60{\deg}, 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 larger than 57{\deg}. The bandwidth, manifested as narrow tunneling conductance peaks, is estimated less than 10meV, 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 the theoretical predictions incredibly well, 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., Comment: 17 pages, 4 figures

The recently discovered nonlinear Hall effect (NHE) in a few non-interacting systems provides a novel mechanism to generate second harmonic electrical Hall signals under time-reversal-symmetric conditions. Here, we introduce a new approach to engineering NHE by using twisted moir\'e structures. We find that the twisted WSe$_2$ bilayer exhibits a NHE when tuning the Fermi level to the moir\'e flat bands. Near half-filling of the first moir\'e band, the nonlinear Hall signal shows a sharp peak with the generation efficiency at least two orders of magnitude larger than those in previous experiments. We propose that the giant NHE and diverging generation efficiency originate from a mass-diverging type continuous Mott transition, which is evidenced by resistivity measurements. This work demonstrates not only how interaction effects can couple to Berry curvature dipoles to produce novel quantum phenomena, but also what NHE measurements can provide for developing a new tool to study the quantum criticality., Comment: Main text (15 pages, 4 figures), Supplemental Material (12 pages, 8 figures)

We report in this paper our numerical analysis of energy level spacing statistics for the one-dimensional spin-$1/2$ XXZ model in random on-site longitudinal magnetic fields $B_i$ ($-h\leq B_i\leq h$)). We concentrate on the strong disorder limit $J_{\perp}<

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 new 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.

The noncentrosymmetric Td-WTe$_2$, previously known as a type-II Weyl semimetal, is expected to have higher order topological phases with topologically protected, helical one-dimensional (1D) hinge states when their scarcely separated Weyl points get annihilated. However, the detection of these hinge states is difficult in the presence of the semimetallic behaviour of the bulk. Here, we spatially resolved the hinge states by analysing the magnetic field interference of supercurrent in Nb-WTe$_2$-Nb proximity Josephson junctions. The Josephson current along the a-axis of the WTe$_2$ crystal, but not along the b-axis, showed sharp enhancements at the edges of the junction; the amount of enhanced Josephson current was comparable to the upper limits of a single 1D conduction channel. Our experimental observations provide evidence of the higher order topological phase in WTe$_2$ and its corresponding anisotropic topological hinge states, in good agreement with theoretical calculations. Our work paves the way for hinge transport studies on topological semimetals in superconducting heterostructures, including their topological superconductivity., Comment: 29 pages, 11 figures

The interplay between disorder and superconductivity is a subtle and fascinating phenomenon in quantum many body physics. The conventional superconductors are insensitive to dilute nonmagnetic impurities, known as the Anderson's theorem. Destruction of superconductivity and even superconductor-insulator transitions occur in the regime of strong disorder. Hence disorder-enhanced superconductivity is rare and has only been observed in some alloys or granular states. Because of the entanglement of various effects, the mechanism of enhancement is still under debate. Here we report well-controlled disorder effect in the recently discovered monolayer NbSe$_2$ superconductor. The superconducting transition temperatures of NbSe$_2$ monolayers are substantially increased by disorder. Realistic theoretical modeling shows that the unusual enhancement possibly arises from the multifractality of electron wave functions. This work provides the first experimental evidence of the multifractal superconducting state.

Time reversal and spatial inversion are two key symmetries for conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity. Breaking inversion symmetry can lead to mixed-parity Cooper pairing and unconventional superconducting properties. Two-dimensional (2D) NbSe$_2$ has emerged as a new non-centrosymmetric superconductor with the unique out-of-plane or Ising spin-orbit coupling (SOC). Here, we report the observation of an unusual continuous paramagnetic-limited superconductor-normal metal transition in 2D NbSe$_2$. Using tunneling 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 superconductors. 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 NbSe$_2$. Our findings establish 2D NbSe$_2$ as a promising platform for exploring novel spin-dependent superconducting phenomena and device concepts, such as equal-spin Andreev reflection and topological superconductivity.

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 quantum origin of valley Hall effects and marks a significant step towards the purely electrical control of valley degree of freedom in topological valleytronics., Comment: 22 pages, 4 figures

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) MX2 (M=W, Mo, Nb, and X=Te, Se, S) with strong spin-orbit coupling (SOC) possess plenty of novel physics including superconductivity. Due to the Ising SOC, monolayer NbSe$_2$ and gated MoS$_2$ of 2H structure can realize the Ising superconductivity phase, which manifests itself with in-plane upper critical field far exceeding Pauli paramagnetic limit. Surprisingly, we find that a few-layer 1Td structure MoTe$_2$ also exhibits an in-plane upper critical field ($H_{c2,//}$) 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 $H_{c2,//}$ in 2H structure TMDCs. We show that this is a result of an asymmetric SOC in 1Td structure TMDCs. The asymmetric SOC is very strong and estimated to be on the order of tens of meV. Our work provides the first transport evidence of a new type of asymmetric SOC in TMDCs which may give rise to novel superconducting and spin transport properties. Moreover, our findings mostly depend on the symmetry of the crystal and apply to a whole class of 1Td TMDCs such as 1Td-WTe$_2$ which is under intense study due to its topological properties., Comment: 34 pages, 12 figures

A nematic topological superconductor has an order parameter symmetry, which spontaneously breaks the crystalline symmetry in its superconducting state. This state can be observed, for example, by thermodynamic or upper critical field experiments in which a magnetic field is rotated with respect to the crystalline axes. The corresponding physical quantity then directly reflects the symmetry of the order parameter. We present a study on the superconducting upper critical field of the Nb-doped topological insulator NbxBi2Se3 for various magnetic field orientations parallel and perpendicular to the basal plane of the Bi2Se3 layers. The data were obtained by two complementary experimental techniques, magnetoresistance and DC magnetization, on three different single crystalline samples of the same batch. Both methods and all samples show with perfect agreement that the in-plane upper critical fields clearly demonstrate a two-fold symmetry that breaks the three-fold crystal symmetry. The two-fold symmetry is also found in the absolute value of the magnetization of the initial zero-field-cooled branch of the hysteresis loop and in the value of the thermodynamic contribution above the irreversibility field, but also in the irreversible properties such as the value of the characteristic irreversibility field and in the width of the hysteresis loop. This provides strong experimental evidence that Nb-doped Bi2Se3 is a nematic topological superconductor similar to the Cu- and Sr-doped Bi2Se3.

Superconducting proximity effect (SPE) in topological insulator (TI) and superconductor (SC) hybrid structure has attracted intense attention in recent years in an effort to search for mysterious Majorana fermions (MFs) in condensed matter systems. Here we report on the SPE in a Bi2Se3/NbSe2 junction fabricated with an all-dry transfer method. Resulting from the highly transparent interface, two sharp resistance drops are observed at 7 K and 2 K, respectively, corresponding to the superconducting transition of NbSe2 flake and the SPE induced superconductivity in Bi2Se3 flake. Experimentally measured differential conductance spectra exhibit a bias-independent conductance plateau (BICP) in the vicinity of zero bias below 7 K. As temperatures further decrease a zero bias conductance peak (ZBCP) emerges from the plateau and becomes more enhanced and sharpened at lower temperatures. Our numerically simulated differential conductance spectra reproduce the observed BICP and ZBCP and show that the SPE in topological surface states (TSS) is much stronger than that in the bulk states of Bi2Se3. The SPE induced superconducting gap for the TSS of Bi2Se3 is comparable to that of NbSe2 and gives rise to the observed BICP below 7 K. In contrast, the SPE induced superconducting gap for the bulk states of Bi2Se3 is an order of magnitude smaller than that of NbSe2 and superconducting TSS. These weakly paired bulk states in Bi2Se3 give rise to the ZBCP below 2 K. Our study has clearly unveiled the different roles of TSS and bulk stats in SPE, clarified the physical origin of the SPE induced features, and shined light on further investigation of SPE and MF in TI/SC hybrid structures.

Two-dimensional transition metal dichalcogenides with strong spin-orbit interactions and valley-dependent Berry curvature effects have attracted tremendous recent interests. Although novel single-particle and excitonic phenomena related to spin-valley coupling have been extensively studied, effects of spin-momentum locking on collective quantum phenomena remain unexplored. Here we report an observation of superconducting monolayer NbSe$_2$ with an in-plane upper critical field over six times of the Pauli paramagnetic limit by magneto-transport measurements. The effect can be understood in terms of the competing Zeeman effect and large intrinsic spin-orbit interactions in non-centrosymmetric NbSe$_2$ monolayers, where the electronic spin is locked to the out-of-plane direction. Our results provide a strong evidence of unconventional Ising pairing protected by spin-momentum locking and open up a new avenue for studies of non-centrosymmetric superconductivity with unique spin and valley degrees of freedom in the exact two-dimensional limit.

Superconductivity at the interface of a heterostructure confined to nanometer-sized scale offers unique opportunities to study the exotic physics of two-dimensional superconductivity. 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 induced by the Bi2Te3 epilayer with thickness even down to one quintuple layer. 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., Comment: 24 pages, 5 figures and supplementary information