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Superconductivity and magnetism are antagonistic quantum matter, while their intertwining has long been considered in frustrated-lattice systems1-3. In this work, we utilize scanning tunneling microscopy and muon spin resonance to discover time-reversal symmetry-breaking superconductivity in kagome metal Cs(V,Ta)3Sb5, where the Cooper pairing exhibits magnetism and is modulated by it. In the magnetic channel, we observe spontaneous internal magnetism in a full-gap superconducting state. Under perturbations of inverse magnetic fields, we detect a time-reversal asymmetrical interference of Bogoliubov quasi-particles at a circular vector. At this vector, the pairing gap spontaneously modulates, which is distinct from pair density waves occurring at a point vector and consistent with the theoretical proposal of unusual interference effect under time-reversal symmetry-breaking. The correlation between internal magnetism, Bogoliubov quasi-particles, and pairing modulation provides a chain of experimental clues for time-reversal symmetry-breaking kagome superconductivity., Comment: To appear in Nature Materials (2024)

Superconductivity involving finite momentum pairing can lead to spatial gap and pair density modulations, as well as Bogoliubov Fermi states within the superconducting gap. However, the experimental realization of their intertwined relations has been challenging. Here, we detect chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5 by normal and Josephson scanning tunneling microscopy down to 30mK with resolved electronic energy difference at microelectronvolt level. We observe a U-shaped superconducting gap with flat residual in-gap states. This gap exhibits chiral 2 by 2 spatial modulations with magnetic field tunable chirality, which align with the chiral 2 by 2 pair density modulations observed through Josephson tunneling. These findings demonstrate a chiral pair density wave (PDW) that breaks time-reversal symmetry. Quasiparticle interference imaging of the in-gap zero-energy states reveals segmented arcs, with high-temperature data linking them to parts of the reconstructed V d-orbital states within the charge order. The detected residual Fermi arcs can be explained by the partial suppression of these d-orbital states through an interorbital 2 by 2 PDW and thus serve as candidate Bogoliubov Fermi states. Additionally, we differentiate the observed PDW order from impurity-induced gap modulations. Our observations not only uncover a chiral PDW order with orbital-selectivity, but also illuminate the fundamental space-momentum correspondence inherent in finite momentum paired superconductivity., Comment: To appear in Nature (2024)

The pursuit for "ferroelectric metal" which combines seemingly incompatible spontaneous electric polarization and metallicity, has been assiduously ongoing but remains elusive. Unlike traditional ferroelectrics with a wide band gap, ferroelectric (FE) metals can naturally incorporate nontrivial band topology near the Fermi level, endowing them with additional exotic properties. Here, we show first-principles evidence that the metallic PtBi2 monolayer is an intrinsic two-dimensional (2D) topological FE metal, characterized by out-of-plane polarization and a moderate switching barrier. Moreover, it exhibits a topologically nontrivial electronic structure with Z2 invariant equal to 1, leading to a significant FE bulk photovoltaic effect. A slight strain can further enhance this effect to a remarkable level, which far surpass that of previously reported 2D/3D FE materials. Our work provides an important step towards realizing intrinsic monolayer topological FE metals and paves a promising way for future nonlinear optical devices., Comment: 7 pages, 5 figures

The Weyl semimetals represent a distinct category of topological materials wherein the low-energy excitations appear as the long-sought Weyl fermions. Exotic transport and optical properties are expected because of the chiral anomaly and linear energy-momentum dispersion. While three-dimensional Weyl semimetals have been successfully realized, the quest for their two-dimensional (2D) counterparts is ongoing. Here, we report the realization of 2D Weyl fermions in monolayer PtTe$_{1.75}$, which has strong spin-orbit coupling and lacks inversion symmetry, by combined angle-resolved photoemission spectroscopy, scanning tunneling microscopy, second harmonic generation, X-ray photoelectron spectroscopy measurements, and first-principles calculations. The giant Rashba splitting and band inversion lead to the emergence of three pairs of critical Weyl cones. Moreover, monolayer PtTe$_{1.75}$ exhibits excellent chemical stability in ambient conditions, which is critical for future device applications. The discovery of 2D Weyl fermions in monolayer PtTe$_{1.75}$ opens up new possibilities for designing and fabricating novel spintronic devices., Comment: Nano Letters, In Press

Kagome superconductors AV3Sb5 (A = K, Rb, Cs) exhibit a characteristic superconducting and charge-density wave (CDW) phase diagram upon carrier doping and chemical substitution. However, the key electronic states responsible for such a phase diagram have yet to be clarified. Here we report a systematic micro-focused angle-resolved photoemission spectroscopy (ARPES) study of Cs(V1-xCrx)3Sb5 as a function of Cr content x, where Cr substitution causes monotonic reduction of superconducting and CDW transition temperatures. We found that the V-derived bands forming saddle points at the M point and Dirac nodes along high-symmetry cuts show an energy shift due to electron doping by Cr substitution, whereas the Sb-derived electron band at the Gamma point remains almost unchanged, signifying an orbital-selective band shift. We also found that band doubling associated with the emergence of three-dimensional CDW identified at x = 0 vanishes at x = 0.25, in line with the disappearance of CDW. A comparison of band diagrams among Ti-, Nb-, and Cr-substituted Cs(V1-xCrx)3Sb5 suggests the importance to simultaneously take into account the two saddle points at the M point and their proximity to the Fermi energy, to understand the complex phase diagram against carrier doping and chemical pressure., Comment: 7 pages, 4 figures

The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of band complexes. By translating the symmetry conditions into a set of band balance equations, we show that all possible band structure solutions can be described by a positive affine monoid structure, which has a unique minimal set of generators, called Hilbert basis. We show that Hilbert basis completely determine whether a band complex is reducible and how it can be decomposed. The band complexes corresponding to Hilbert basis vectors, termed as Hilbert band complexes (HBCs), can be regarded as elementary building blocks of band structures. We develop algorithms to construct HBCs, analyze their graph features, and merge them into large complexes. We find some interesting examples, such as HBCs corresponding to complete bipartite graphs, and complexes which can grow without bound by successively merging a HBC., Comment: 9 pages, 7 figures

Kagome metal CsV$_3$Sb$_5$ has attracted much recent attention due to the coexistence of multiple exotic orders and the associated proposals to mimic unconventional high temperature superconductors. Nevertheless, magnetism and strong electronic correlations -- two essential ingredients for unconventional superconductivity, are absent in this V-based Kagome metal. CsCr$_3$Sb$_5$ is a newly discovered Cr-based parallel of CsV$_3$Sb$_5$, in which magnetism appears with charge density wave and superconductivity at different temperature and pressure regions. Enhanced electronic correlations are also suggested by theoretical proposals due to the calculated flat bands. Here, we report angle-resolved photoemission measurements and first-principles calculations on this new material system. Electron energy bands and the associated orbitals are resolved. Flat bands are observed near the Fermi level. Doping dependent measurements on Cs(Cr$_x$V$_{1-x}$)$_3$Sb$_5$ reveal a gradually enhanced band renormalization from CsV$_3$Sb$_5$ to CsCr$_3$Sb$_5$, accompanied by distinct spatial symmetry breaking states in the phase diagram.

Despite the rapid progress in the study of planar Hall effect (PHE) in recent years, all the previous works only showed that the PHE is connected to local geometric quantities, such as Berry curvature. Here, for the first time, we point out that the PHE in magnetic Weyl semimetals is directly related to a global quantity, namely, the Chern number of the Weyl point. This leads to a remarkable consequence that the PHE observation predicted here is robust against many system details, including the Fermi energy. The main difference between non-magnetic and magnetic Weyl points is that the latter breaks time-reversal symmetry T, thus generally possessing an energy tilt. Via semiclassical Boltzmann theory, we investigate the PHE in generic magnetic Weyl models with energy tilt and arbitrary Chern number. We find that by aligning the magnetic and electric fields in the same direction, the trace of the PHE conductivity contributed from Berry curvature and orbital moment is proportional to the Chern number and the energy tilt of the Weyl points, resulting in previously undiscovered quantized PHE plateau by varying Fermi energy. We further confirm the existence of PHE plateaus in a more realistic lattice model without T symmetry. By proposing a new quantized physical quantity, our work not only provides a new tool for extracting the topological character of the Weyl points but also suggests that the interplay between topology and magnetism can give rise to intriguing physics., Comment: 15 pages, 5 figures

Recent developments have introduced a groundbreaking form of collinear magnetism known as "altermagnetism". This emerging magnetic phase is characterized by robust time-reversal symmetry breaking, antiparallel magnetic order, and alternating spin-splitting band structures, yet it exhibits vanishing net magnetization constrained by symmetry. Altermagnetism uniquely integrates traits previously considered mutually exclusive to conventional collinear ferromagnetism and antiferromagnetism, thereby facilitating phenomena and functionalities previously not achievable within these traditional categories of magnetism. Initially proposed theoretically, the existence of the altermagnetic phase has since been corroborated by a range of experimental studies, which have confirmed its unique properties and potential for applications. This review explores the rapidly expanding research on altermagnets, emphasizing the novel physical phenomena they manifest, methodologies for inducing altermagnetism, and promising altermagnetic materials. The goal of this review is to furnish readers with a comprehensive overview of altermagnetism and to inspire further innovative studies on altermagnetic materials which could potentially revolutionize applications in technology and materials science., Comment: Submitted to Adv. Funct. Mater

Exploring new Hall effect is always a fascinating research topic. The ordinary Hall effect and the quantum Hall effect, initially discovered in two-dimensional (2D) non-magnetic systems, are the phenomena that a transverse current is generated when a system carrying an electron current is placed in a magnetic field perpendicular to the currents. In this work, we propose the electric counterparts of these two Hall effects, termed as electric Hall effect (EHE) and quantum electric Hall effect (QEHE). The EHE and QEHE emerge in 2D magnetic systems, where the transverse current is generated by applying an electric gate-field instead of a magnetic field. We present a symmetry requirement for intrinsic EHE and QEHE. With a weak gate-field, we establish an analytical expression of the intrinsic EHE coefficient. We show that it is determined by intrinsic band geometric quantities: Berry curvature and its polarizability which consists of both intraband and interband layer polarization. Via first-principles calculations, we investigate the EHE in the monolayer Ca(FeN)$_2$, where significant EHE coefficient is observed around band crossings. Furthermore, we demonstrate that the QEHE can appear in the semiconductor monolayer $\rm BaMn_2S_3$, of which the Hall conductivity exhibits steps that take on the quantized values $0$ and $\pm1$ in the unit of $e^2/h$ by varying the gate-field within the experimentally achievable range. Due to the great tunability of the electric gate-field, the EHE and QEHE proposed here can be easily controlled and should have more potential applications., Comment: 7 pages, 3 figures

There has been a significant focus on real topological systems that enjoy space-time inversion symmetry (PT ) and lack spin-orbit coupling. While the theoretical classification of the real topology has been established, more progress has yet to be made in the materials realization of such real topological systems in three dimensions (3D). To address this crucial issue, by selecting the carbon-based material candidates as targets, we perform high-throughput computing to inspect the real topology in the phonon spectrums of the 3D carbon allotropes in the Samara Carbon Allotrope Database (SACADA). Among 1192 kinds of 3D carbon allotropes, we find 65 real topological systems with a phononic real Chern insulating (PRCI) state, 2 real topological systems with a phononic real nodal line (PRNL) state, 10 real topological systems with a phononic real Dirac point (PRDP) state, and 8 real topological systems with a phononic real triple-point pair (PRTPP) state. This extremely expands the material candidates with real topology, especially for the gapless topological phonons. We exhibit the PRCI, PRNL, PRTPP, and PRDP states of 27-SG. 166-pcu-h, 1081-SG. 194- 4 2T13-CA, 52-SG. 141-gis, and 132-SG. 191-3,4T157 as illustrative examples, and explore the second-order boundary mode, i.e., phononic hinge mode. Among the four examples, the materials 1081-SG. 194-42T13-CA and 52-SG. 141-gis are so ideal that the PRNL and PRTPP in them are well separated from other bands, and the phononic hinge mode can be clearly observed. This study aims to broaden the understanding of 3D topological phonons, and emphasizes the potential of 3D carbon allotropes as a valuable framework for exploring the fascinating physics related to phononic hinge modes and phononic real topology.

Transition metal compounds with kagome structure have been found to exhibit a variety of exotic structural, electronic, and magnetic orders. These orders are competing with energies very close to each other, resulting in complex phase transitions. Some of the phases are easily observable, such as the charge density wave (CDW) and the superconducting phase, while others are more challenging to identify and characterize. Here we present magneto-transport evidence of a new phase below ~35 K in the kagome topological metal CsV$_3$Sb$_5$ (CVS) thin flakes between the CDW and the superconducting transition temperatures. This phase is characterized by six-fold rotational symmetry in the in-plane magnetoresistance (MR) and is connected to the orbital current order in CVS. Furthermore, the phase is characterized by a large in-plane negative magnetoresistance, which suggests the existence of a three-dimensional, magnetic field-tunable orbital current ordered phase. Our results highlight the potential of magneto-transport to reveal the interactions between exotic quantum states of matter and to uncover the symmetry of such hidden phases.

Nonvolatile optical manipulation of material properties on demand is a highly sought-after feature in the advancement of future optoelectronic applications. While the discovery of such metastable transition in various materials holds good promise for achieving this goal, their practical implementation is still in the nascent stage. Here, we unravel the nature of the ultrafast laser-induced hidden state in 1T-TaS2 by systematically characterizing the electronic structure evolution throughout the reversible transition cycle. We identify it as a mixed-stacking state involving two similarly low-energy interlayer orders, which is manifested as the charge density wave phase disruption. Furthermore, our comparative experiments utilizing the single-pulse writing, pulse-train erasing and pulse-pair control explicitly reveal the distinct mechanism of the bidirectional transformations -- the ultrafast formation of the hidden state is initiated by a coherent phonon which triggers a competition of interlayer stacking orders, while its recovery to the initial state is governed by the progressive domain coarsening. Our work highlights the deterministic role of the competing interlayer orders in the nonvolatile phase transition in the layered material 1T-TaS2, and promises the coherent control of the phase transition and switching speed. More importantly, these results establish all-optical engineering of stacking orders in low-dimensional materials as a viable strategy for achieving desirable nonvolatile electronic devices.

In the recently discovered kagome superconductor AV3Sb5 (A = K, Rb, and Cs), the superconductivity is intertwined with an unconventional charge density wave order. Its pairing symmetry remains elusive owing to the lack of direct measurement of the superconducting gap in the momentum space. In this letter, utilizing laser-based ultra-high-resolution and low-temperature angle-resolved photoemission spectroscopy, we observe anisotropic Cooper pairing in kagome superconductor CsV3Sb5. We detect a highly anisotropic superconducting gap structure with an anisotropy over 80% and the gap maximum along the V-V bond direction on a Fermi surface originated from the 3d-orbital electrons of the V kagome lattice. It is in stark contrast to the isotropic superconducting gap structure on the other Fermi surface that is occupied by Sb 5p-orbital electrons. Our observation of the anisotropic Cooper pairing in pristine CsV3Sb5 is fundamental for understanding intertwined orders in the ground state of kagome superconductors.

We find that the Berry curvature splits the edge plasmons propagating along the opposite directions in quantum anomalous Hall insulators even with vanishing Chern number. When the bulk is insulating, only one unidirectional edge plasmon mode survives whose direction can be changed by external fields. The unidirectional edge plasmon in the long-wavelength limit is acoustic and essentially determined by the anomalous Hall conductivity. The group velocity of the chiral edge plasmon would change its sign for a large wave vector, which originates from the k-quadratic correction to the effective mass. The impacts of the Fermi level and the wave vector on the bulk and edge plasmons are discussed. Our work provides a well quantitative explanation of the recent observation of the chiral edge plasmon in quantum anomalous Hall insulators and some insight into the application of realistic topological materials in chiral plasmonics., Comment: 6 pages, 4 figures

There is a common belief that superconductivity and charge density wave (CDW) order accommodate homogenously in real space but compete with each other for the effective density of states in momentum space in CDW superconductors. By measuring resistivity along the $c$-axis in Cs(V$_{1-x}$Ta$_{x}$)$_{3}$Sb$_{5}$, we observe strong superconducting fluctuation behavior coexisting with the CDW order in the pristine CsV$_{3}$Sb$_{5}$, and the fluctuation region becomes narrowed when the Ta doping suppresses the CDW order. The onset transition temperature barely changes with the Ta doping. Therefore, the bulk superconductivity may be established by a doping-independent local pairing, and it can be suppressed in some regions by the spatially variable CDW order along the $c$-axis. Our results violate the above-mentioned belief about CDW superconductors and demonstrate the intricate interaction between superconductivity and CDW order in this kagome superconductor., Comment: 9 pages, 5 figures

By measuring magnetizations of pristine and Ta-doped CsV$_{3}$Sb$_{5}$ single crystals, we have carried out systematic studies on the lower critical field, critical current density, and equilibrium magnetization of this kagome system. The lower critical field has been investigated in the two typical samples, and the temperature dependent lower critical field obtained in Ta-doped sample can be fitted by using the model with two $s$-wave superconducting gaps yielding the larger gap of $2\Delta_{s1}/k_\mathrm{B}T_\mathrm{c}=7.9\;(\pm1.8)$. This indicates a strong-coupling feature of the V-based superconductors. The measured magnetization hysteresis loops allow us to calculate the critical current density, which shows a very weak bulk vortex pinning. The magnetization hysteresis loops measured in these two kinds of samples can be well described by a recently proposed generalized phenomenological model, which leads to the determination of many fundamental parameters for these superconductors. Our systematic results and detailed analysis conclude that this V-based kagome system has features of strong-coupling superconductivity, relatively large Ginzburg-Landau parameter and weak vortex coupling., Comment: 11 pages, 6 figures

We develop a comprehensive logical framework for effectively handling the overcomplete basis set in the Bogoliubov-de Gennes equation that contains two orthonormal basis sets conjugate with each other, such as particle and hole orthonormal basis sets. We highlight the significant implications of our logical framework from theoretical concepts and experimental predictions. Firstly, we rigorously derive all many-body eigenfunctions of arbitrary nonuniform superconductors and uncover that the many-body eigenstates are full of superconducting spin clouds-the electron configuration within the Cooper-like pair of an arbitrary nonuniform superconductor. Secondly, we demonstrate a conjugate loop formed by the effective vacuum states of two orthonormal basis sets conjugate with each other, such as the Fermi sea and sky-the effective vacuum states of positive and negative orthonormal basis sets, respectively. Thirdly, we present a gate-, field-, and phase-tunable tunnel spectroscopy asymmetry arising from the imbalanced particle-hole distribution of the subgap quasiparticles in a quantum-dot Josephson junction. These findings underscore the power of our logical framework and its implications for advancing our understanding and utilization of solid-state devices based on superconductivity., Comment: 28 page, 6 figures

A hallmark of unconventional superconductors is their complex electronic phase diagrams where "intertwined orders" of charge-spin-lattice degrees of freedom compete and coexist as in copper oxides and iron pnictides. While the electronic phase diagram of kagome lattice superconductor such as CsV3Sb5 also exhibits complex behavior involving coexisting and competing charge density wave order and superconductivity, much is unclear about the microscopic origin of superconductivity. Here, we study the vortex lattice (VL) in superconducting state of Cs(V0.86Ta0.14)3Sb5, where the Ta-doping suppresses charge order and enhances superconductivity. Using small-angle neutron scattering, a strictly bulk probe, we show that the VL exhibits a strikingly conventional behavior. This includes a triangular VL with a period consistent with 2e-pairing, a field dependent scattering intensity that follows a London model, and a temperature dependence consistent with a uniform superconducting gap expected for s-wave pairing. These results suggest that optimal bulk superconductivity in Cs(V1-xTax)3Sb5 arises from a conventional Bardeen-Cooper-Schrieffer electron-lattice coupling, different from spin fluctuation mediated unconventional copper and iron based superconductors., Comment: Multiple revisions

It has been theoretically predicted that perturbation of the Berry curvature by electromagnetic fields gives rise to intrinsic nonlinear anomalous Hall effects that are independent of scattering. Two types of nonlinear anomalous Hall effects are expected. The electric nonlinear Hall effect has recently begun to receive attention, while very few studies are concerned with the magneto-nonlinear Hall effect. Here, we combine experiment and first-principles calculations to show that the kagome ferromagnet Fe$_3$Sn$_2$ displays such a magneto-nonlinear Hall effect. By systematic field angular and temperature-dependent transport measurements, we unambiguously identify a large anomalous Hall current that is linear in both applied in-plane electric and magnetic fields, utilizing a unique in-plane configuration. We clarify its dominant orbital origin and connect it to the magneto-nonlinear Hall effect. The effect is governed by the intrinsic quantum geometric properties of Bloch electrons. Our results demonstrate the significance of the quantum geometry of electron wave functions from the orbital degree of freedom and open up a new direction in Hall transport effects., Comment: 18 pages, 4 figures, featured in Physics: Viewpoint and Editors' suggestions

The orbital Hall effect in light materials has attracted considerable attention for developing novel orbitronic devices. Here we investigate the orbital torque efficiency and demonstrate the switching of the perpendicularly magnetized materials through the orbital Hall material (OHM), i.e., Zirconium (Zr). The orbital torque efficiency of approximately 0.78 is achieved in the Zr OHM with the perpendicularly magnetized [Co/Pt]3 sample, which significantly surpasses that of the perpendicularly magnetized CoFeB/Gd/CoFeB sample (approximately 0.04). Such notable difference is attributed to the different spin-orbit correlation strength between the [Co/Pt]3 sample and the CoFeB/Gd/CoFeB sample, which has been confirmed through the theoretical calculations. Furthermore, the full magnetization switching of the [Co/Pt]3 sample with a switching current density of approximately 2.6x106 A/cm2 has been realized through Zr, which even outperforms that of the W spin Hall material. Our finding provides a guideline to understand orbital torque efficiency and paves the way to develop energy-efficient orbitronic devices., Comment: 21 pages, 4 figures, submitted

A real Chern insulator (RCI) featuring a real Chern number and a second-order boundary mode appears in a two-dimensional (2D) system with the space-time inversion symmetry (PT ). Here, we propose a kind of RCI: mirror real Chern insulator (MRCI) which emerges from the system having additional horizontal mirror symmetry Mz. The MRCI generally is characterized by two independent real Chern numbers, respectively defined in the two mirror subsystems of the system. Hence, the MRCI may host the second-order boundary modes different from the conventional RCI. We show that for spinless systems, the definition of the MRCI is straightforward, as PT keeps each mirror subsystem invariant. For the spinful systems with both PT and Mz, the real Chern number for the total system remain well defined, as MzPT = C2zT , and (C2zT )2= 1. However, since C2zT exchanges the two mirror subsystems, the definition of the MRCI in spinful systems requires the help of projective symmetry algebra. We also discuss the MRCIs in 3D systems, where the MRCI is defined on certain mirror-invariant 2D planes. Compared with its 2D counterpart, the 3D MRCI can exhibit more abundant physics when the systems have additional nonsymmorphic operators. Several concrete MRCI models including 2D and 3D, spinless and spinful models are constructed to further demonstrate our ideas.

Vortices and bound states offer an effective means of comprehending the electronic properties of superconductors. Recently, surface dependent vortex core states have been observed in the newly discovered kagome superconductors CsV3Sb5. Although the spatial distribution of the sharp zero energy conductance peak appears similar to Majorana bound states arising from the superconducting Dirac surface states, its origin remains elusive. In this study, we present observations of tunable vortex bound states (VBSs) in two chemically doped kagome superconductors Cs(V1-xTrx)3Sb5 (Tr=Ta or Ti), using low temperature scanning tunneling microscopy/spectroscopy. The CsV3Sb5-derived kagome superconductors exhibit full gap pairing superconductivity accompanied by the absence of long range charge orders, in contrast to pristine CsV3Sb5. Zero energy conductance maps demonstrate a field-driven continuous reorientation transition of the vortex lattice, suggesting multiband superconductivity. The Ta doped CsV3Sb5 displays the conventional cross shaped spatial evolution of Caroli de Gennes Matricon bound states, while the Ti doped CsV3Sb5 exhibits a sharp, non split zero bias conductance peak (ZBCP) that persists over a long distance across the vortex. The spatial evolution of the non split ZBCP is robust against surface effects and external magnetic field but is related to the doping concentrations. Our study reveals the tunable VBSs in multiband chemically doped CsV3Sb5 system and offers fresh insights into previously reported Y shaped ZBCP in a non quantum limit condition at the surface of kagome superconductor., Comment: accepted by Science Bulletin DOI:10.1016/j.scib.2024.01.036

Charge density waves (CDWs) appear in numerous condensed matter platforms, ranging from high-Tc superconductors to quantum Hall systems. Despite such ubiquity, there has been a lack of direct experimental study on boundary states that can uniquely stem from the charge order. Here, using scanning tunneling microscopy, we directly visualize the bulk and boundary phenomenology of CDW in a topological material, Ta2Se8I. Below the transition temperature (TCDW = 260 K), tunneling spectra on an atomically resolved lattice reveal a large insulating gap in the bulk and on the surface, exceeding 500 meV, surpassing predictions from standard weakly-coupled mean-field theory. Spectroscopic imaging confirms the presence of CDW, with LDOS maxima at the conduction band corresponding to the LDOS minima at the valence band, thus revealing a {\pi} phase difference in the respective CDW order. Concomitantly, at a monolayer step edge, we detect an in-gap boundary mode with modulations along the edge that match the CDW wavevector along the edge. Intriguingly, the phase of the edge state modulation shifts by {\pi} within the charge order gap, connecting the fully gapped bulk (and surface) conduction and valence bands via a smooth energy-phase relation. This bears similarity to the topological spectral flow of edge modes, where the boundary modes bridge the gapped bulk modes in energy and momentum magnitude but in Ta2Se8I, the connectivity distinctly occurs in energy and momentum phase. Notably, our temperature-dependent measurements indicate a vanishing of the insulating gap and the in-gap edge state above TCDW, suggesting their direct relation to CDW. The theoretical analysis also indicates that the observed boundary mode is topological and linked to CDW., Comment: Nature Physics (2024); in press

In this work, we establish a theoretical analysis of the emergence of layer-contrasted Nernst response perpendicular to the direction of the temperature gradient in twisted moir\'{e} layers, called layer Nernst effect (LNE). This phenomenon arises from the trigonal warping of the Fermi surface along with a layer-contrasted pseudomagnetic field. Interestingly, the Fermi surface's warping explicitly breaks intra-valley inversion symmetry, which leads to an imbalance between left- and right-moving carriers, thus resulting in a non-vanishing LNE. We then validate our theoretical scheme by applying it to twisted bilayer graphene (TBG). Importantly, we find that the LNE coefficient in TBG can reach values as high as $10^3$A/(m$\cdot$K), surpassing those of previously known materials by at least one order of magnitude. These results provide a theoretical foundation for utilizing TBG and other twisted moir\'{e} layers as promising platforms to explore layer caloritronics and develop thermoelectric devices., Comment: 6 pages, 4 figures

Mn$_3$Sn has garnered significant attention due to its kagome lattice, 120$^\circ$ noncollinear antiferromagnetic order, and substantial anomalous Hall effect. In this study, we comprehensively explore intrinsic and extrinsic contributions to anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, employing first-principle calculations and group theory analysis. Comparative analysis between our theoretical results and available experimental data underscores the predominance of intrinsic mechanism in shaping anomalous transport properties at low temperatures. Specifically, Weyl fermions are identified as the primary contributors to intrinsic anomalous Hall conductivity. The significance of extrinsic mechanisms becomes evident at high temperatures, especially when the longitudinal charge conductivity falls into the dirty regime, where the side jump mechanism plays a vital role. Extrinsic contributions to anomalous transport properties are primarily influenced by the electronic states residing at the Fermi surfaces. Furthermore, anomalous transport properties exhibit periodic variations when subjected to spin rotations within the kagome plane, achievable by applying an external magnetic field. Our findings advance the understanding of anomalous transport phenomena in Mn$_3$Sn and offer insights into potential applications of noncollinear antiferromagnetic materials in spintronics and spin caloritronics., Comment: 12 pages, 5 figures

Topology and correlations are fundamental concepts in modern physics, but their simultaneous occurrence within a single quantum phase is exceptionally rare. In this study, we present the discovery of such a phase of matter in Ta2Pd3Te5, a semimetal where the Coulomb interaction between electrons and holes leads to the spontaneous formation of excitonic bound states below T=100 K. Our spectroscopy unveils the development of an insulating gap stemming from the condensation of these excitons, thus giving rise to a highly sought-after correlated quantum phase known as the excitonic insulator. Remarkably, our scanning tunneling microscopy measurements reveal the presence of gapless boundary modes in the excitonic insulator state. Their magnetic field response and our theoretical calculations suggest a topological origin of these modes, rendering Ta2Pd3Te5 as the first experimentally identified topological excitonic insulator in a three-dimensional material not masked by any structural phase transition. Furthermore, our study uncovers a secondary excitonic instability below T=5 K, which differs from the primary one in having finite momentum. We observe unprecedented tunability of its wavevector by an external magnetic field. These findings unlock a frontier in the study of novel correlated topological phases of matter and their tunability.

Electronic topological phases are renowned for their unique properties, where conducting surface states exist on the boundary of an insulating three-dimensional bulk. While the transport response of the surface states has been extensively studied, the response of the topological hinge modes remains elusive. Here, we investigate a layered topological insulator $\alpha$-Bi$_4$Br$_4$, and provide the first evidence for quantum transport in gapless topological hinge states existing within the insulating bulk and surface energy gaps. Our magnetoresistance measurements reveal pronounced h/e periodic (where h denotes Planck's constant and e represents the electron charge) Aharonov-Bohm oscillation. The observed periodicity, which directly reflects the enclosed area of phase-coherent electron propagation, matches the area enclosed by the sample hinges, providing compelling evidence for the quantum interference of electrons circumnavigating around the hinges. Notably, the h/e oscillations evolve as a function of magnetic field orientation, following the interference paths along the hinge modes that are allowed by topology and symmetry, and in agreement with the locations of the hinge modes according to our scanning tunneling microscopy images. Remarkably, this demonstration of quantum transport in a topological insulator can be achieved using a flake geometry and we show that it remains robust even at elevated temperatures. Our findings collectively reveal the quantum transport response of topological hinge modes with both topological nature and quantum coherence, which can be directly applied to the development of efficient quantum electronic devices., Comment: Nature Physics, in press (2023)

Recently, the real topology has been attracting widespread interest in two dimensions (2D). Here, based on first-principles calculations and theoretical analysis, we reveal the monolayer Cr$_2$Se$_2$O (ML-CrSeO) as the first material example of a 2D antiferromagnetic (AFM) real Chern insulator (RCI) with topologically protected corner states. Unlike previous RCIs, we find that the real topology of the ML-CrSeO is rooted in one certain mirror subsystem of the two spin channels, and can not be directly obtained from all the valence bands in each spin channel as commonly believed. In particular, due to antiferromagnetism, the corner modes in ML-CrSeO exhibit strong corner-contrasted spin polarization, leading to spin-corner coupling (SCC). This SCC enables a direct connection between spin space and real space. Consequently, large and switchable net magnetization can be induced in the ML-CrSeO nanodisk by electrostatic means, such as potential step and in-plane electric field, and the corresponding magnetoelectric responses behave like a sign function, distinguished from that of the conventional multiferroic materials. Our work considerably broadens the candidate range of RCI materials, and opens up a new direction for topo-spintronics and 2D AFM materials research.

Topological transition metal dichalcogenides (TMDCs) have attracted much attention due to its potential applications in spintronics and quantum computations. In this work, we systematically investigate the structural and electronic properties of topological TMDCs candidate ZrTe2 under high pressure. A pressure-induced Lifshitz transition is evidenced by the change of charge carrier type as well as the Fermi surface. Superconductivity was observed at around 8.3 GPa without structural phase transition. A typical dome-shape phase diagram is obtained with the maximum Tc of 5.6 K for ZrTe2. Furthermore, our theoretical calculations suggest the presence of multiple pressure-induced topological quantum phase transitions, which coexists with emergence of superconductivity. The results demonstrate that ZrTe2 with nontrivial topology of electronic states display new ground states upon compression., Comment: Accepted for publication in Advanced Science 2023

Layered SnAs-based Zintl compounds exhibit a distinctive electronic structure, igniting extensive research efforts in areas of superconductivity, topological insulators and quantum magnetism. In this paper, we systematically investigate the crystal structures and electronic properties of the Zintl compound SrSn2As2 under high-pressure. At approximately 20.8 GPa, pressure-induced superconductivity is observed in SrSn2As2 with a characteristic dome-like evolution of Tc. Theoretical calculations together with high pressure synchrotron X-ray diffraction and Raman spectroscopy have identified that SrSn2As2 undergoes a structural transformation from a trigonal to a monoclinic structure. Beyond 28.3 GPa, the superconducting transition temperature is suppressed due to a reduction of the density of state at the Fermi level. The discovery of pressure-induced superconductivity, accompanied by structural transitions in SrSn2As2, greatly expands the physical properties of layered SnAs-based compounds and provides a new ground states upon compression., Comment: 15 pages, 6 figures. arXiv admin note: text overlap with arXiv:2307.15629

Ever since the discovery of the charge density wave (CDW) transition in the kagome metal CsV$_3$Sb$_5$, the nature of its symmetry breaking is under intense debate. While evidence suggests that the rotational symmetry is already broken at the CDW transition temperature ($T_{\rm CDW}$), an additional electronic nematic instability well below $T_{\rm CDW}$ has been reported based on the diverging elastoresistivity coefficient in the anisotropic channel ($m_{E_{2g}}$). Verifying the existence of a nematic transition below $T_{\rm CDW}$ is not only critical for establishing the correct description of the CDW order parameter, but also important for understanding low-temperature superconductivity. Here, we report elastoresistivity measurements of CsV$_3$Sb$_5$ using three different techniques probing both isotropic and anisotropic symmetry channels. Contrary to previous reports, we find the anisotropic elastoresistivity coefficient $m_{E_{2g}}$ is temperature-independent, except for a step jump at $T_{\rm CDW}$. The absence of nematic fluctuations is further substantiated by measurements of the elastocaloric effect, which show no enhancement associated with nematic susceptibility. On the other hand, the symmetric elastoresistivity coefficient $m_{A_{1g}}$ increases below $T_{\rm CDW}$, reaching a peak value of 90 at $T^* = 20$ K. Our results strongly indicate that the phase transition at $T^*$ is not nematic in nature and the previously reported diverging elastoresistivity is due to the contamination from the $A_{1g}$ channel., Comment: 11 pages, 5 figures, to appear in Physical Review X

Xenes, two-dimensional (2D) monolayers composed of a single element, with graphene as a typical representative, have attracted widespread attention. Most of the previous Xenes, X from group-IIIA to group-VIA elements have bonding characteristics of covalent bonds. In this work, we for the first time unveil the pivotal role of a halogen bond, which is a distinctive type of bonding with interaction strength between that of a covalent bond and a van der Waals interaction, in 2D group-VIIA monolayers. Combing the ingenious non-edge-to-edge tiling theory and state-of-art ab initio method with refined local density functional M06-L, we provide a precise and effective bottom-up construction of 2D iodine monolayer sheets, iodinenes, primarily governed by halogen bonds, and successfully design a category of stable iodinenes, encompassing herringbone, Pythagorean, gyrated truncated hexagonal, i.e. diatomic-kagome, and gyrated hexagonal tiling pattern. These iodinene structures exhibit a wealth of properties, such as flat bands, nontrivial topology, and fascinating optical characteristics, offering valuable insights and guidance for future experimental investigations. Our work not only unveils the unexplored halogen bonding mechanism in 2D materials but also opens a new avenue for designing other non-covalent bonding 2D materials., Comment: 6 pages, 4 figures

The interplay among frustrated lattice geometry, nontrivial band topology and correlation yields rich quantum states of matter in Kagome systems. A series of recent members in this family, AV3Sb5 (A= K, Rb, Cs), exhibit a cascade of symmetry-breaking transitions, involving the 3Q chiral charge ordering, electronic nematicity, roton pair-density-wave and superconductivity. The nature of the superconducting order is yet to be resolved. Here, we report an indication of chiral superconducting domains with boundary supercurrents in intrinsic CsV3Sb5 flakes. Magnetic field-free superconducting diode effect is observed with polarity modulated by thermal histories, suggesting dynamical superconducting order domains in a spontaneous time-reversal symmetry breaking background. Strikingly, the critical current exhibits the double-slit superconducting interference patterns when subjected to an external magnetic field. Characteristics of the patterns are modulated by thermal cycling. These phenomena are proposed as a consequence of periodically modulated supercurrents flowing along certain domain boundaries constrained by fluxoid quantization. Our results imply a chiral superconducting order, opening a potential for exploring exotic physics, e.g. Majorana zero modes, in this intriguing topological Kagome system., Comment: 17 pages,13 figures

The Zintl compound AIn2X2 (A = Ca, Sr, and X = P, As), as a theoretically predicted new non-magnetic topological insulator, requires experiments to understand their electronic structure and topological characteristics. In this paper, we systematically investigate the crystal structures and electronic properties of the Zintl compound SrIn2As2 under both ambient and high-pressure conditions. Based on systematic angle-resolved photoemission spectroscopy (ARPES) measurements, we observed the topological surface states on its (001) surface as predicted by calculations, indicating that SrIn2As2 is a strong topological insulator. Interestingly, application of pressure effectively tuned the crystal structure and electronic properties of SrIn2As2. Superconductivity is observed in SrIn2As2 for pressure where the temperature dependence of the resistivity changes from a semiconducting-like behavior to that of a metal. The observation of nontrivial topological states and pressure-induced superconductivity in SrIn2As2 provides crucial insights into the relationship between topology and superconductivity, as well as stimulates further studies of superconductivity in topological materials., Comment: 15 pages,5 figures

Stacking bilayer structures is an efficient way to tune the topology of polaritons in in-plane anisotropic films, e.g., by leveraging the twist angle (TA). However, the effect of another geometric parameter, film thickness ratio (TR), on manipulating the plasmon topology in bilayers is elusive. Here, we fabricate bilayer structures of WTe2 films, which naturally host in-plane hyperbolic plasmons in the terahertz range. Plasmon topology is successfully modified by changing the TR and TA synergistically, manifested by the extinction spectra of unpatterned films and the polarization dependence of the plasmon intensity measured in skew ribbon arrays. Such TR- and TA-tunable topological transitions can be well explained based on the effective sheet optical conductivity by adding up those of the two films. Our study demonstrates TR as another degree of freedom for the manipulation of plasmonic topology in nanophotonics, exhibiting promising applications in bio-sensing, heat transfer and the enhancement of spontaneous emission., Comment: 18 pages, 4 figures

Three-dimensional nodal line semimetals (NLSMs) provide remarkable importance for both enrich topological physics and wave management. However, NLSMs realized in acoustic systems are twofold bands degenerate, which are called Weyl NLSMs. Here, we first report on the experimental observation of novel Dirac NLSMs with fourfold degenerate in sonic crystals. We reveal that the topological properties of the Dirac NLSMs are entirely different than that of the conventional Weyl NLSMs. The Berry phase related to the Dirac nodal line (DNL) is 2{\pi}, which results in the surface responses of the Dirac NLSMs with two radically different situations: a torus surface state occupying the entire surface Brillouin zone (SBZ) and without any surface state in the SBZ. We further reveal that topological surface arcs caused by DNL can change from open to closed contours. The findings of Dirac NLSMs and their unique surface response may provoke exciting frontiers for flexible manipulation of acoustic surface waves., Comment: 6 pages, 4 figures

Two-dimensional (2D) magnetic transition metal compounds with atomic thickness exhibit intriguing physics in fundamental research and great potential for device applications. Understanding the correlations between their macrosopic magnetic properties and the dimensionality of microscopic magnetic exchange interactions are valuable for the designing and applications of 2D magnetic crystals. Here, using spin-polarized scanning tunneling microscopy, magnetization and magneto-transport measurements, we identify the zigzag-antiferromagnetism in monolayer CrTe2, incipient ferromagnetism in bilayer CrTe2, and robust ferromagnetism in bilayer Cr3Te4 films. Our density functional theory calculations unravel that the magnetic ordering in ultrathin CrTe2 is sensitive to the lattice parameters, while robust ferromagnetism with large perpendicular magnetic anisotropy in Cr3Te4 is stabilized through its anisotropic 3D magnetic exchange interactions.

Van Hove singularity (VHS) has been considered as a driving source for unconventional superconductivity. A VHS in two-dimensional (2D) materials consists of a saddle point connecting electron-like and hole-like bands. In a rare case, when a VHS appears at Fermi level, both electron-like and hole-like conduction can coexist, giving rise to an enhanced density of states as well as an attractive component of Coulomb interaction for unconventional electronic pairing. However, this van Hove scenario is often destroyed by an incorrect chemical potential or competing instabilities. Here, by using angle-resolved photoemission measurements, we report the observation of a VHS perfectly aligned with the Fermi level in a kagome superconductor CsV$_{3-x}$Ta$_x$Sb$_5$ (x~0.4), in which a record-high superconducting transition temperature is achieved among all the current variants of AV$_3$Sb$_5$ (A=Cs, Rb, K) at ambient pressure. Doping dependent measurements reveal the important role of van Hove scenario in boosting superconductivity, and spectroscopic-imaging scanning tunneling microscopy measurements indicate a distinct superconducting state in this system., Comment: 20 pages, 4 figures

The TiSiCO-family monolayers have recently been attracting significant attention due to their unique valley-layer coupling (VLC). In this work, we present a minimal, four-band tight-binding (TB) model to capture the low-energy physics of the TiSiCO-family monolayers $X_{2}Y$CO$_{2}$ ($X=$ Ti, Zr, Hf; $Y=$ Si, Ge) with strong VLC. These monolayers comprise two $X$ atom layers separated by approximately $4$ \AA ~in the out-of-plane direction. Around each valley ($X$ or $X'$), the conduction and valence bands are mainly dominated by the $A_{1}\{d_{z^{2}(x^{2}-y^{2})}\}$ and $B_{2}\{d_{yz}\}$ orbitals of the top $X$ atoms,and the $A_{1}\{d_{z^{2}(x^{2}-y^{2})}\}$ and $B_{1}\{d_{xz}\}$ orbitals of the bottom $X$ atoms. Using these four states as a basis, we construct a symmetry-allowed TB model. Through parameter fitting from first-principles calculations, the four-band TB model not only reproduces the electronic band structure, but also captures the strong VLC, high-order topology, and valley-contrasting linear dichroism of the monolayers. Furthermore, the TB model reveals that these monolayers may exhibit various intriguing topological phases under electric fields and biaxial strains. Hence, the TB model established here can serve as the starting point for future research exploring the physics related to VLC and the $X_{2}Y$CO$_{2}$ monolayers., Comment: 8 pages

Despite the extensive studies of topological systems, the experimental characterizations of strongly nonlinear topological phases have been lagging. To address this shortcoming, we design and build elliptically geared isostatic metamaterials. Their nonlinear topological transitions can be realized by collective soliton motions, which stem from the transition of nonlinear Berry phase. Endowed by the intrinsic nonlinear topological mechanics, surface polar elasticity and dislocation-bound zero modes can be created or annihilated as the topological polarization reverses orientation. Our approach integrates topological physics with strongly nonlinear mechanics and promises multi-phase structures at the micro and macro scales., Comment: 5+19 pages, 4+20 figures

Spintronics, a technology harnessing electron spin for information transmission, offers a promising avenue to surpass the limitations of conventional electronic devices. While the spin directly interacts with the magnetic field, its control through the electric field is generally more practical, and has become a focal point in the field of spintronics. Current methodologies for generating spin polarization via an electric field generally necessitate spin-orbit coupling. Here, we propose an innovative mechanism that accomplishes this task without dependence on spin-orbit coupling. Our method employs two-dimensional altermagnets with valley-mediated spin-layer coupling (SLC), in which electronic states display symmetry-protected and valley-contrasted spin and layer polarization. The SLC facilitates predictable, continuous, and reversible control of spin polarization using a gate electric field. Through symmetry analysis and ab initio calculations, we pinpoint high-quality material candidates that exhibit SLC. We ascertain that applying a gate field of $0.2$ eV/\AA~ to monolayer Ca(CoN)$_2$ can induce significant spin splitting up to 123 meV. As a result, perfect and switchable spin/valley-currents, and substantial tunneling magnetoresistance can be achieved in these materials using only a gate field. These findings provide new opportunities for generating predictable spin polarization and designing novel spintronic devices based on coupled spin, valley and layer physics.

Traditional electronic devices rely on electron's intrinsic degrees of freedom (d.o.f.) to process information. However, additional d.o.f. like the valley, can emerge in the low-energy states of certain systems. Here, we show that the quantum dots (QDs) constructed from two-dimensional (2D) second-order topological insulator (SOTI) posses a new kind of d.o.f., namely corner freedom, related to the topological corner states that reside at different corners of the systems. Since the corner states are well separated in real space, they can be intuitively addressed and manipulated individually, giving rise to the concept of cornertronics. Via symmetry analysis and material search, we identify the TiSiCO-family monolayers as the first prototype of cornertronics materials, where the corner states can be controlled by both electric and optical fields, due to the novel corner-layer coupling (CLC) effect and the corner-contrasted optical selection rules. Furthermore, we find that the band gap of the TiSiCO nanodisk lies in the terahertz region and is robust to size reduction. These results indicate that the TiSiCO nanodisks can be used to design terahertz devices with ultrasmall size, electric-field tunable band gap, and the ability to simultaneously detect the strength and polarization of terahertz waves, which is not possible for previously reported QDs. Our findings not only pave the way for the cornertronics, but also open a new direction for the research in 2D SOTI, QD and terahertz electronics.

We elucidate the interplay between diverse two-dimensional melting pathways and establish solid/hexatic and hexatic/liquid transition criteria via the numerical simulations of the melting transition of two- and three-component mixtures of hard polygons and disks. We show that a mixture's melting pathway may differ from its components and demonstrate eutectic mixtures that crystallize at a higher density than their pure components. Comparing the melting scenario of many two- and three-component mixtures, we establish universal melting criteria: the solid and hexatic phases become unstable as the density of topological defects respectively overcomes $\rho_{d,{\rm s}} \simeq 0.046$ and $\rho_{d,{\rm h}}\simeq 0.123$., Comment: Phys. Rev. Lett, in press

Two-dimensional checkerboard lattice, the simplest line-graph lattice, has been intensively studied as a toy model, while material design and synthesis remain elusive. Here, we report theoretical prediction and experimental realization of the checkerboard lattice in monolayer Cu$_2$N. Experimentally, monolayer Cu$_2$N can be realized in the well-known N/Cu(100) and N/Cu(111) systems that were previously mistakenly believed to be insulators. Combined angle-resolved photoemission spectroscopy measurements, first-principles calculations, and tight-binding analysis show that both systems host checkerboard-derived hole pockets near the Fermi level. In addition, monolayer Cu$_2$N has outstanding stability in air and organic solvents, which is crucial for further device applications., Comment: Nano Letters, in press

We demonstrate the emergence of a pronounced thermal transport in the recently discovered class of magnetic materials-altermagnets. From symmetry arguments and first-principles calculations performed for the showcase altermagnet, RuO2, we uncover that crystal Nernst and crystal thermal Hall effects in this material are very large and strongly anisotropic with respect to the Neel vector. We find the large crystal thermal transport to originate from three sources of Berry's curvature in momentum space: the Weyl fermions due to crossings between well-separated bands, the strong spin-flip pseudonodal surfaces, and the weak spin-flip ladder transitions, defined by transitions among very weakly spin-split states of similar dispersion crossing the Fermi surface. Moreover, we reveal that the anomalous thermal and electrical transport coefficients in RuO2 are linked by an extended Wiedemann-Franz law in a temperature range much wider than expected for conventional magnets. Our results suggest that altermagnets may assume a leading role in realizing concepts in spin caloritronics not achievable with ferromagnets or antiferromagnets., Comment: 6 pages

This work reports the thermal conductivity of RbV3Sb5 and CsV3Sb5 with three-dimensional charge density wave phase transitions from 80 K to 400 K measured by pump-probe thermoreflectance techniques. The in-plane (basal plane) thermal conductivities are found moderate, i.e., 12 W/mK of RbV3Sb5 and 8.8 W/mK of CsV3Sb5 at 300 K. Low cross-plane (stacking direction) thermal conductivities are observed, with 0.72 W/mK of RbV3Sb5 and 0.49 W/mK of CsV3Sb5 at 300 K. A unique glass-like temperature dependence in the cross-plane thermal conductivity is observed, which decreases monotonically even lower than the Cahill-Pohl limit as the temperature decreases below the phase transition point TCDW. This temperature dependence is found to obey the hopping transport picture. In addition, a peak in cross-plane thermal conductivity is observed at TCDW as a fingerprint of the modulated structural distortion along the stacking direction.