Maksim Litskevich

Topology, – and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three important research directions: (1) the competition between distinct interactions, as in several intertwined phases, (2) the interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and (3) the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies. Here, using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis, we unveil a ‘hybrid’ topological phase of matter in the simple elemental-solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a …

HH05. 00010: Energy-phase relation of a boundary mode in a charge density wave state*

The transport response of topological surface states in strong topological insulators has undergone extensive investigation, yet the behavior of topological hinge modes remains enigmatic. Here, we uncover phase-coherent transport facilitated by the topological hinge states in a higher-order topological insulator. These conducting hinge states reside within the insulating bulk and surface, both gapped across the entire Brillouin zone. Our magnetoresistance measurements reveal pronounced h/e periodic (where h denotes Planck’s constant and e represents the electron charge) Aharonov–Bohm oscillation. Notably, the observed periodicity, which directly reflects the enclosed area of phase-coherent electron propagation, matches the area enclosed by the sample hinges. Furthermore, the h/e oscillations evolve as a function of magnetic field orientation, following the interference paths along the hinge modes allowed …

Electronic topological phases are typified by the conducting surface states that exist on the boundary of an insulating three-dimensional bulk. While the transport response of the two-dimensional surface states has been studied, the quantum response of the one-dimensional hinge modes has not been demonstrated. Here we provide evidence for quantum transport in gapless topological hinge states existing within the insulating bulk and surface energy gaps in the intrinsic topological insulator α-Bi4Br4. Our magnetoresistance measurements reveal pronounced Aharonov–Bohm oscillations that are periodic in h/e (where h denotes Planck’s constant and e is the electron charge). The observed periodicity evinces quantum interference of electrons circumnavigating around the hinges. We also demonstrate that the h/e oscillations evolve as a function of magnetic field orientation, following the interference paths along …

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 …

Topology and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three significant research directions: competition between distinct interactions, as in the multiple intertwined phases, interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and the coalescence of multiple topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, while the last example remains mostly untouched, mainly because of the lack of a material platform for experimental studies. Here, using tunneling microscopy, photoemission spectroscopy, and theoretical analysis, we unveil a "hybrid" and yet novel topological phase of matter in the simple elemental solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology, stabilizing a hybrid topological phase. While momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topology-induced step edge conduction channels revealed on various forms of natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step edge states in arsenic relies on the simultaneous presence of both a nontrivial strong Z2 invariant and a nontrivial higher-order topological invariant, providing experimental evidence for hybrid topology and its realization in a single crystal. Our discovery highlights pathways to explore the interplay of different …

The exotic properties of topological semimetals (TSMs) have attracted great attention and significant efforts have been made in exploring new topological phases and materials. Some of the TSMs are predicated to host exotic band properties, such as butterflylike coplanar ellipses nodal lines. Here in such a TSM, our transport experiments reveal a 2D superconductivity. This is very surprising given that our quantum oscillations experiments show 3D Fermi surface. We discuss the possible origin of the superconductivity in light of our angle-resolved photoemission spectroscopy and first-principles calculation results.

Topological phases of matter are at the frontier of scientific research and have a potential to become a building block of future electronic devices. Using scanning tunneling microscopy (STM) we probe a Weyl semiconductor material and reveal defect-free atomically flat surfaces with an energy gap of We observe that the atomic surfaces separated by a monolayer step edge exhibit a switch of the intensity of the tunneling spectrum below and above the Fermi level and develop a gap difference of at 4.2 K, thus effectively realizing AB stacking sequence of atomic layers. Temperature dependent STM measurements on AB surfaces show spectroscopic contrast weakening and gap difference shrinkage with the increasing temperature. The results of our STM study indicate a surprising electronic AB stacking of layers, possibly linked to the presence of a phonon-induced instability in the material.

The presence of a gapless edge state within a bulk energy gap, namely the bulk-boundary correspondence, is a hallmark of topology. Using scanning tunneling microscopy, we uncover such an edge state in a Rashba compound containing a Rashba-split surface state. In an atomically resolved surface, we observe a small gap near the Fermi level. On the other hand, a monolayer atomic step edge features an in-gap, gapless edge state. We argue the topological nature of the edge state based on two experimental findings:(i) an energy gap opens when applying a magnetic field, pointing to a time-reversal symmetry protected nature of the edge state.(ii) the edge spectra show intriguing differences depending on the height of the step edge, consistent with the hybridization of the edge state.

Search for macroscopic quantum phenomena at room temperature is a major pursuit in physics. There has been only a single definitive report of such a phenomenon, namely the room-temperature integer quantum Hall effect at ultra-high magnetic fields. In this poster, I will present our discovery of a zero-magnetic field, room-temperature quantum phenomena-quantum spin Hall state featuring a bulk energy gap and a gapless, in-gap edge state protected by the time-reversal symmetry. Our material platform is Bi4Br4, which has a large energy gap, facilitating the high-temperature robustness of the quantum spin Hall state.

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to form our foundation for understanding superfluids, magnets, the quantum Hall effect, topological insulators and Weyl semimetals. We introduce a remarkable linking number (knot theory) invariant associated with loops of electronic band crossings in the mirror-symmetric ferromagnet Co 2 MnGa. By ARPES, we observe three intertwined degeneracy loops in the bulk Brillouin zone three-torus, T 3, and find that each loop links each other loop twice. We explicitly draw the link diagram of this linked loop quantum state and conclude, in analogy with knot theory, a linking number of (2, 2, 2). On the sample surface, we further predict and observe Seifert boundary states protected by the bulk linked loops, suggestive of a Seifert …

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin–orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle‐resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out‐of‐plane dispersion in the A–A stacked kagome magnet GdMn6Sn6. Remarkably, the Weyl lines exhibit a strong magnetization‐direction‐tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn6Sn6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum …

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 -BiBr, 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 …

Ongoing advances in superconductors continue to revolutionize technology thanks to the increasingly versatile and robust availability of lossless supercurrents. In particular, high supercurrent density can lead to more efficient and compact power transmission lines, high-field magnets, as well as high-performance nanoscale radiation detectors and superconducting spintronics. Here, we report the discovery of an unprecedentedly high superconducting critical current density (17 MA/c m 2 at 0 T and 7 MA/c m 2 at 8 T) in 1 T′− W S 2, exceeding those of all reported two-dimensional superconductors to date. 1 T′− W S 2 features a strongly anisotropic (both in-and out-of-plane) superconducting state that violates the Pauli paramagnetic limit signaling the presence of unconventional superconductivity. Spectroscopic imaging of the vortices further substantiates the anisotropic nature of the superconducting state. More …

The distorted phases (such as 2M) of transition metal dichalcogenides (TMDCs) exhibit exotic physical properties, such as superconductivity, topological energy gap, and Majorana bound states [1-2]. However, because the distorted phases are metastable and they usually appear in domains within their thermodynamically stable counterpart, transport experiments of these phases have been limited. Here we present a TMDC with a purely distorted phase that features unconventional superconductivity with an extremely anisotropic upper critical field. Remarkably, the critical field along the in-plane direction violates the well-established Pauli limit. We find that this superconductor shows a surprisingly large critical current density, which is two orders of magnitude higher than that in typical two-dimensional superconductors. Our work provides a promising route to understand the nature of superconductivity in distorted …

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics,. The quantum spin Hall phase, , – is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi4Br4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk–boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical …

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state, , , , , , , , , , , –. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids, magnets,, the quantum Hall effect,, topological insulators,, Weyl semimetals, – and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet, , , , , –. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material’s three-torus, T3, bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with …

The interplay between topology and charge order is at the frontier of condensed matter research. However, there is no direct experimental evidence for a topological bulk-boundary correspondence within a fully gapped charge-ordered state yet. Here, using scanning tunneling microscopy, we directly visualize the topological bulk-boundary correspondence in a topological charge density wave (CDW) material. Below the CDW transition temperature, tunneling spectra on an atomically resolved lattice reveals a large insulating gap (over 500 meV) whose△/k B T c~ 20, suggesting a strong coupling nature of the CDW. Remarkably, in an atomically sharp monolayer step edge, we find an in-gap gapless helical state. Both the insulating gap and the gapless edge state disappear above the CDW transition temperature. The presence of the edge state within the insulating CDW gap indicates the topological bulk-boundary …

Realizing macroscopic quantum phenomena at room temperature is a major pursuit in physics. The quantum spin Hall (QSH) state, a prototypical quantum phenomenon that features a two-dimensional insulating bulk and a topologically protected helical edge state at zero magnetic field, has not been realized at room temperature. Here, using scanning tunneling microscopy, we directly visualize a QSH edge state on the surface of the higher-order topological insulator Bi 4 Br 4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200meV while an atomically sharp monolayer step edge hosts an in-gap gapless state, which is the hallmark of topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection of the underlying topology. Furthermore, via directly identifying the geometrical hybridization of such …

The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co 3 Sn 2 S 2, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl points. Our findings indicate that magnetic exchange collapse naturally drives Weyl fermion annihilation, opening new opportunities for engineering topology under correlated order parameters.

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics, , –. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect, in topological materials and for the hidden phase in cuprate high-temperature superconductors,. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the …

Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature T c up to 7 K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than T c. In this work, we use scanning tunneling microscopy to study the charge order in kagome superconductor Rb V 3 Sb 5. We observe both a 2× 2 chiral charge order and nematic surface superlattices (predominantly 1× 4). We find that the 2× 2 charge order exhibits intrinsic chirality with magnetic field tunability. Defects can scatter electrons to introduce standing waves, which couple with the charge order to cause extrinsic effects. While the chiral charge order resembles that discovered in K V 3 Sb 5, it further interacts with the nematic surface superlattices that are absent in K …

We use scanning tunneling microscopy (STM) to image the electronic impact of Co atoms on the ground state of the LiFe 1-x Co x As system. We observe that impurities progressively suppress the global superconducting gap and introduce low energy states near the gap edge, with the superconductivity remaining in the strong-coupling limit. Unexpectedly, the fully opened gap evolves into a nodal state before the Cooper pair coherence is fully destroyed. Our systematic theoretical analysis shows that these new observations can be quantitatively understood by the nonmagnetic Born-limit scattering effect in a s+/--wave superconductor, unveiling the driving force of the superconductor to metal quantum phase transition.

Quantum states induced by single-atomic impurities are at the frontier of physics and material science. While such states have been reported in high-temperature superconductors and dilute magnetic semiconductors, they are unexplored in topological magnets which can feature spin-orbit tunability. Here we use spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) to study the engineered quantum impurity in a topological magnet Co3Sn2S2. We find that each substituted In impurity introduces a striking localized bound state. Our systematic magnetization-polarized probe reveals that this bound state is spin-down polarized, in lock with a negative orbital magnetization. Moreover, the magnetic bound states of neighboring impurities interact to form quantized orbitals, exhibiting an intriguing spin-orbit splitting, analogous to the splitting of the topological fermion line. Our work collectively demonstrates …

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics, , , , , , , , , , , , , –. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry,. However, quantum materials hosting ideal spin–orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking, , , , –. Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn6Sn6, that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk …

Three types of fermions have been extensively studied in topological quantum materials: Dirac, Weyl, and Majorana fermions. Beyond the fundamental fermions in high energy physics, exotic fermions are allowed in condensed matter systems residing in three-, six-or eightfold degenerate band crossings. Here, we use angle-resolved photoemission spectroscopy to directly visualize three-doubly-degenerate bands in PdS b 2. The ultrahigh energy resolution we are able to achieve allows for the confirmation of all the sixfold degenerate bands at the R point, in remarkable consistency with first-principles calculations. Moreover, we find that this sixfold degenerate crossing has quadratic dispersion as predicted by theory. Finally, we compare sixfold degenerate fermions with previously confirmed fermions to demonstrate the importance of this work: our study indicates a topological fermion beyond the constraints of high …

Superconducting materials exhibiting topological properties are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. In this letter, we explore the possibility of a field-free platform for generating Majorana zero energy excitations by depositing magnetic Fe impurities on the surface of candidate topological superconductors, LiFeAs and PbTaS e 2. We use scanning tunneling microscopy to probe localized states induced at the Fe adatoms on the atomic scale and at sub-Kelvin temperatures. We find that each Fe adatom generates a striking zero-energy bound state inside the superconducting gap, which do not split in magnetic fields up to 8 T, underlining a nontrivial topological origin. Our findings point to magnetic Fe adatoms evaporated on bulk superconductors with topological surface states for exploring Majorana zero modes and quantum information …

Topological electronic phases in intrinsic magnets are of current interest. One common magnetic topological object is the Weyl line, a two-fold band degeneracy along a closed curve in bulk momentum space. Weyl lines arise naturally in the absence of time-reversal symmetry (absent in magnets) and in the presence of mirror symmetry (common in many space groups). I will present the observation of Weyl lines by ARPES in the room temperature magnet Co 2 MnGa [1]. On the surface of the magnet, I observe drumhead surface states, pinpointing the bulk-boundary correspondence and suggesting a Berry phase topological invariant associated with the Weyl line. Next, the intrinsic Berry curvature contribution to the anomalous Hall response, determined from quantum transport, agrees with a prediction of the Weyl line Berry curvature based on ARPES and first-principles calculations [1]. I will comment on composite …