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

Layer-coupled corner states in two-dimensional topological multiferroics

The structural diversity and controllability in two-dimensional (2D) materials offers an intriguing platform for exploring a wide range of topological phenomena. The layer degree of freedom, as a novel technique for material manipulation, requires further investigation regarding its association with topological states. Here, using first-principles calculations and a tight-binding model, we propose a novel mechanism that couples the second-order topological corner states with the layer degree of freedom. By analyzing the edge states, topological indices, and spectra of nanoflakes, we identify ferromagnetic H'-Co2XF2 (X = C, N) as 2D second-order topological insulators with intrinsic ferroelectricity. Moreover, the topological corner states strongly couple with the layer degree of freedom, and, remarkably, ferroelectricity provides a nonvolatile handle to manipulate the layer-polarized corner states. These findings open an avenue for the manipulation of second-order topological states and establish a bridge between ferroelectricity and nontrivial topology.

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

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

In-plane anisotropic two-dimensional materials for twistronics

In-plane anisotropic two-dimensional (2D) materials exhibit in-plane orientation-dependent properties. The anisotropic unit cell causes these materials to show lower symmetry but more diverse physical properties than in-plane isotropic 2D materials. In addition, the artificial stacking of in-plane anisotropic 2D materials can generate new phenomena that cannot be achieved in in-plane isotropic 2D materials. In this perspective we provide an overview of representative in-plane anisotropic 2D materials and their properties, such as black phosphorus, group IV monochalcogenides, group VI transition metal dichalcogenides with 1T' and Tdphases, and rhenium dichalcogenides. In addition, we discuss recent theoretical and experimental investigations of twistronics using in-plane anisotropic 2D materials. Both in-plane anisotropic 2D materials and their twistronics hold considerable potential for advancing the field of 2D materials, particularly in the context of orientation-dependent optoelectronic devices.

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

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

Quantifying the thickness of WTe2 using atomic-resolution STEM simulations and supervised machine learning

For two-dimensional (2D) materials, the exact thickness of the material often dictates its physical and chemical properties. The 2D quantum material WTe2 possesses properties that vary significantly from a single layer to multiple layers, yet it has a complicated crystal structure that makes it difficult to differentiate thicknesses in atomic-resolution images. Furthermore, its air sensitivity and susceptibility to electron beam-induced damage heighten the need for direct ways to determine the thickness and atomic structure without acquiring multiple measurements or transferring samples in ambient atmosphere. Here, we demonstrate a new method to identify the thickness up to ten van der Waals layers in Td-WTe2 using atomic-resolution high-angle annular dark-field scanning transmission electron microscopy image simulation. Our approach is based on analyzing the intensity line profiles of overlapping atomic columns and building a standard neural network model from the line profile features. We observe that it is possible to clearly distinguish between even and odd thicknesses (up to seven layers), without using machine learning, by comparing the deconvoluted peak intensity ratios or the area ratios. The standard neural network model trained on the line profile features allows thicknesses to be distinguished up to ten layers and exhibits an accuracy of up to 94% in the presence of Gaussian and Poisson noise. This method efficiently quantifies thicknesses in Td-WTe2, can be extended to related 2D materials, and provides a pathway to characterize precise atomic structures, including local thickness variations and atomic defects, for few-layer 2D materials with overlapping atomic column positions.

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

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

Spin-resolved topology and partial axion angles in three-dimensional insulators

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ([Formula: see text]-) invariant (helical) 3D TCIs-termed higher-order TCIs (HOTIs)-the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and [Formula: see text]-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes.

Asymmetric edge supercurrents in MoTe2 Josephson junctions

To investigate the higher order topology in MoTe2, the supercurrent interference phenomena in Nb/MoTe2/Nb planar Josephson junctions have been systematically studied. By analyzing the obtained interference pattern of the critical supercurrents and performing a comparative study of the edge-touched and untouched junctions, it's found that the supercurrent is dominated by the edges, rather than the bulk or surfaces of MoTe2. An asymmetric Josephson effect with a field-tunable sign is also observed, indicating the nontrivial origin of the edge states. These results not only provide initial evidence for the hinge states in the higher order topological insulator MoTe2, but also demonstrate the potential applications of MoTe2-based Josephson junctions in rectifying the supercurrent.

Physically Exfoliating 2D Materials: A Versatile Combination of Different Materials into a Layered Structure

Improving the properties of the existing two-dimensional (2D) materials is a major concern for many researchers today. Synergistic coupling of single-phase 2D material species with secondary functional materials has resulted in 2D nanohybrids with significantly enhanced properties beyond the sum of their individual components. In particular, nanohybrids created by alternatingly integrating different material species in the confined 2D nanometer regime have the potential to meet the needs of a wide variety of applications, particularly the many important energy-related applications that are of interest. However, scaling up production of 2D nanohybrids is still challenging, which is a major barrier to their practical application. Delamination and exfoliation by physical means separate the weakly bound 2D nanosheets into kinetically stable single- or few-layers. Herein, we provide a concise overview of recent achievements in the physical exfoliation-based fabrication of 2D nanohybrids featuring controlled heterolayered structures. Several strategies to efficiently produce heterolayered 2D nanohybrids in large quantities are described, such as (i) coexfoliation of different 2D species, (ii) aqueous-phase synthesis, and (iii) gas-phase synthesis. The versatility of the 2D nanohybrids was also illustrated by remarkable research examples, especially in energy-related applications.

Broad and colossal edge supercurrent in Dirac semimetal Cd3As2 Josephson junctions

Edge supercurrent has attracted great interest recently due to its crucial role in achieving and manipulating topological superconducting states. Proximity-induced superconductivity has been realized in quantum Hall and quantum spin Hall edge states, as well as in higher-order topological hinge states. Non-Hermitian skin effect, the aggregation of non-Bloch eigenstates at open boundaries, promises an abnormal edge channel. Here we report the observation of broad edge supercurrent in Dirac semimetal Cd3As2-based Josephson junctions. The as-grown Cd3As2 nanoplates are electron-doped by intrinsic defects, which enhance the non-Hermitian perturbations. The superconducting quantum interference indicates edge supercurrent with a width of ~1.6 μm and a magnitude of ~1 μA at 10 mK. The wide and large edge supercurrent is inaccessible for a conventional edge system and suggests the presence of non-Hermitian skin effect. A supercurrent nonlocality is also observed. The interplay between band topology and non-Hermiticity is beneficial for exploiting exotic topological matter.

Magnetic Second-Order Topological Insulators in 2H-Transition Metal Dichalcogenides

The transition metal dichalcogenides, 2H-VX2 (X = S, Se, Te), are identified as two-dimensional second-order topological insulator (SOTI) with a ferromagnetic ground state by first-principles calculations. The 2H-VX2 (X = S, Se, Te) materials have a nontrivial band gap in two spin channels is found and exhibit topologically protected corner states with spin-polarization. These corner states only accommodate the quantized fractional charge (e/3). And the charge is bound at the corners of the nanodisk geometry 2H-VX2 (X = S, Se, Te) in real space. The corner states are robust against symmetry-breaking perturbations, which makes them more easily detectable in experiments. Further, it is demonstrated that the SOTI properties of 2H-VX2 (X = S, Se, Te) materials can be maintained in the presence of spin-orbit coupling and are stable against magnetization. Overall, the results reveal 2H-VX2 (X = S, Se, Te) as an ideal platform for the exploration of magnetic SOTI and suggest its great potential in experimental detection.

Theoretical studies of magneto-optical Kerr and Faraday effects in two-dimensional second-order topological insulators

Optical approaches are useful for studying the electronic and spin structure of materials. Here, based on the tight-binding model and linear response theory, we investigate the magneto-optical Kerr and Faraday effects in two-dimensional second-order topological insulators (SOTI) with external magnetization. We find that orbital-dependent Zeeman term induces band crossings for SOTI phase, which are absent for trivial phase. In the weak-magnetization regime, these crossings give rise to giant jumps (peaks) of Kerr and Faraday angles (ellipticity) for SOTI phase. In the strong-magnetization regime, we find that two nearly flat bands are formed at the high-symmetry point of Brillouin zone of SOTI phase. These flat bands give rise to two successive giant jumps (peaks) of Kerr and Faraday angles (ellipticity). These phenomena provide new possibilities to characterize and detect the two-dimensional SOTI phase.

Anisotropic proximity-induced superconductivity and edge supercurrent in Kagome metal, K1-xV3Sb5

Materials with Kagome nets are of particular importance for their potential combination of strong correlation, exotic magnetism, and electronic topology. KV₃Sb₅ was discovered to be a layered topological metal with a Kagome net of vanadium. Here, we fabricated Josephson Junctions of K_1-xV₃Sb₅ and induced superconductivity over long junction lengths. Through magnetoresistance and current versus phase measurements, we observed a magnetic field sweeping direction-dependent magnetoresistance and an anisotropic interference pattern with a Fraunhofer pattern for in-plane magnetic field but a suppression of critical current for out-of-plane magnetic field. These results indicate an anisotropic internal magnetic field in K_1-xV₃Sb₅ that influences the superconducting coupling in the junction, possibly giving rise to spin-triplet superconductivity. In addition, the observation of long-lived fast oscillations shows evidence of spatially localized conducting channels arising from edge states. These observations pave the way for studying unconventional superconductivity and Josephson device based on Kagome metals with electron correlation and topology.

Current-Phase Relation of a WTe2 Josephson Junction

When a topological insulator is incorporated into a Josephson junction, the system is predicted to reveal the fractional Josephson effect with a 4π-periodic current-phase relation. Here, we report the measurement of a 4π-periodic switching current through an asymmetric SQUID, formed by the higher-order topological insulator WTe₂. Contrary to the established opinion, we show that a high asymmetry in critical current and negligible loop inductance are not sufficient by themselves to reliably measure the current-phase relation. Instead, we find that our measurement is heavily influenced by additional inductances originating from the self-formed PdTe_x inside the junction. We therefore develop a method to numerically recover the current-phase relation of the system and find the 1.5 μm long junction to be best described in the short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topological signatures in transport measurements.

Engineering Second-Order Corner States in 2D Multiferroics

The understanding and manipulate of the second-order corner states are central to both fundamental physics and future topotronics applications. Despite the fact that numerous second-order topological insulators (SOTIs) are achieved, the efficient engineering in a given material remains elusive. Here, the emergence of 2D multiferroics SOTIs in SbAs and BP₅ monolayers is theoretically demonstrated, and an efficient and straightforward way for engineering the nontrivial corner states by ferroelasticity and ferroelectricity is remarkably proposed. With ferroelectric polarization of SbAs and BP₅ monolayers, the nontrivial corner states emerge in the mirror symmetric corners and are perpendicular to orientations of the in-plane spontaneous polarization. And remarkably the spatial distribution of the corner states can be effectively tuned by a ferroelastic switching. At the intermediate states of both ferroelectric and ferroelastic switchings, the corner states disappear. These finding not only combines exotic SOTIs with multiferroics but also pave the way for experimental discovery of 2D tunable SOTIs.

Spinful hinge states in the higher-order topological insulators WTe2

Higher-order topological insulators are recently discovered quantum materials exhibiting distinct topological phases with the generalized bulk-boundary correspondence. T_d-WTe₂ is a promising candidate to reveal topological hinge excitation in an atomically thin regime. However, with initial theories and experiments focusing on localized one-dimensional conductance only, no experimental reports exist on how the spin orientations are distributed over the helical hinges-this is critical, yet one missing puzzle. Here, we employ the magneto-optic Kerr effect to visualize the spinful characteristics of the hinge states in a few-layer T_d-WTe₂. By examining the spin polarization of electrons injected from WTe₂ to graphene under external electric and magnetic fields, we conclude that WTe₂ hosts a spinful and helical topological hinge state protected by the time-reversal symmetry. Our experiment provides a fertile diagnosis to investigate the topologically protected gapless hinge states, and may call for new theoretical studies to extend the previous spinless model.

Robust Second-Order Topological Insulators with Giant Valley Polarization in Two-Dimensional Honeycomb Ferromagnets

Magnetic topological states have attracted great attention that provide exciting platforms for exploring prominent physical phenomena and applications of topological spintronics. Here, using a tight-binding model and first-principles calculations, we put forward that, in contrast to previously reported magnetic second-order topological insulators (SOTIs), robust SOTIs can emerge in two-dimensional ferromagnets regardless of magnetization directions. Remarkably, we identify intrinsic ferromagnetic 2H-RuCl₂ and Janus VSSe monolayers as experimentally feasible candidates of predicted robust SOTIs with the emergence of nontrivial corner states along different magnetization directions. Moreover, under out-of-plane magnetization, we unexpectedly point out that the valley polarization of SOTIs can be huge and much larger than that of the known ferrovalley materials, opening up a technological avenue to bridge the valleytronics and higher-order topology with high possibility of innovative applications in topological spintronics and valleytronics.

Topological zero-dimensional defect and flux states in three-dimensional insulators

In insulating crystals, it was previously shown that defects with two fewer dimensions than the bulk can bind topological electronic states. We here further extend the classification of topological defect states by demonstrating that the corners of crystalline defects with integer Burgers vectors can bind 0D higher-order end (HEND) states with anomalous charge and spin. We demonstrate that HEND states are intrinsic topological consequences of the bulk electronic structure and introduce new bulk topological invariants that are predictive of HEND dislocation states in solid-state materials. We demonstrate the presence of first-order 0D defect states in PbTe monolayers and HEND states in 3D SnTe crystals. We relate our analysis to magnetic flux insertion in insulating crystals. We find that π-flux tubes in inversion- and time-reversal-symmetric (helical) higher-order topological insulators bind Kramers pairs of spin-charge-separated HEND states, which represent observable signatures of anomalous surface half quantum spin Hall states.

Quantum Spin Hall Edge States and Interlayer Coupling in Twisted Bilayer WTe2

The quantum spin Hall (QSH) effect, characterized by topologically protected spin-polarized edge states, was recently demonstrated in monolayers of the transition metal dichalcogenide (TMD) WTe₂. However, the robustness of this topological protection remains largely unexplored in van der Waals heterostructures containing one or more layers of a QSH insulator. In this work, we use scanning tunneling microscopy and spectroscopy (STM/STS) to explore the topological nature of twisted bilayer (tBL) WTe₂. At the tBL edges, we observe the characteristic spectroscopic signatures of the QSH edge states. For small twist angles, a rectangular moiré pattern develops, which results in local modifications of the band structure. Using first-principles calculations, we quantify the interactions in tBL WTe₂ and its topological edge states as a function of interlayer distance and conclude that it is possible to engineer the topology of WTe₂ bilayers via the twist angle as well as interlayer interactions.

Traversing Double-Well Potential Energy Surfaces: Photoinduced Concurrent Intralayer and Interlayer Structural Transitions in XTe2 (X = Mo, W)

The microscopic arrangement of atoms and molecules is the determining factor in how materials behave and perform; i.e., the structure determines the property, a traditional paradigm in materials science. Photoexcitation-driven manipulation of the crystal structure and associated electronic properties in quantum materials provides opportunities for the exploration of exotic physics and practical applications; however, a generalized mechanism for such symmetry engineering is absent. Here, by ultrafast electron diffraction, structure factor calculation, and TDDFT-MD simulations, we report the photoinduced concurrent intralayer and interlayer structural transitions in the Td and 1T' phases of XTe₂ (X = Mo, W). We discuss the modification of multiple quantum electronic states associated with the intralayer and interlayer structural transitions, such as the topological band inversion and the higher-order topological state. The twin structures and the stacking faults in XTe₂ are also identified by ultrafast structural responses. The comprehensive study of the ultrafast structural response in XTe₂ suggests the traversal of all double-well potential energy surfaces (DWPES) by laser excitation, which is expected to be an intrinsic mechanism in the field of photoexcitation-driven global/local symmetry engineering and also a critical ingredient inducing the exotic properties in the non-equilibrium state in a large number of material systems.

Ultrahigh transverse thermoelectric power factor in flexible Weyl semimetal WTe2

Topological semimetals are well known for their interesting physical properties, while their mechanical properties have rarely received attention. With the increasing demand for flexible electronics, we explore the great potential of the van der Waals bonded Weyl semimetal WTe₂ for flexible thermoelectric applications. We find that WTe₂ single crystals have an ultrahigh Nernst power factor of ~3 Wm⁻¹K⁻², which outperforms the conventional Seebeck power factors of the state-of-the-art thermoelectric semiconductors by 2–3 orders of magnitude. A unique band structure that hosts compensated electrons and holes with extremely high mobilities is the primary mechanism for this huge Nernst power factor. Moreover, a large Ettingshausen signal of ~5 × 10⁻⁵ KA⁻¹m is observed at 23.1 K and 9 T. In this work, the combination of the exceptional Nernst–Ettingshausen performance and excellent mechanical transformative ability of WTe₂ would be instructive for flexible micro-/nano-thermoelectric devices.

Flexible thermoelectrics are of great interest with increasing demand of flexible and wearable electronics. Here, the authors demonstrate that the Weyl semimetal, WTe2, has a high Nernst power factor and great mechanical flexibility.

Acoustic Realization of Surface-Obstructed Topological Insulators

Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without bulk closure and exhibits as an obstruction of higher-dimensional boundary states. Here, we report the first experimental realization of three-dimensional surface-obstructed topological insulators with using acoustic crystals. Our acoustic measurements demonstrate unambiguously the emergence of one-dimensional topological hinge states in the middle of the bulk and surface band gaps, as a direct manifestation of the higher-order band topology. Together with comparative measurements for the trivial and phase-transition-point insulators, our experimental data conclusively evidence the unique bulk-boundary physics for the surface-obstructed band topology. That is, the topological phase transition is determined by the closure of the surface gap, rather than by closing the bulk gap. Our study might spur on new activities to deepen the understanding of such elusive topological phases.

All topological bands of all nonmagnetic stoichiometric materials

Topological quantum chemistry and symmetry-based indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy (E_F). We report the implementation of a publicly accessible catalog of stable and fragile topology in all of the bands both at and away from E_F in the 96,196 processable entries in the Inorganic Crystal Structure Database. Our calculations, which represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, have enabled the discovery of repeat-topological and supertopological materials, including rhombohedral bismuth and Bi₂Mg₃. We find that 52.65% of all materials are topological at E_F, roughly two-thirds of bands across all materials exhibit symmetry-indicated stable topology, and 87.99% of all materials contain at least one stable or fragile topological band.

Nonmonotonic wavelength dependence of the polarization-sensitive infrared photoresponse of an anisotropic semimetal

Layered semimetals with in-plane anisotropy are promising for advanced polarization-sensitive infrared detection. The investigation of the polarization-dependent photoresponse of semimetals over the whole visible-to-long-wave-infrared range and revealing the physical connection between their optoelectronic properties, optical properties, and electronic band structures is required, but there have been very few studies of this kind. In this work, we conducted a thorough investigation on the polarization-dependent infrared photoresponse of WTe₂ over the visible-to-long-wave-infrared range and discovered a textbook-like perfect consistency between the wavelength-dependent polarization-sensitive photoresponse and the anisotropic dielectric constant mainly affected by interband transitions near the Weyl point. It is revealed that the polarization sensitivity and the responsivity both vary non-monotonically with the wavelength. This phenomenon is attributed to the polarization selective excitation of interband transitions associated with asymmetrically distributed electron orbitals around the Weyl points. Concerning the infrared detection properties of WTe₂, a maximum responsivity of 0.68 mA W^-1 is obtained under self-powered operation. The power dependence of the photoresponse is linear, and the response time is around 14 μs. This work would provoke further studies about the anisotropic photoresponse associated with the transitions even closer to the Dirac or Weyl points, and it provides an approach to select the right semimetal for the right wavelength range of infrared polarization detection.

Kekulé Lattice in Graphdiyne: Coexistence of Phononic and Electronic Second-Order Topological Insulator

Topological physics has been extensively studied in different kinds of bosonic and Fermionic systems, but the coexistence of topological phonons and electrons in one single material has seldom been reported. Recently, graphdiyne has been proposed as a two-dimensional (2D) electronic second-order topological insulator (SOTI). In this work, we found that graphdiyne is equivalent to Kekulé lattice, also realizing a 2D phononic SOTI in both out-of-plane and in-plane modes. Depending on edge terminations, the characterized topological corner states can be either inside or outside the bulk gap and are tunable by the local corner potential. Most remarkably, a unique selectivity of space and symmetry is revealed in the electron-phonon coupling between the localized phononic and electronic topological corner states. Our results not only demonstrate the phononic higher-order band topology in a real carbon material but also provide an opportunity to investigate the interplay between phononic and electronic higher-order topological states.

2D Heterostructures for Ubiquitous Electronics and Optoelectronics: Principles, Opportunities, and Challenges

A grand family of two-dimensional (2D) materials and their heterostructures have been discovered through the extensive experimental and theoretical efforts of chemists, material scientists, physicists, and technologists. These pioneering works contribute to realizing the fundamental platforms to explore and analyze new physical/chemical properties and technological phenomena at the micro-nano-pico scales. Engineering 2D van der Waals (vdW) materials and their heterostructures via chemical and physical methods with a suitable choice of stacking order, thickness, and interlayer interactions enable exotic carrier dynamics, showing potential in high-frequency electronics, broadband optoelectronics, low-power neuromorphic computing, and ubiquitous electronics. This comprehensive review addresses recent advances in terms of representative 2D materials, the general fabrication methods, and characterization techniques and the vital role of the physical parameters affecting the quality of 2D heterostructures. The main emphasis is on 2D heterostructures and 3D-bulk (3D) hybrid systems exhibiting intrinsic quantum mechanical responses in the optical, valley, and topological states. Finally, we discuss the universality of 2D heterostructures with representative applications and trends for future electronics and optoelectronics (FEO) under the challenges and opportunities from physical, nanotechnological, and material synthesis perspectives.

Persistence of Monoclinic Crystal Structure in 3D Second-Order Topological Insulator Candidate 1T'-MoTe2 Thin Flake Without Structural Phase Transition

A van der Waals material, MoTe₂ with a monoclinic 1T' crystal structure is a candidate for 3D second-order topological insulators (SOTIs) hosting gapless hinge states and insulating surface states. However, due to the temperature-induced structural phase transition, the monoclinic 1T' structure of MoTe₂ is transformed into the orthorhombic T_d structure as the temperature is lowered, which hinders the experimental verification and electronic applications of the predicted SOTI state at low temperatures. Here, systematic Raman spectroscopy studies of the exfoliated MoTe₂ thin flakes with variable thicknesses at different temperatures, are presented. As a spectroscopic signature of the orthorhombic T_d structure of MoTe₂ , the out-of-plane vibration mode D at ≈ 125 cm^-1 is always visible below a certain temperature in the multilayer flakes thicker than ≈ 27.7 nm, but vanishes in the temperature range from 80 to 320 K when the flake thickness becomes lower than ≈ 19.5 nm. The absence of the out-of-plane vibration mode D in the Raman spectra here demonstrates not only the disappearance of the monoclinic-to-orthorhombic phase transition but also the persistence of the monoclinic 1T' structure in the MoTe₂ thin flakes thinner than ≈ 19.5 nm at low temperatures down to 80 K, which may be caused by the high enough density of the holes introduced during the gold-enhanced exfoliation process and exposure to air. The MoTe₂ thin flakes with the low-temperature monoclinic 1T' structure provide a material platform for realizing SOTI states in van der Waals materials at low temperatures, which paves the way for developing a new generation of electronic devices based on SOTIs.

Higher-order topological insulator in cubic semiconductor quantum wells

The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order topological insulator state in quantum wells based on the most common semiconducting materials. By successively deriving the bulk and boundary Hamiltonians, we theoretically prove the existence of topological corner states due to cubic symmetry in quantum wells with double band inversion. We show that the appearance of corner states does not depend solely on the crystallographic orientation of the meeting edges, but also on the growth orientation of the quantum well. Our theoretical results significantly extend the application potential of topological quantum wells based on IV, II–VI and III–V semiconductors with diamond or zinc-blende structures.

Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals

Recently, higher-order topological matter and 3D quantum Hall effects have attracted a great amount of attention. The Fermi-arc mechanism of the 3D quantum Hall effect proposed to exist in Weyl semimetals is characterized by the one-sided hinge states, which do not exist in all the previous quantum Hall systems, and more importantly, pose a realistic example of the higher-order topological matter. The experimental effort so far is in the Dirac semimetal Cd_{3}As_{2}, where, however, time-reversal symmetry leads to hinge states on both sides of the top and bottom surfaces, instead of the aspired one-sided hinge states. We propose that under a tilted magnetic field, the hinge states in Cd_{3}As_{2}-like Dirac semimetals can be one sided, highly tunable by field direction and Fermi energy, and robust against weak disorder. Furthermore, we propose a scanning tunneling Hall measurement to detect the one-sided hinge states. Our results will be insightful for exploring not only the quantum Hall effects beyond two dimensions, but also other higher-order topological insulators in the future.

Evidence for higher order topology in Bi and Bi0.92Sb0.08

Higher order topological insulators (HOTIs) are a new class of topological materials which host protected states at the corners or hinges of a crystal. HOTIs provide an intriguing alternative platform for helical and chiral edge states and Majorana modes, but there are very few known materials in this class. Recent studies have proposed Bi as a potential HOTI, however, its topological classification is not yet well accepted. In this work, we show that the (110) facets of Bi and BiSb alloys can be used to unequivocally establish the topology of these systems. Bi and Bi_0.92Sb_0.08 (110) films were grown on silicon substrates using molecular beam epitaxy and studied by scanning tunneling spectroscopy. The surfaces manifest rectangular islands which show localized hinge states on three out of the four edges, consistent with the theory for the HOTI phase. This establishes Bi and Bi_0.92Sb_0.08 as HOTIs, and raises questions about the topological classification of the full family of Bi_xSb_1−x alloys.

The experimental realization of higher order topological insulator (HOTI) in solid state materials remains elusive. Here, Aggarwal et al. reveal hinge states on three edges of both Bi and Bi_0.92Sb_0.08 (110) islands, supporting them as a class of HOTI.

Higher-Order Fabry-Pérot Interferometer from Topological Hinge States

We propose an intrinsic three-dimensional Fabry-Pérot type interferometer, coined "higher-order interferometer," that is based on the chiral hinge states of second-order topological insulators and cannot be mapped to an equivalent two-dimensional setting because of higher-order topological obstructions. Quantum interference patterns in the two-terminal conductance of this interferometer are controllable not only by tuning the strength but also, particularly, by rotating the direction of the magnetic field applied perpendicularly to the transport direction. Remarkably, the conductance exhibits a characteristic beating pattern with multiple frequencies depending on the field strength and direction in a unique fashion. Our novel interferometer thus provides feasible and robust magnetotransport signatures for hinge states of higher-order topological insulators.

Kramers nodal line metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

Quantum spin Hall and quantum anomalous Hall states in magnetic Ti2Te2O single layer

Magnetic topological insulators, such as MnBi₂Te₄have attracted great attention recently due to their application to the quantum anomalous Hall (QAH) effect. However, the magnetic quantum spin Hall (QSH) effect in two-dimensional (2D) materials has not yet been reported. Here based on first-principle calculations we find that Ti₂Te₂O, a van der Waals layered compound, can cherish both the QAH and QSH states, depending on the magnetic order in its single layer. If the single layer was in a chessboard antiferromagnetic (FM) state, it is a QSH insulator which carries two counterpropagating helical edge states. The spin-orbit-couplings induced bulk band gap can approach as large as 0.31 eV. On the other hand, if the monolayer becomes FM, exchange interactions would push one pair of bands away from the Fermi energy and leave only one chiral edge state remaining, which turns the compound into a Chern insulator (precisely, it is semimetallic with a topologically direct band gap). Both magnetic orders explicitly break the time reversal symmetry and split the energy bands of different spin orientations. To our knowledge, Ti₂Te₂O is the first compound that predicted to possess both intrinsic QSH and QAH effects. Our works provide new possibilities to reach a controllable phase transition between two topological nontrivial phases through magnetism tailoring.

Edge superconductivity in multilayer WTe2 Josephson junction

WTe₂, as a type-II Weyl semimetal, has 2D Fermi arcs on the (001) surface in the bulk and 1D helical edge states in its monolayer. These features have recently attracted wide attention in condensed matter physics. However, in the intermediate regime between the bulk and monolayer, the edge states have not been resolved owing to its closed band gap which makes the bulk states dominant. Here, we report the signatures of the edge superconductivity by superconducting quantum interference measurements in multilayer WTe₂ Josephson junctions and we directly map the localized supercurrent. In thick WTe₂ ([Formula: see text], the supercurrent is uniformly distributed by bulk states with symmetric Josephson effect ([Formula: see text]). In thin WTe₂ (10 nm), however, the supercurrent becomes confined to the edge and its width reaches up to [Formula: see text]and exhibits non-symmetric behavior [Formula: see text]. The ability to tune the edge domination by changing thickness and the edge superconductivity establishes WTe₂ as a promising topological system with exotic quantum phases and a rich physics.