Quantum Spin Hall Insulator State in HgTe Quantum Wells

Dual Dirac Nodal Line in Nearly Freestanding Electronic Structure of β-Sn Monolayer

Two-dimensional topological insulators (2D TIs) have distinct electronic properties that make them attractive for various applications, especially in spintronics. The conductive edge states in 2D TIs are protected from disorder and perturbations and are spin-polarized, which restrict current flow to a single spin orientation. In contrast, topological nodal line semimetals (TNLSM) are distinct from TIs because of the presence of a 1D ring of degeneracy formed from two bands that cross each other along a line in the Brillouin zone. These nodal lines are protected by topology and can be destroyed only by breaking certain symmetry conditions, making them highly resilient to disorder and defects. However, 2D TNLSMs do not possess protected boundary modes, which makes their investigation challenging. There have been several theoretical predictions of 2D TNLSMs, however, experimental realizations are rare. β-Sn, a metallic allotrope of tin with a superconducting temperature of 3.72 K, may be a candidate for a topological superconductor that can host Majorana Fermions for quantum computing. In this work, single layers of α-Sn and β-Sn on a Cu(111) substrate are successfully prepared and studied using scanning tunneling microscopy, angle-resolved photoemission spectroscopy, and density functional theory calculations. The lattice and electronic structure undergo a topological transition from 2D topological insulator α-Sn to 2D TNLSM β-Sn, with two types of nodal lines coexisting in monolayer β-Sn. Such a realization of two types of nodal lines in one 2D material has not been reported to date. Moreover, we also observed an unexpected phenomenon of freestanding-like electronic structures of β-Sn/Cu(111), highlighting the potential of ultrathin β-Sn films as a platform for exploring the electronic properties of 2D TNLSM and topological superconductors, such as few-layer superconducting β-Sn in lateral contact with topological nodal line single-layer β-Sn.

High-temperature quantum valley Hall effect with quantized resistance and a topological switch

Edge states of a topological insulator can be used to explore fundamental science emerging at the interface of low dimensionality and topology. Achieving a robust conductance quantization, however, has proven challenging for helical edge states. In this work, we show wide resistance plateaus in kink states-a manifestation of the quantum valley Hall effect in Bernal bilayer graphene-quantized to the predicted value at zero magnetic field. The plateau resistance has a very weak temperature dependence up to 50 kelvin and is flat within a dc bias window of tens of millivolts. We demonstrate the electrical operation of a topology-controlled switch with an on/off ratio of 200. These results demonstrate the robustness and tunability of the kink states and its promise in constructing electron quantum optics devices.

Recent progress of MnBi2Te4 epitaxial thin films as a platform for realising the quantum anomalous Hall effect

Since the first realisation of the quantum anomalous Hall effect (QAHE) in a dilute magnetic-doped topological insulator thin film in 2013, the quantisation temperature has been limited to less than 1 K due to magnetic disorder in dilute magnetic systems. With magnetic moments ordered into the crystal lattice, the intrinsic magnetic topological insulator MnBi2Te4 has the potential to eliminate or significantly reduce magnetic disorder and improve the quantisation temperature. Surprisingly, to date, the QAHE has yet to be observed in molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films at zero magnetic field, and what leads to the difficulty in quantisation is still an active research area. Although bulk MnBi2Te4 and exfoliated flakes have been well studied, revealing both the QAHE and axion insulator phases, experimental progress on MBE thin films has been slower. Understanding how the breakdown of the QAHE occurs in MnBi2Te4 thin films and finding solutions that will enable mass-produced millimetre-size QAHE devices operating at elevated temperatures are required. In this mini-review, we will summarise recent studies on the electronic and magnetic properties of MBE MnBi2Te4 thin films and discuss mechanisms that could explain the failure of the QAHE from the aspects of defects, electronic structure, magnetic order, and consequences of their delicate interplay. Finally, we propose several strategies for realising the QAHE at elevated temperatures in MnBi2Te4 thin films.

Interaction- and phonon-induced topological phase transitions in double helical liquids

Helical liquids, formed by time-reversal pairs of interacting electrons in topological edge channels, provide a platform for stabilizing topological superconductivity upon introducing local and nonlocal pairings through the proximity effect. Here, we investigate the effects of electron-electron interactions and phonons on the topological superconductivity in two parallel channels of such helical liquids. Interactions between electrons in different channels tend to reduce nonlocal pairing, suppressing the topological regime. Additionally, electron-phonon coupling breaks the self duality in the electronic subsystem and renormalizes the pairing strengths. Notably, while earlier perturbative calculations suggested that longitudinal phonons have no effect on helical liquids themselves to the leading order, our nonperturbative analysis shows that phonons can induce transitions between topological and trivial superconductivity, thereby weakening the stability of topological zero modes. Our findings highlight practical limitations in realizing topological zero modes in various systems hosting helical channels, including quantum spin Hall insulators, higher-order topological insulators, and their fractional counterparts recently observed in twisted bilayer systems.

Realization of Honeycomb Tellurene with Topological Edge States

The two-dimensional (2D) honeycomb lattice has attracted intensive research interest due to the appearance of Dirac-type band structures as the consequence of two sublattices in the honeycomb structure. Introducing strong spin-orbit coupling (SOC) leads to a gap opening at the Dirac point, transforming the honeycomb lattice into a 2D topological insulator as a platform for the quantum spin Hall effect (QSHE). In this work, we realize a 2D honeycomb-structured film with tellurium, the heaviest nonradioactive element in Group VI, namely, tellurene, via molecular beam epitaxy. We revealed the gap opening of 160 meV at the Dirac point due to the strong SOC in the honeycomb-structured tellurene by angle-resolved photoemission spectroscopy. The topological edge states of tellurene are detected via scanning tunneling microscopy/spectroscopy. These results demonstrate that tellurene is a novel 2D honeycomb lattice with strong SOC, and they unambiguously prove that tellurene is a promising candidate for a room-temperature QSHE system.

Probing the Spatial Homogeneity of Exfoliated HfTe5 Films

In van der Waals materials, external strain is an effective tool to manipulate and control electronic responses by changing the electronic bands upon lattice deformation. In particular, the band gap of the layered transition metal pentatelluride HfTe5 is sufficiently small to be inverted by subtle changes of the lattice parameters resulting in a strain-tunable topological phase transition. In that case, knowledge about the spatial homogeneity of electronic properties becomes crucial, especially for the microfabricated thin film circuits used in typical transport measurements. Here, we reveal the homogeneity of exfoliated HfTe5 thin films by spatially resolved Raman microscopy. Comparing the Raman spectra under applied external strain to unstrained bulk references, we pinpoint local variations of Raman signatures to inhomogeneous strain profiles in the sample. Importantly, our results demonstrate that microfabricated contacts can act as sources of significant inhomogeneities. To mitigate the impact of unintentional strain and its corresponding modifications of the electronic structure, careful Raman microscopy constitutes a valuable tool for quantifying the homogeneity of HfTe5 films and circuits fabricated thereof.

Memristive switching in the surface of a charge-density-wave topological semimetal

Owing to the outstanding properties provided by nontrivial band topology, topological phases of matter are considered as a promising platform towards low-dissipation electronics, efficient spin-charge conversion, and topological quantum computation. Achieving ferroelectricity in topological materials enables the non-volatile control of the quantum states, which could greatly facilitate topological electronic research. However, ferroelectricity is generally incompatible with systems featuring metallicity due to the screening effect of free carriers. In this study, we report the observation of memristive switching based on the ferroelectric surface state of a topological semimetal (TaSe4)2I. We find that the surface state of (TaSe4)2I presents out-of-plane ferroelectric polarization due to surface reconstruction. With the combination of ferroelectric surface and charge-density-wave-gapped bulk states, an electric-switchable barrier height can be achieved in (TaSe4)2I-metal contact. By employing a multi-terminal-grounding design, we manage to construct a prototype ferroelectric memristor based on (TaSe4)2I with on/off ratio up to 103, endurance over 103 cycles, and good retention characteristics. The origin of the ferroelectric surface state is further investigated by first-principles calculations, which reveal an interplay between ferroelectricity and band topology. The emergence of ferroelectricity in (TaSe4)2I not only demonstrates it as a rare but essential case of ferroelectric topological materials, but also opens new routes towards the implementation of topological materials in functional electronic devices.

Perfect Zeeman Anisotropy in Rotationally Symmetric Quantum Dots with Strong Spin-Orbit Interaction

In nanoscale structures with rotational symmetry, such as quantum rings, the orbital motion of electrons combined with a spin-orbit interaction can produce a very strong and anisotropic Zeeman effect. Since symmetry is sensitive to electric fields, ring-like geometries provide an opportunity to manipulate magnetic properties over an exceptionally wide range. In this work, we show that it is possible to form rotationally symmetric confinement potentials inside a semiconductor quantum dot, resulting in electron orbitals with large orbital angular momentum and strong spin-orbit interactions. We find complete suppression of Zeeman spin splitting for magnetic fields applied in the quantum dot plane, similar to the expected behavior of an ideal quantum ring. Spin splitting reappears as orbital interactions are activated with symmetry-breaking electric fields. For two valence electrons, representing a common basis for spin-qubits, we find that modulating the rotational symmetry may offer new prospects for realizing tunable protection and interaction of spin-orbital states.

Electron-electron interactions in partially mixed helical states

We theoretically study the effect of electron-electron interactions in one-dimensional partially mixed helical states. These helical states can be realized at the edges of two-dimensional topological insulators with partially broken time-reversal symmetry, resulting in helical gapped states. Using the bosonization method and renormalization group analysis, we identify weak gap, crossover, and strong gap regimes in the phase diagram. We find that strong electron-electron interaction mixes the helicity of the states, leading to the relevant strong gap regime. We investigate the charge and spin density wave correlation functions in different relevancy regimes of the gap mediated by interactions, where in the case of strong repulsive interaction, the spin density wave dominates the charge density wave. Additionally, employing the Memory function technique, we calculate the effect of mixed helicity on the charge transport in a sufficiently long edge. We find a non-uniform temperature dependence for the charge conductivity in both the strong and weak gap regimes with distinct features.

Observation of edge states derived from topological helix chains

Introducing the concept of topology has revolutionized materials classification, leading to the discovery of topological insulators and Dirac-Weyl semimetals1-3. One of the most fundamental theories underpinning topological materials is the Su-Schrieffer-Heeger (SSH) model4,5, which was developed in 1979-decades before the recognition of topological insulators-to describe conducting polymers. Distinct from the vast majority of known topological insulators with two and three dimensions1-3, the SSH model predicts a one-dimensional analogue of topological insulators, which hosts topological bound states at the endpoints of a chain4-8. To establish this unique and pivotal state, it is crucial to identify the low-energy excitations stemming from bound states, but this has remained unknown in solids because of the absence of suitable platforms. Here we report unusual electronic states that support the emergent bound states in elemental tellurium, the single helix of which was recently proposed to realize an extended version of the SSH chain9,10. Using spin- and angle-resolved photoemission spectroscopy with a micro-focused beam, we have shown spin-polarized in-gap states confined to the edges of the (0001) surface. Our density functional theory calculations indicate that these states are attributed to the interacting bound states originating from the one-dimensional array of SSH tellurium chains. Helices in solids offer a promising experimental platform for investigating exotic properties associated with the SSH chain and exploring topological phases through dimensionality control.

Rashba-like Spin Textures in Graphene Promoted by Ferromagnet-Mediated Electronic Hybridization with a Heavy Metal

Epitaxial graphene/ferromagnetic metal (Gr/FM) heterostructures deposited onto heavy metals have been proposed for the realization of spintronic devices because of their perpendicular magnetic anisotropy and sizable Dzyaloshinskii-Moriya interaction (DMI), allowing for both enhanced thermal stability and stabilization of chiral spin textures. However, establishing routes toward this goal requires the fundamental understanding of the microscopic origin of their unusual properties. Here, we elucidate the nature of the induced spin-orbit coupling (SOC) at Gr/Co interfaces on Ir. Through spin- and angle-resolved photoemission spectroscopy along with density functional theory, we show that the interaction of the heavy metals with the Gr layer via hybridization with the FM is the source of strong SOC in the Gr layer. Furthermore, our studies on ultrathin Co films underneath Gr reveal an energy splitting of ∼100 meV for in-plane and negligible for out-of-plane spin polarized Gr π-bands, consistent with a Rashba-SOC at the Gr/Co interface, which is either the fingerprint or the origin of the DMI. This mechanism vanishes at large Co thicknesses, where neither in-plane nor out-of-plane spin-orbit splitting is observed, indicating that Gr π-states are electronically decoupled from the heavy metal. The present findings are important for future applications of Gr-based heterostructures in spintronic devices.

First principles prediction of novel quantum topological insulator state in two-dimensional XMg2Bi2(X=Eu/Yb)

Topological insulator (TIs), a novel quantum state of materials, has a lot of significance in the development of low-power electronic equipments as the conducting edge states display exceptional endurance against back-scattering. The absence of suitable materials with high fabrication feasibility and significant nontrivial bandgap, is now the biggest hurdle in their potential applications in devices. Here, we illustrate using first principles density functional calculations that the quintuplet layers of EuMg2Bi2and YbMg2Bi2crystals are potential two-dimensional TIs with a sizeable nontrivial gaps of 72 meV and 147 meV respectively. Dynamical stability of these quintuplet layers of EuMg2Bi2and YbMg2Bi2is confirmed by our phonon calculations. The weakly coupled layered structure of parent compounds makes it possible for simple exfoliation from a three-dimensional structure. We observed gapless edge states inside the bulk band gap in both the systems which indicate their TI nature. Further, we observed the anomalous and spin Hall conductivities to be quantized in two dimensional EuMg2Bi2and YbMg2Bi2respectively. Our findings predict two viable candidate materials as two dimensional quantum TIs which can be explored by future experimental investigations and possible applications of quantized spin and anomalous Hall conductance in spintronics.

Nanowires: Exponential speedup in quantum computing

This review paper examines the crucial role of nanowires in the field of quantum computing, highlighting their importance as versatile platforms for qubits and vital building blocks for creating fault-tolerant and scalable quantum information processing systems. Researchers are studying many categories of nanowires, including semiconductor, superconducting, and topological nanowires, to explore their distinct quantum features that play a role in creating various qubit designs. The paper explores the interdisciplinary character of quantum computing, combining the fields of quantum physics and materials science. This text highlights the significance of quantum gate operations in manipulating qubits for computation, thus creating the toolbox of quantum algorithms. The paper emphasizes the key research areas in quantum technology, such as entanglement engineering, quantum error correction, and a wide range of applications spanning from encryption to climate change modeling. The research highlights the importance of tackling difficulties related to decoding mitigation, error correction, and hardware scalability to fully utilize the transformative potential of quantum computing in scientific, technical, and computational fields.

Anisotropic structural, vibrational, electronic, optical, and elastic properties of single-layer hafnium pentatelluride: an ab initio study

Motivated by the highly anisotropic nature of bulk hafnium pentatelluride (HfTe5), the structural, vibrational, electronic, optical, and elastic properties of single-layer two-dimensional (2D) HfTe5 were investigated by performing density functional theory (DFT)-based first-principles calculations. Total energy and geometry optimizations reveal that the 2D single-layer form of HfTe5 exhibits in-plane anisotropy. The phonon band structure shows dynamic stability of the free-standing layer and the predicted Raman spectrum displays seven characteristic Raman-active phonon peaks. In addition to its dynamic stability, HfTe5 is shown to exhibit thermal stability at room temperature, as confirmed by quantum molecular dynamics simulations. Moreover, the obtained elastic stiffness tensor elements indicate the mechanical stability of HfTe5 with its orientation-dependent soft nature. The electronic band structure calculations show the indirect-gap semiconducting behavior of HfTe5 with a narrow electronic band gap energy. The optical properties of HfTe5, in terms of its imaginary dielectric function, absorption coefficient, reflectance, and transmittance, are shown to exhibit strong in-plane anisotropy. Furthermore, structural analysis of several point defects and their oxidized structures was performed by means of simulated STM images. Among the considered vacancy defects, namely , , VTeout, VTein, , and VHf, the formation of VTeout is revealed to be the most favorable defect. While and VHf defects lead to local magnetism, only the oxygen-substituted VHf structure possesses magnetism among the oxidized defects. Moreover, it is found that all the bare and oxidized vacant sites can be distinguished from each other through the STM images. Overall, our study indicates not only the fundamental anisotropic features of single-layer HfTe5, but also shows the signatures of feasible point defects and their oxidized structures, which may be useful for future experiments on 2D HfTe5.

Superconducting Field-Effect Transistors with PdxTe-Te Intimate Contacts

Superconducting-based electronic devices have shown great potential for future quantum computing applications. One key building block device is a superconducting field-effect transistor based on a superconductor-semiconductor-superconductor Josephson-junction (JJ) with a gate-tunable semiconducting channel. However, the performance of such devices is highly dependent on the quality of the superconductor to semiconductor interface. In this study, we present an alternative method to obtain a high-quality interface by using intimate contact. We investigate the proximity-induced superconductivity in chiral crystal tellurium (Te) and fabricate a PdxTe-Te-PdxTe JJ with an ambipolar supercurrent that is gate-tunable and exhibits multiple Andreev reflections. The semiconducting two-dimensional Te single crystal is grown hydrothermally and partially converted to superconducting PdxTe by controlled annealing. Our work demonstrates a promising path for realizing controllable superconducting electronic devices with high-quality superconducting interfaces; thus, we can continue to advance the field of quantum computing and other interface-based technologies.

Graphite/h-BN van der Waals heterostructure as a gate stack for HgTe quantum wells

Two-dimensional topological insulators have attracted much interest due to their potential applications in spintronics and quantum computing. To access the exotic physical phenomena, a gate electric field is required to tune the Fermi level into the bulk band gap. Hexagonal boron nitride (h-BN) is a promising alternative gate dielectric due to its unique advantages such as flat and charge-free surface. Here we present a h-BN/graphite van der Waals heterostructure as a top gate on HgTe heterostructure-based Hall bar devices. We compare our results to devices with h-BN/Ti/Au and HfO2/Ti/Au gates. Devices with a h-BN/graphite gate show no charge carrier density shift compared to as-grown structures, in contrast to a significant n-type carrier density increase for HfO2/Ti/Au. We attribute this observation mainly to the comparable work function of HgTe and graphite. In addition, devices with h-BN gate dielectric show slightly higher electron mobility compared to HfO2-based devices. Our results demonstrate the compatibility between layered materials transfer and wet-etched structures and provide a strategy to solve the issue of significant shifts of the carrier density in gated HgTe heterostructures.

Tuning Displacement Fields in a Two-Dimensional Topological Insulator Using Nanopatterned Gates

Epitaxial heterostructures with topological insulators enable novel quantum phases and practical device applications. Their topological electronic states are sensitive to the microscopic parameters, including structural inversion asymmetry (SIA), which is an inherent feature of many real heterostructures. Controlling SIA is challenging, because it requires the ability to tune the displacement field across the topological film. Here, using nanopatterned gates, we demonstrate a tunable displacement field in a heterostructure of the two-dimensional topological insulator cadmium arsenide. Transport studies in magnetic fields reveal an extreme sensitivity of the band inversion to SIA. We show that a relatively small displacement field (∼50 mV/nm) converts the crossing of the two zeroth Landau levels in magnetic field to an avoided crossing, signaling a change to trivial band order. This work demonstrates a universal methodology for tuning electronic states in topological thin films.

An Electrically Pumped Topological Polariton Laser

With a seminal work of Raghu and Haldane in 2008, concepts of topology have been introduced into optical systems, where some of the most promising routes to an application are efficient and highly coherent topological lasers. While some attempts have been made to excite such structures electrically, the majority of published experiments use a form of laser excitation. In this paper, we use a lattice of vertical resonator polariton micropillars to form an exponentially localized topological Su-Schrieffer-Heeger defect. Upon electrical excitation, the system unequivocally shows polariton lasing from the topological defect using a carefully placed gold contact. Despite the presence of doping and electrical contacts, the polariton band structure clearly preserves its topological properties. At high excitation power the Mott density is exceeded, leading to highly efficient lasing in the weak coupling regime. This work is an important step toward applied topological lasers using vertical resonator microcavity structures.

Realization of monolayer ZrTe5 topological insulators with wide band gaps

Two-dimensional topological insulators hosting the quantum spin Hall effect have application potential in dissipationless electronics. To observe the quantum spin Hall effect at elevated temperatures, a wide band gap is indispensable to efficiently suppress bulk conduction. Yet, most candidate materials exhibit narrow or even negative band gaps. Here, via elegant control of van der Waals epitaxy, we have successfully grown monolayer ZrTe5 on a bilayer graphene/SiC substrate. The epitaxial ZrTe5 monolayer crystalizes in two allotrope isomers with different intralayer alignments of ZrTe3 prisms. Our scanning tunneling microscopy/spectroscopy characterization unveils an intrinsic full band gap as large as 254 meV and one-dimensional edge states localized along the periphery of the ZrTe5 monolayer. First-principles calculations further confirm that the large band gap originates from strong spin-orbit coupling, and the edge states are topologically nontrivial. These findings thus provide a highly desirable material platform for the exploration of the high-temperature quantum spin Hall effect.

Non-Abelian Topological Phases and Their Quotient Relations in Acoustic Systems

Non-Abelian topological phases (NATPs) exhibit enigmatic intrinsic physics distinct from well-established Abelian topological phases, while lacking straightforward configuration and manipulation, especially for classical waves. In this Letter, we exploit novel braiding-type couplings among a pair of triple-component acoustic dipoles, which act as functional elements with effective imaginary couplings. Sequencing them in one dimension allows us to generate acoustic NATPs in a compact yet time-reversal invariant Hermitian system. We further provide the whole phase diagram that encompasses all i, j, and k non-Abelian phases, and directly demonstrate their unique quotient relations via different end point states. Our NATPs based on real-space braiding may inspire the exploration of acoustic devices with non-commutative characters.

Br-Vacancies Induced Variable Ranging Hopping Conduction in High-Order Topological Insulator Bi4Br4

The defects have a remarkable influence on the electronic structures and the electric transport behaviors of the matter, providing the additional means to engineering their physical properties. In this work, a comprehensive study on the effect of Br-vacancies on the electronic structures and transport behaviors in the high-order topological insulator Bi4Br4 is performed by the combined techniques of the scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and physical properties measurement system along with the first-principle calculations. The STM results show the defects on the cleaved surface of a single crystal and reveal that the defects are correlated to the Br-vacancies with the support of the simulated STM images. The role of the Br-vacancies in the modulation of the band structures has been identified by ARPES spectra and the calculated energy-momentum dispersion. The relationship between the Br-vacancies and the semiconducting-like transport behaviors at low temperature has been established, implying a Mott variable ranging hopping conduction in Bi4Br4. The work not only resolves the unclear transport behaviors in this matter, but also paves a way to modulate the electric conduction path by the defects engineering.

Bias-Free Access to Orbital Angular Momentum in Two-Dimensional Quantum Materials

The demonstration of a topological band inversion constitutes the most elementary proof of a quantum spin Hall insulator (QSHI). On a fundamental level, such an inverted band gap is intrinsically related to the bulk Berry curvature, a gauge-invariant fingerprint of the wave function's quantum geometric properties in Hilbert space. Intimately tied to orbital angular momentum (OAM), the Berry curvature can be, in principle, extracted from circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES), were it not for interfering final state photoelectron emission channels that obscure the initial state OAM signature. Here, we outline a full-experimental strategy to avoid such interference artifacts and isolate the clean OAM from the CD-ARPES response. Bench-marking this strategy for the recently discovered atomic monolayer system indenene, we demonstrate its distinct QSHI character and establish CD-ARPES as a scalable bulk probe to experimentally classify the topology of two-dimensional quantum materials with time reversal symmetry.

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.

Spectral Asymmetry Induces a Re-Entrant Quantum Hall Effect in a Topological Insulator

The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of 2D massless Dirac fermions, known from quantum field theory. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., an imbalance between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. This work reports the realization of this 2D Dirac physics at a single surface of the 3D topological insulator (Hg,Mn)Te. An unconventional re-entrant sequence of quantized Hall plateaus in the measured Hall resistance can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.

Selective-Area-Grown PbTe-Pb Planar Josephson Junctions for Quantum Devices

Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two-dimensional electron gases (InAs, InSb, InAsSb, and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrents and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection wherein phase bias and tunneling spectroscopy are applicable.

Observation of D-class topology in an acoustic metamaterial

Topological materials and metamaterials opened new paradigms to create and manipulate phases of matter with unconventional properties. Topological D-class phases (TDPs) are archetypes of the ten-fold classification of topological phases with particle-hole symmetry. In two dimensions, TDPs support propagating topological edge modes that simulate the elusive Majorana elementary particles. Furthermore, a piercing of π-flux Dirac-solenoids in TDPs stabilizes localized Majorana excitations that can be braided for the purpose of topological quantum computation. Such two-dimensional (2D) TDPs have been a focus in the research frontier, but their experimental realizations are still under debate. Here, with a novel design scheme, we realize 2D TDPs in an acoustic crystal by synthesizing both the particle-hole and fermion-like time reversal symmetries for a wide range of frequencies. The design scheme leverages an enriched unit cell structure with real-valued couplings that emulate the targeted Hamiltonian of TDPs with complex hoppings: A technique that could unlock the realization of all topological classes with passive metamaterials. In our experiments, we realize a pair of TDPs with opposite Chern numbers in two independent sectors that are connected by an intrinsic fermion-like time-reversal symmetry built in the system. We measure the acoustic Majorana-like helical edge modes and visualize their robust topological transport, thus revealing the unprecedented D and DIII class topologies with direct evidence. Our study opens up a new pathway for the experimental realization of two fundamental classes of topological phases and may offer new insights in fundamental physics, materials science, and phononic information processing.

Evidence of the fractional quantum spin Hall effect in moiré MoTe2

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities1-6. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0 = e2/h (with e and h denoting the electron charge and Planck's constant, respectively)7-14. Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands15,16. At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance3 2 G 0 with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials17-19.

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter1. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order2-8, not possible in quantum Hall and Chern insulator systems. Here we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe4. This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism2-4,9,10.

Topological spin-orbit-coupled fermions beyond rotating wave approximation

The realization of spin-orbit-coupled ultracold gases has driven a wide range of research and is typically based on the rotating wave approximation (RWA). By neglecting the counter-rotating terms, RWA characterizes a single near-resonant spin-orbit (SO) coupling in a two-level system. Here, we propose and experimentally realize a new scheme for achieving a pair of two-dimensional (2D) SO couplings for ultracold fermions beyond RWA. This work not only realizes the first anomalous Floquet topological Fermi gas beyond RWA, but also significantly improves the lifetime of the 2D-SO-coupled Fermi gas. Based on pump-probe quench measurements, we observe a deterministic phase relation between two sets of SO couplings, which is characteristic of our beyond-RWA scheme and enables the two SO couplings to be simultaneously tuned to the optimum 2D configurations. We observe intriguing band topology by measuring two-ring band-inversion surfaces, quantitatively consistent with a Floquet topological Fermi gas in the regime of high Chern numbers. Our study can open an avenue to explore exotic SO physics and anomalous topological states based on long-lived SO-coupled ultracold fermions.

Bulk-Edge Correspondence for Nonlinear Eigenvalue Problems

Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.

Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static non-Hermitian systems and discuss the establishment of its generalized bulk-boundary correspondence (BBC). Ultimately, we focus on the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven non-Hermitian system and periodically quenched non-Hermitian system. The non-Bloch topological invariants were defined on the generalized Brillouin zone and the real space wave functions to characterize the Floquet non-Hermtian topological phases. Then, the generalized BBC was established for the two typical periodically driven non-Hermitian systems. Additionally, we review novel phenomena in the higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. The experimental realizations and recent advances have also been surveyed. Finally, we end with a summarization and hope this pedagogical review can motivate further research on Floquet non-Hermtian topological physics.

Experimental Demonstration of Topological Catalysis for CO2 Electroreduction

The past decade has witnessed substantial progress in understanding nontrivial band topology and discovering exotic topological materials in condensed-matter physics. Recently, topological physics has been further extended to the chemistry discipline, leading to the emergence of topological catalysis. In principle, the topological effect is detectable in catalytic reactions, but no conclusive evidence has been reported yet. Herein, by precisely manipulating the topological surface state (TSS) of Bi2Se3 nanosheets through thickness control and the application of a magnetic field, we provide direct experimental evidence to illustrate topological catalysis for CO2 electroreduction. With and without the cooperation of TSS, CO2 is mainly reduced into liquid fuels (HCOOH and H2C2O4) and CO, exhibiting high (up to 90% at -1.1 V versus reversible hydrogen electrode) and low Faradaic efficiency (FE), respectively. Theoretically, the product and FE difference can be attributed to the TSS-regulated adsorption of key intermediates and the reduced barrier of the potential-determining step. Our work demonstrates the inherent correlation between band topology and electrocatalysis, paving a new avenue for designing high-performance catalysts.

Parity-time-symmetric photonic topological insulator

Topological insulators are a concept that originally stems from condensed matter physics. As a corollary to their hallmark protected edge transport, the conventional understanding of such systems holds that they are intrinsically closed, that is, that they are assumed to be entirely isolated from the surrounding world. Here, by demonstrating a parity-time-symmetric topological insulator, we show that topological transport exists beyond these constraints. Implemented on a photonic platform, our non-Hermitian topological system harnesses the complex interplay between a discrete coupling protocol and judiciously placed losses and, as such, inherently constitutes an open system. Nevertheless, even though energy conservation is violated, our system exhibits an entirely real eigenvalue spectrum as well as chiral edge transport. Along these lines, this work enables the study of the dynamical properties of topological matter in open systems without the instability arising from complex spectra. Thus, it may inspire the development of compact active devices that harness topological features on-demand.

Tuning d-orbitals to control spin-orbit coupling in terminated MXenes

Theory and experiment have revealed that spin-orbit coupling (SOC) strongly depends on the relativistic effect in topological insulators (TIs), while the influence of orbitals is always ignored. Herein, we provide a direct way of controlling effective SOC with the help of orbital effects, reducing the dependence on elements. Taking 5d W2CO2 and 4d Mo2CO2 MXenes as a specific example, we predict that by decreasing the hybridization strength of W atoms with C or O atoms in 2D W2CO2, the nontrivial bandgaps at the Γ-point are directly enhanced. The weak hybridization of W atoms with ligand elements enhances the electron localization of degenerate d-orbitals of three groups under the triangular prism crystal field, inducing stronger on-site Coulomb repulsion that enhances orbital polarization as well as boosts the SOC effect. Meanwhile, similar results have also been observed in 4d Mo2CO2. This implies that the orbital effects are an efficient and straightforward way to control the nontrivial bandgap in 2D MXene TIs. Our work not only provides an alternative perspective on designing large nontrivial bandgaps but also brings a possibility to control the SOC effect for TI devices.

Achieving environmental stability in an atomically thin quantum spin Hall insulator via graphene intercalation

Atomic monolayers on semiconductor surfaces represent an emerging class of functional quantum materials in the two-dimensional limit - ranging from superconductors and Mott insulators to ferroelectrics and quantum spin Hall insulators. Indenene, a triangular monolayer of indium with a gap of ~ 120 meV is a quantum spin Hall insulator whose micron-scale epitaxial growth on SiC(0001) makes it technologically relevant. However, its suitability for room-temperature spintronics is challenged by the instability of its topological character in air. It is imperative to develop a strategy to protect the topological nature of indenene during ex situ processing and device fabrication. Here we show that intercalation of indenene into epitaxial graphene provides effective protection from the oxidising environment, while preserving an intact topological character. Our approach opens a rich realm of ex situ experimental opportunities, priming monolayer quantum spin Hall insulators for realistic device fabrication and access to topologically protected edge channels.

Observation of Emergent Superconductivity in the Topological Insulator Ta2Pd3Te5 via Pressure Manipulation

Topological insulators offer significant potential to revolutionize diverse fields driven by nontrivial manifestations of their topological electronic band structures. However, the realization of superior integration between exotic topological states and superconductivity for practical applications remains a challenge, necessitating a profound understanding of intricate mechanisms. Here, we report experimental observations for a novel superconducting phase in the pressurized second-order topological insulator candidate Ta2Pd3Te5, and the high-pressure phase maintains its original ambient pressure lattice symmetry up to 45 GPa. Our in situ high-pressure synchrotron X-ray diffraction, electrical transport, infrared reflectance, and Raman spectroscopy measurements, in combination with rigorous theoretical calculations, provide compelling evidence for the association between the superconducting behavior and the densified phase. The electronic state change around 20 GPa was found to modify the topology of the Fermi surface directly, which synergistically fosters the emergence of robust superconductivity. In-depth comprehension of the fascinating properties exhibited by the compressed Ta2Pd3Te5 phase is achieved, highlighting the extraordinary potential of topological insulators for exploring and investigating high-performance electronic advanced devices under extreme conditions.

Observation of Anomalous Planar Hall Effect Induced by One-Dimensional Weak Antilocalization

The confinement of electrons in one-dimensional (1D) space highlights the prominence of the role of electron interactions or correlations, leading to a variety of fascinating physical phenomena. The quasi-1D electron states can exhibit a unique spin texture under spin-orbit interaction (SOI) and thus could generate a robust spin current by forbidden electron backscattering. Direct detection of such 1D spin or SOI information, however, is challenging due to complicated techniques. Here, we identify an anomalous planar Hall effect (APHE) in the magnetotransport of quasi-1D van der Waals (vdW) topological materials as exemplified by Bi4Br4, which arises from the quantum interference correction of 1D weak antilocalization (WAL) to the ordinary planar Hall effect and demonstrates a deviation from the usual sine and cosine curves. The occurrence of 1D WAL is correlated to the line-shape Fermi surface and persistent spin texture of (100) topological surface states of Bi4Br4, as revealed by both our angle-resolved photoemission spectroscopy and first-principles calculations. By generalizing the observation of APHE to other non-vdW bulk materials, this work provides a possible characteristic of magnetotransport for identifying the spin/SOI information and quantum interference behavior of 1D states in 3D topological material.

In-Plane Anisotropy in the Layered Topological Insulator Ta2Ni3Te5 Investigated via TEM and Polarized Raman Spectroscopy

Layered Ta2M3Te5 (M = Pd, Ni) has emerged as a platform to study 2D topological insulators, which have exotic properties such as spin-momentum locking and the presence of Dirac fermions for use in conventional and quantum-based electronics. In particular, Ta2Ni3Te5 has been shown to have superconductivity under pressure and is predicted to have second-order topology. Despite being an interesting material with fascinating physics, the detailed crystalline and phononic properties of this material are still unknown. In this study, we use transmission electron microscopy (TEM) and polarized Raman spectroscopy (PRS) to reveal the anisotropic properties of exfoliated few-layer Ta2Ni3Te5. An electron diffraction and TEM study reveals structural anisotropy in the material, with a preferential crystal orientation along the [010] direction. Through Raman spectroscopy, we discovered 15 vibrational modes, 3 of which are ultralow-frequency modes, which show anisotropic response with sample orientation varying with the polarization of the incident beam. Using angle-resolved PRS, we assigned the vibrational symmetries of 11 modes to Ag and two modes to B3g. We also found that linear dichroism plays a role in understanding the Raman signature of this material, which requires the use of complex elements in the Raman tensors. The anisotropy of the Raman scattering also depends on the excitation energies. Our observations reveal the anisotropic nature of Ta2Ni3Te5, establish a quick and nondestructive Raman fingerprint for determining sample orientation, and represent a significant advance in the fundamental understanding of the two-dimensional topological insulator (2DTI) Ta2Ni3Te5 material.

Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators

The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.

Progress on the antiferromagnetic topological insulator MnBi2Te4

Topological materials, which feature robust surface and/or edge states, have now been a research focus in condensed matter physics. They represent a new class of materials exhibiting nontrivial topological phases, and provide a platform for exploring exotic transport phenomena, such as the quantum anomalous Hall effect and the quantum spin Hall effect. Recently, magnetic topological materials have attracted considerable interests due to the possibility to study the interplay between topological and magnetic orders. In particular, the quantum anomalous Hall and axion insulator phases can be realized in topological insulators with magnetic order. MnBi2Te4, as the first intrinsic antiferromagnetic topological insulator discovered, allows the examination of existing theoretical predictions; it has been extensively studied, and many new discoveries have been made. Here we review the progress made on MnBi2Te4 from both experimental and theoretical aspects. The bulk crystal and magnetic structures are surveyed first, followed by a review of theoretical calculations and experimental probes on the band structure and surface states, and a discussion of various exotic phases that can be realized in MnBi2Te4. The properties of MnBi2Te4 thin films and the corresponding transport studies are then reviewed, with an emphasis on the edge state transport. Possible future research directions in this field are also discussed.

On the topological surface states of the intrinsic magnetic topological insulator Mn-Bi-Te family

We review recent progress in the electronic structure study of intrinsic magnetic topological insulators (MnBi2Te4) · (Bi2Te3)n ([Formula: see text]) family. Specifically, we focus on the ubiquitously (nearly) gapless behavior of the topological Dirac surface state observed by photoemission spectroscopy, even though a large Dirac gap is expected because of surface ferromagnetic order. The dichotomy between experiment and theory concerning this gap behavior is perhaps the most critical and puzzling question in this frontier. We discuss various proposals accounting for the lack of magnetic effect on the topological Dirac surface state, which are mainly categorized into two pictures, magnetic reconfiguration and topological surface state redistribution. Band engineering towards opening a magnetic gap of topological surface states provides great opportunities to realize quantized topological transport and axion electrodynamics at higher temperatures.

ARPES investigation of the electronic structure and its evolution in magnetic topological insulator MnBi2+2nTe4+3n family

In the past 5 years, there has been significant research interest in the intrinsic magnetic topological insulator family compounds MnBi2+2nTe4+3n (where n = 0, 1, 2 …). In particular, exfoliated thin films of MnBi2Te4 have led to numerous experimental breakthroughs, such as the quantum anomalous Hall effect, axion insulator phase and high-Chern number quantum Hall effect without Landau levels. However, despite extensive efforts, the energy gap of the topological surface states due to exchange magnetic coupling, which is a key feature of the characteristic band structure of the system, remains experimentally elusive. The electronic structure measured by using angle-resolved photoemission (ARPES) shows significant deviation from ab initio prediction and scanning tunneling spectroscopy measurements, making it challenging to understand the transport results based on the electronic structure. This paper reviews the measurements of the band structure of MnBi2+2nTe4+3n magnetic topological insulators using ARPES, focusing on the evolution of their electronic structures with temperature, surface and bulk doping and film thickness. The aim of the review is to construct a unified picture of the electronic structure of MnBi2+2nTe4+3n compounds and explore possible control of their topological properties.

Ideal two-dimensional quantum spin Hall insulators MgA2Te4 (A = Ga, In) with Rashba spin splitting and tunable properties

For decades, topological insulators have played a pivotal role in fundamental condensed-matter physics owing to their distinctive edge states and electronic properties. Here, based on in-depth first-principles calculations, we investigate the MgA2Te4 (A = Ga, In) structures belonging to the MA2Z4 2D material family. Among them, the topological insulator MgGaInTe4 exhibits band inversion and a sizeable bandgap of up to 60.8 meV which satisfies the requirement for room-temperature realization. Under the spin-orbit coupling effect, MgGaInTe4 with inversion asymmetry undergoes Rashba spin splitting. The Rashba-like and Dirac-type edge states emerge from different terminals along (010) for MgGaInTe4. The external vertical electric field is verified to modulate the inverted bandgap and topological state of MgGaInTe4 by converting a nontrivial state to a trivial state and MgIn2Te4 with the original trivial state to a nontrivial one. Accordingly, MgGaInTe4 and MgIn2Te4 have significant potential for application in topological quantum field-effect transistors. Our research identifies that the MgA2Te4 (A = Ga, In) structures have huge potential to be candidate 2D materials for spintronics and topological quantum devices.

Phase transitions, conductance fluctuations and distributions in disordered topological insulator stanene

It is essential to understand to what extent the protected edge states of topological insulators (TIs) can survive against the degradation of the ubiquitous disorders in realistic devices. From a different perspective, disorders can also help to enrich the applications by modulation of the phases in TIs. In this work, the phases and phase transitions in stanene, a two-dimensional TI, have been investigated via the statistical approach based on the random matrix theory. Using a tight binding model with Aderson disorder term and the Landauer-Büttiker formalism, we calculated the conductance of realistic stanene ribbons of tens of nanometers long with random disorders. The calculated phase diagram presents TI in the gap, metal in high energy and ordinary insulator in large disorder region. Increasing the width of the ribbon can significantly enhance the robustness of TI phase against disorders. Due to different underlying symmetries, the metallic phase can be further categorized into unitary and orthogonal classes according to the calculated universal conductance fluctuations. The local density of states is calculated, showing characteristic patterns, which can facilitate the experimental identification of the phases. It is found that different phases have distinguishing statistical distribution of conductance. Whereas at the phase boundary the distribution exhibits intermediate features to show where the phase transition occurs. To reveal the phase evolution process, we further studied the effects of the disorders on respective transmission channels. It is found that when phase transition takes place, the major transmission channels of the old phase are fading and the new channels of the new phase are emerging.

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.

Controllable strain-driven topological phase transition and dominant surface-state transport in HfTe5

The fine-tuning of topologically protected states in quantum materials holds great promise for novel electronic devices. However, there are limited methods that allow for the controlled and efficient modulation of the crystal lattice while simultaneously monitoring the changes in the electronic structure within a single sample. Here, we apply significant and controllable strain to high-quality HfTe5 samples and perform electrical transport measurements to reveal the topological phase transition from a weak topological insulator phase to a strong topological insulator phase. After applying high strain to HfTe5 and converting it into a strong topological insulator, we found that the resistivity of the sample increased by 190,500% and that the electronic transport was dominated by the topological surface states at cryogenic temperatures. Our results demonstrate the suitability of HfTe5 as a material for engineering topological properties, with the potential to generalize this approach to study topological phase transitions in van der Waals materials and heterostructures.

Light-Induced Ideal Weyl Semimetal in HgTe via Nonlinear Phononics

Interactions between light and matter allow the realization of out-of-equilibrium states in quantum solids. In particular, nonlinear phononics is one of the most efficient approaches to realizing the stationary electronic state in nonequilibrium. Herein, by an extended ab initio molecular dynamics method, we identify that long-lived light-driven quasistationary geometry could stabilize the topological nature in the material family of HgTe compounds. We show that coherent excitation of the infrared-active phonon mode results in a distortion of the atomic geometry with a lifetime of several picoseconds. We show that four Weyl points are located exactly at the Fermi level in this nonequilibrium geometry, making it an ideal long-lived metastable Weyl semimetal. We propose that such a metastable topological phase can be identified by photoelectron spectroscopy of the Fermi arc surface states or ultrafast pump-probe transport measurements of the nonlinear Hall effect.

Spin-orbit-coupled fractional oscillators and trapped Bose-Einstein condensates

We study the ensemble of pseudo-spin 1/2 ultracold bosons, performing Lévy flights, confined in a parabolic potential. The (pseudo-) spin-orbit coupling (SOC) is additionally imposed on these particles. We consider the structure and dynamics of macroscopic pseudospin qubits based on Bose-Einstein condensates, obtained from the above "fractional" bosons. Under "fractional" we understand the substitution of the ordinary second derivative (kinetic energy term) in the Gross-Pitaevskii equation by a so-called fractional Laplacian, characterized by the Lévy index μ. We show that the joint action of interparticle interaction, SOC, and Zeeman splitting in a synthetic magnetic field makes the dynamics of corresponding qubit highly nontrivial with evident chaotic features at both strong interactions and Lévy indices μ→1 when the Lévy trajectories of bosons with long jumps dominated over those derived from ordinary Gaussian distribution, corresponding to μ=2. Using analytical and numerical arguments, we discuss the possibilities to control the above qubit using the synergy of SOC, interaction strength, and "fractionality," characterized by the Lévy index μ.

Synthesis and Future Electronic Applications of Topological Nanomaterials

Over the last ten years, the discovery of topological materials has opened up new areas in condensed matter physics. These materials are noted for their distinctive electronic properties, unlike conventional insulators and metals. This discovery has not only spurred new research areas but also offered innovative approaches to electronic device design. A key aspect of these materials is now that transforming them into nanostructures enhances the presence of surface or edge states, which are the key components for their unique electronic properties. In this review, we focus on recent synthesis methods, including vapor-liquid-solid (VLS) growth, chemical vapor deposition (CVD), and chemical conversion techniques. Moreover, the scaling down of topological nanomaterials has revealed new electronic and magnetic properties due to quantum confinement. This review covers their synthesis methods and the outcomes of topological nanomaterials and applications, including quantum computing, spintronics, and interconnects. Finally, we address the materials and synthesis challenges that need to be resolved prior to the practical application of topological nanomaterials in advanced electronic devices.