Conflux of spin Nernst and spin Hall effect in ZnCu2SnSe4Topological Insulator.

A comprehensive exploration of the intriguing phenomena known as the spin Nernst effect (SNE) and the spin Hall effect (SHE) within the context of nonmagnetic strong topological insulatorZnCu2SnSe4, has been carried out employing first-principles calculations. Our theoretical calculations unveil significantly large intrinsic spin Nernst conductivity (SNC) and spin Hall conductivity (SHC) in the bulk topological insulatorZnCu2SnSe4. Delving deeper into the intricacies of our findings, we elucidate how the inverted band order in the topological materials drastically influences the spin Berry curvature, consequently exerting a profound impact on SHC and SNC. Detailed analyses reveal that the contribution from the bulk to the generation of pure spin current in a topological insulator is comparable to that of a surface. This underscores the potential role of topological insulators in the development of spin-switching devices. We present compelling evidence thatZnCu2SnSe4holds immense promise as an optimal candidate for the generation of pure spin currents, achieved through the application of both thermal gradients and electric fields. This, in turn, opens up exciting avenues for its utilization in the realms of spin-caloritronics, spin-orbitronics, and spintronics.

Design of Antiferromagnetic Second-Order Band Topology with Rotation Topological Invariants in Two Dimensions.

The existence of fractionally quantized topological corner charge serves as a key indicator for two-dimensional (2D) second-order topological insulators (SOTIs), yet it has not been experimentally observed in realistic materials. Here, based on effective model analysis and symmetry arguments, we propose a strategy for achieving SOTI phases with in-gap corner states in 2D systems with antiferromagnetic (AFM) order. We discover that the band topology originates from the interplay between intrinsic spin-orbital coupling and interlayer AFM exchange interactions. Using first-principles calculations, we show that the 2D AFM SOTI phase can be realized in (MnBi2Te4)(Bi2Te3)m films. Moreover, we demonstrate that the SOTI states are linked to rotation topological invariants under 3-fold rotation symmetry C3, resulting in fractionally quantized corner charge, i.e., n3|e| (mod e). Due to the great achievements in (MnBi2Te4)(Bi2Te3)m systems, our results providing reliable material candidates for experimentally accessible AFM SOTIs should draw intense attention.

Tailored Triggering of High-Quality Multi-Dimensional Coupled Topological States in Valley Photonic Crystals.

The combination of higher-order topological insulators and valley photonic crystals has recently aroused extensive attentions due to the great potential in flexible and efficient optical field manipulations. Here, we computationally propose a photonic device for the 1550 nm communication band, in which the topologically protected electromagnetic modes with high quality can be selectively triggered and modulated on demand. Through introducing two valley photonic crystal units without any structural alteration, we successfully achieve multi-dimensional coupled topological states thanks to the diverse electromagnetic characteristics of two valley edge states. According to the simulations, the constructed topological photonic devices can realize Fano lines on the spectrum and show high-quality localized modes by tuning the coupling strength between the zero-dimensional valley corner states and the one-dimensional valley edge states. Furthermore, we extend the valley-locked properties of edge states to higher-order valley topological insulators, where the selected corner states can be directionally excited by chiral source. More interestingly, we find that the modulation of multi-dimensional coupled photonic topological states with pseudospin dependence become more efficient compared with those uncoupled modes. This work presents a valuable approach for multi-dimensional optical field manipulation, which may support potential applications in on-chip integrated nanophotonic devices.

Metal-Semiconductor Behavior along the Line of Stacking Order Change in Gated Multilayer Graphene.

We investigated gated multilayer graphene with stacking order changes along the armchair direction. We consider that some layers cracked to release shear strain at the stacking domain wall. The energy cones of graphene overlap along the corresponding direction in the k-space, so the topological gapless states from different valleys also overlap. However, these states strongly interact and split due to atomic-scale defects caused by the broken layers, yielding an effective energy gap. We find that for some gate voltages, the gap states cross and the metallic behavior along the stacking domain wall can be restored. In particular cases, a flat band appears at the Fermi energy. We show that for small variations in the gate voltage, the charge occupying this band oscillates between the outer layers.

Engineering Small HOMO-LUMO Gaps in Polycyclic Aromatic Hydrocarbons with Topologically Protected States.

Topological phases in laterally confined low-dimensional nanographenes have emerged as versatile design tools that can imbue otherwise unremarkable materials with exotic band structures ranging from topological semiconductors and quantum dots to intrinsically metallic bands. The periodic boundary conditions that define the topology of a given lattice have thus far prevented the translation of this technology to the quasi-zero-dimensional (0D) domain of small molecular structures. Here, we describe the synthesis of a polycyclic aromatic hydrocarbon (PAH) featuring two localized zero modes (ZMs) formed by the topological junction interface between a trivial and nontrivial phase within a single molecule. First-principles density functional theory calculations predict a strong hybridization between adjacent ZMs that gives rise to an exceptionally small HOMO-LUMO gap. Scanning tunneling microscopy and spectroscopy corroborate the molecular structure of 9/7/9-double quantum dots and reveal an experimental quasiparticle gap of 0.16 eV, corresponding to a carbon-based small molecule long-wavelength infrared (LWIR) absorber.

Signatures of Topological States in Conjugated Macrocycles.

Single-molecule electrical junctions possess a molecular core connected to source and drain electrodes via anchor groups, which feed and extract electricity from specific atoms within the core. As the distance between electrodes increases, the electrical conductance typically decreases, which is a feature shared by classical Ohmic conductors. Here we analyze the electrical conductance of cycloparaphenylene (CPP) macrocycles and demonstrate that they can exhibit a highly nonclassical increase in their electrical conductance as the distance between electrodes increases. We demonstrate that this is due to the topological nature of the de Broglie wave created by electrons injected into the macrocycle from the source. Although such topological states do not exist in isolated macrocycles, they are created when the molecule is in contact with the source. They are predicted to be a generic feature of conjugated macrocycles and open a new avenue to implementing highly nonclassical transport behavior in molecular junctions.

Transfer learning from Hermitian to non-Hermitian quantum many-body physics.

Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.

Observation of the geometry-dependent skin effect and dynamical degeneracy splitting.

The non-Hermitian skin effect is a distinctive phenomenon in non-Hermitian systems, which manifests as the anomalous localization of bulk states at the boundary. To understand the physical origin of the non-Hermitian skin effect, a bulk band characterization based on the dynamical degeneracy on an equal frequency contour is proposed, which reflects the strong anisotropy of the spectral function. In this paper, we report the experimental observation of a newly-discovered geometry-dependent non-Hermitian skin effect and dynamical degeneracy splitting in a two-dimensional acoustic crystal and reveal their remarkable correspondence by performing single-frequency excitation measurements. Our work not only provides a controllable experimental platform for studying the non-Hermitian physics, but also confirms the unique correspondence between the non-Hermitian skin effect and the dynamical degeneracy splitting, paving a new way to characterize the non-Hermitian skin effect.

Effects of Coulomb Blockade on the Charge Transport through the Topological States of Finite Armchair Graphene Nanoribbons and Heterostructures.

In this study, we investigate the charge transport properties of semiconducting armchair graphene nanoribbons (AGNRs) and heterostructures through their topological states (TSs), with a specific focus on the Coulomb blockade region. Our approach employs a two-site Hubbard model that takes into account both intra- and inter-site Coulomb interactions. Using this model, we calculate the electron thermoelectric coefficients and tunneling currents of serially coupled TSs (SCTSs). In the linear response regime, we analyze the electrical conductance (Ge), Seebeck coefficient (S), and electron thermal conductance (κe) of finite AGNRs. Our results reveal that at low temperatures, the Seebeck coefficient is more sensitive to many-body spectra than electrical conductance. Furthermore, we observe that the optimized S at high temperatures is less sensitive to electron Coulomb interactions than Ge and κe. In the nonlinear response regime, we observe a tunneling current with negative differential conductance through the SCTSs of finite AGNRs. This current is generated by electron inter-site Coulomb interactions rather than intra-site Coulomb interactions. Additionally, we observe current rectification behavior in asymmetrical junction systems of SCTSs of AGNRs. Notably, we also uncover the remarkable current rectification behavior of SCTSs of 9-7-9 AGNR heterostructure in the Pauli spin blockade configuration. Overall, our study provides valuable insights into the charge transport properties of TSs in finite AGNRs and heterostructures. We emphasize the importance of considering electron-electron interactions in understanding the behavior of these materials.

Tunable Topological States in Stacked Chern Insulator Bilayers.

The emergence of intrinsic quantum anomalous Hall (QAH) insulators with a long-range ferromagnetic (FM) order triggers unprecedented prosperity for combining topology and magnetism in low dimensions. Built upon atom-thin Chern insulator monolayer MnBr3, we propose that the topologically nontrivial electronic states can be systematically tuned by inherent magnetic orders and external electric/optical fields in stacked Chern insulator bilayers. The FM bilayer illustrates a high-Chern-number QAH state characterized by both quantized Hall plateaus and specific magneto-optical Kerr angles. In antiferromagnetic bilayers, Berry curvature singularity induced by electrostatic fields or lasers emerges, which further leads to a novel implementation of the layer Hall effect depending on the chirality of irradiated circularly polarized light. These results demonstrate that abundant tunable topological properties can be achieved in stacked Chern insulator bilayers, thereby suggesting a universal routine to modulate d-orbital-dominated topological Dirac fermions.

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.

Observation of fractal higher-order topological states in acoustic metamaterials.

Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpinski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly, the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpinski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.

Phase driven topological states in correlated Haldane model on a honeycomb lattice.

Using mean field method and random phase approximation, we studied the phase driven topological exotic states in correlated Haldane model on a honeycomb lattice. It is found that topological spin density waves emerge with the phase change of next-nearest-neighbor hopping. We also investigated the topological properties of these spin density waves, including Chern number, edge state and Hall conductivity. Our work provides a new insight for topological phase transitions in correlated quantum anomalous Hall insulators.

The p-orbital magnetic topological states on a square lattice.

Honeycomb or triangular lattices were extensively studied and thought to be proper platforms for realizing the quantum anomalous Hall effect (QAHE), where magnetism is usually caused by d orbitals of transition metals. Here we propose that a square lattice can host three magnetic topological states, including the fully spin-polarized nodal loop semimetal, QAHE and the topologically trivial ferromagnetic semiconductor, in terms of the symmetry and k · p model analyses that are material independent. A phase diagram is presented. We further show that the above three magnetic topological states can indeed be implemented in the two-dimensional (2D) materials ScLiCl5, LiScZ5 (Z=Cl, Br) and ScLiBr5, respectively. The ferromagnetism in these 2D materials is microscopically revealed from p electrons of halogen atoms. This present study opens a door to explore the exotic topological states as well as quantum magnetism from p-orbital electrons by means of the material-independent approach.

Quantum transport and potential of topological states for thermoelectricity in Bi2Te3thin films.

This paper reviews recent developments in quantum transport and it presents current efforts to explore the contribution of topological insulator boundary states to thermoelectricity in Bi2Te3thin films. Although Bi2Te3has been used as a thermoelectric material for many years, it is only recently that thin films of this material have been synthesized as 3D topological insulators with interesting physics and potential applications related to topologically protected surface states. A major bottleneck in Bi2Te3thin films has been eliminating its bulk conductivity while increasing its crystal quality. The ability to grow epitaxial films with high crystal quality and to fabricate sophisticated Bi2Te3-based devices is attractive for implementing a variety of topological quantum devices and exploring the potential of topological states to improve thermoelectric properties. Special emphasis is laid on preparing low-defect-density Bi2Te3epitaxial films, gate-tuning of normal-state transport and Josephson supercurrent in topological insulator/superconductor hybrid devices. Prospective quantum transport experiments on Bi2Te3thin-film devices are discussed as well. Finally, an overview of current progress on the contribution of topological insulator boundary states to thermoelectricity is presented. Future explorations to reveal the potential of topological states for improving thermoelectric properties of Bi2Te3films and realizing high-performance thermoelectric devices are discussed.

Tuning interactions between spins in a superconductor.

Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.

Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity.

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.

Multi-dimensional wave steering with higher-order topological phononic crystal.

The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topology originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide symmetry of the lattice. The multitude of topological states brings diverse possibilities of wave manipulations. Through judicious engineering of the boundary modes, we experimentally demonstrate two functionalities at different dimensions: 2D negative refraction of sound wave enabled by a first-order topological surface state with negative dispersion, and a 3D acoustic interferometer leveraging on second-order topological hinge states. Our work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions.

Topological electronic states and thermoelectric transport at phase boundaries in single-layer WSe2: an effective Hamiltonian theory.

Monolayer transition metal dichalcogenides in the distorted octahedral 1T' phase exhibit a large bulk bandgap and gapless boundary states, which is an asset in the ongoing quest for topological electronics. In single-layer tungsten diselenide (WSe2), the boundary states have been observed at well ordered interfaces between 1T' and semiconducting (1H) phases. This paper proposes an effective 4-band theory for the boundary states in single-layer WSe2, describing a Kramers pair of in-gap states as well as the behaviour at the spectrum termination points on the conduction and valence bands of the 1T' phase. The spectrum termination points determine the temperature and chemical potential dependences of the ballistic conductance and thermopower at the phase boundary. Notably, the thermopower shows an ambipolar behaviour, changing the sign in the bandgap of the 1T'-WSe2and reflecting its particle-hole asymmetry. The theory establishes a link between the bulk band structure and ballistic boundary transport in single-layer WSe2and is applicable to a range of related topological materials.

Contribution of 1D topological states to the extraordinary thermoelectric properties of Bi2Te3.

Topological insulators are frequently also one of the best-known thermoelectric materials. It has been recently discovered that in three-dimensional (3D) topological insulators each skew dislocation can host a pair of one-dimensional (1D) topological states-a helical Tomonaga-Luttinger liquid (TLL). We derive exact analytical formulae for thermoelectric Seebeck coefficient in TLL and investigate up to what extent one can ascribe the outstanding thermoelectric properties of Bi2Te3 to these 1D topological states. To this end we take a model of a dense dislocation network and find an analytic formula for an overlap between 1D (the TLL) and 3D electronic states. Our study is applicable to a weakly n-doped Bi2Te3 but also to a broader class of nano-structured materials with artificially created 1D systems. Furthermore, our results can be used at finite frequency settings, e.g. to capture transport activated by photo-excitations.