Nontrivial Topological States Research Articles

Time-Reversal Symmetry Breaking Driven Topological Phase Transition in EuB6

The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads to nontrivial topological states, such as topological insulators and Dirac semimetals. When the TRS is broken, the exchange field induces spin splitting of the bands. The inversion of a pair of spin-splitting subbands can generate more exotic topological states, such as quantum anomalous Hall insulators and magnetic Weyl semimetals. So far, such topological phase transitions driven by the TRS breaking have not been visualized. In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spin-splitting subbands at the TRI points of Brillouin zone in EuB$_6$, when a long-range ferromagnetic order is developed. The dramatic changes in the electronic structure result in a topological phase transition from a TRI ordinary insulator state to a TRS-broken topological semimetal (TSM) state. Remarkably, the magnetic TSM state has an ideal electronic structure, in which the band crossings are located at the Fermi level without any interference from other bands. Our findings not only reveal the topological phase transition driven by the TRS breaking, but also provide an excellent platform to explore novel physical behavior in the magnetic topological states of quantum matter.

Strain driven emergence of topological non-triviality in YPdBi thin films

Half-Heusler compounds exhibit a remarkable variety of emergent properties such as heavy-fermion behaviour, unconventional superconductivity and magnetism. Several of these compounds have been predicted to host topologically non-trivial electronic structures. Remarkably, recent theoretical studies have indicated the possibility to induce non-trivial topological surface states in an otherwise trivial half-Heusler system by strain engineering. Here, using magneto-transport measurements and first principles DFT-based simulations, we demonstrate topological surface states on strained [110] oriented thin films of YPdBi grown on (100) MgO. These topological surface states arise in an otherwise trivial semi-metal purely driven by strain. Furthermore, we observe the onset of superconductivity in these strained films highlighting the possibility of engineering a topological superconducting state. Our results demonstrate the critical role played by strain in engineering novel topological states in thin film systems for developing next-generation spintronic devices.

Observation of Dirac-like surface state bands on the top surface of BiSe

Weak topological insulators (TIs) host non-trivial topological surface state bands (SSBs) at the side surface of the crystal while the top (001) surface can be topologically either dark or light. In our detailed angle-resolved photoelectron spectroscopy (ARPES) study we found Dirac-like linearly dispersive SSBs on the (001) surface of BiSe and Sb-doped (8%) BiSe. The lower part of the SSBs buries deep in the bulk valence band (BVB) and the overlap region between the SSBs and BVB increases significantly with Sb doping. These results highlight the role of the interlayer coupling between the Bi bilayer and the Bi2Se3 quintuple layer (QL). Furthermore, in the overlap region the SSBs deviate from the Dirac-like linear dispersion. Interestingly, we observed a large intensity imbalance ) in the SSBs located at the positive and negative directions. This asymmetry pattern ) gradually reverses to ) as the excitation energy scans from low (14 eV) to high (34 eV) values. The observed photon energy-dependent intensity variation could be a signature of the mixing between the spin and the orbit texture of the SSBs.

Anomalous Hall effect in graphene coupled to a layered magnetic semiconductor

Graphene is favorable to realize topological nontrivial state by introducing spin-orbit coupling and exchange field through the proximity effect. The recent discovery of van der Waals magnets allows great proximitized modulation on graphene by building atomically clean heterostructures. Here, we realize anomalous Hall effect in graphene coupling with a layered magnetic material, ${\mathrm{Fe}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{S}}_{2}$. The anomalous Hall resistance and the carrier density show a nonmonotonous dependence on the back-gate voltage, indicating emergence of band-structure transformation. Furthermore, low-field quantum interference measurement shows the enhancement of spin-orbit coupling (SOC) in the heterostructure. Our findings confirm that graphene coupling to ${\mathrm{Fe}}_{x}{\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{S}}_{2}$ is an ideal platform that is likely to introduce a strong exchange field and SOC simultaneously, which has outstanding potential in realizing topological nontrivial states and spintronics.

Topological effects of phonons in GaN and AlGaN: A potential perspective for tuning phonon transport

Tuning thermal transport in semiconductor nanostructures is of great significance for thermal management in information and power electronics. With excellent transport properties, such as ballistic transport, immunity to point defects and disorders, and forbidden backscattering, topological phonon surface states show remarkable potential in addressing this issue. Herein, topological phonon analyses are performed on hexagonal wurtzite gallium nitride (GaN) to check the topological characteristics of phonons. And other nitrides of the same family, i.e., AlN and AlGaN crystals, are also calculated from a topological phonon phase transition perspective. With the aid of first-principle calculations and topological phonon theory, Weyl phonon states, which host surfaces states without backscattering, are investigated for all these materials. The results show that there is no nontrivial topological phonon state in GaN. However, by introducing Al atoms, i.e., in wurtzite type AlN and AlGaN, more than one Weyl phonon point is found, confirmed by obvious topological characteristics, including non-zero integer topological charges, source/sink in Berry curvature distributions, surface local density of states, and surface arcs. As AlN and AlGaN are typical materials in AlGaN/GaN heterostructure based electronics, the existence of topological phonon states in them will benefit thermal management by facilitating the design of one-way interfacial phonon transport without backscattering.

Emergence of −s, −p–d band inversion in zincblende gold iodide topological insulator and its thermoelectric properties

We employ first-principles calculations to investigate the topological states (TS) and thermoelectric (TE) transport properties of three dimensional (3D) gold iodide (AuI) which belongs to the zincblende family. We explore, semi-metal (SM) to topological conductor (TC) and topological insulator (TI) phase transitions. Under pristine conditions, AuI exhibits Dirac SM nature but, under the influence of mild isotropic compressive pressure the system undergoes electronic quantum phase transition driving it into non-trivial topological state. This state exhibits Dresselhaus like band spin splitting leading to a TC state. In order to realize TI state from the SM state, we break the cubic symmetry of the system by introducing a compressive pressure along (001) crystal direction. The non-trivial TI nature of the system is characterized by the emergence of robust surface states and the invariant ν 0 = 1 which indicates a strong TI nature. A novel facet of the phase transition discussed here is, the −s and −p, −d orbital band inversion mechanism which is unconventional as compared to previously explored TI families. This mechanism unravels new path by which TI materials can be predicted. Also, we investigated the lattice and electronic contributions to the TE transport properties. We characterize the TE performance by calculating the figure of merit (zT) and find that, at room temperature (300 K) and for a fixed doping concentration (i.e., n = 1 × 1019 cm−3) the zT is 0.55 and 0.53 for electrons and holes respectively. This is quite remarkable since, higher values of zT are generally predicted at higher temperature scales whereas, zT values as in the present case are desired at room temperatures for various energy applications. The manifestation of non-trivial TS governed by the unconventional band inversion mechanism and the TE properties of AuI make it a unique multi-functional candidate with probable thermoelectric and spintronic applications.

Topological quantum optical states in quasiperiodic cold atomic chains

Topological quantum optical states in one-dimensional (1D) quasiperiodic cold atomic chains are studied in this work. We propose that by introducing incommensurate modulations on the interatomic distances of 1D periodic atomic chains, the off-diagonal Aubry-Andr\'e-Harper (AAH) model can be mimicked, although the crucial difference is the existence of long-range dipole-dipole interactions. The discrete band structures with respect to the modulation phase, which plays the role of a dimension extension parameter, are calculated for finite chains beyond the nearest-neighbor approximation. It is found that the present system indeed supports nontrivial topological states localized over the boundaries. Despite the presence of long-range dipole-dipole interactions that leads to an asymmetric band structure, it is demonstrated that this system inherits the topological properties of two-dimensional integer quantum Hall systems. The spectral position, for both real and imaginary frequencies, and number of these topologically protected edge states are still governed by the gap-labeling theorem and characterized by the topological invariant, namely, the (first) Chern number, indicating the validity of bulk-boundary correspondence. Due to the fractal spectrum arising from the quasiperiodicity in a substantially wide range of system parameters, our system provides a large number of topological gaps and optical states readily for practical use. It is also revealed that a substantial proportion of the topological edge states are highly subradiant with extremely low decay rates, which therefore offer an appealing route for controlling the emission of external quantum emitters and achieving high-fidelity quantum state storage.

Enhancement of basal plane electrocatalytic hydrogen evolution activity via joint utilization of trivial and non-trivial surface states

Transition metal dichalcogenide semiconductors, particularly MoS2, are known as promising alternative non-precious hydrogen evolution reaction (HER) electrocatalysts to high-cost Pt. However, their performance is strongly limited by the poor conductivity and lack of active sites in the basal plane. Therefore, it is desirable to find alternatives with active basal plane sites or develop facile strategies to optimize the inert basal plane. In this work, we study the HER over topological semimetal Nb2S2C based on its basal plane. We report the first successful activation and optimization of the basal plane of Nb2S2C by synergistic using trivial surface states (SSs) and nontrivial topological surface states (TSSs). We find that the binding strength towards hydrogen adsorption of the easily cleaved sulfur(S)-terminated Nb2S2C surface can be stronger than that of 2H-MoS2, attributing to the presence of trivial SSs and nontrivial TSSs in Nb2S2C. By creating S vacancy on the basal plane, the binding strength towards hydrogen adsorption can be greatly optimized. The TSSs together with dangling-bonds reduce the Gibbs free energy to 0.31 eV, close to the peak of the volcano plot. This study provides a promising strategy for the joint utilization of the basal plane trivial SSs and TSSs for the HER.

Properties of axion insulator candidate layered Eu<sub>1–<i>x</i></sub>Ca<i><sub>x</sub></i>In<sub>2</sub>As<sub>2</sub>

The study of two-dimensional (2D) magnetic materials has driven the development of modern nano-electronic devices. Exploration of novel intrinsic layered materials with 2D magnetic order will provide a material candidate pool for fabricating 2D devices and searching for new quantum phases. Recently the layered antiferromagnetic (AF) topological insulators have aroused the great interest of researchers. As one of the proposed axion insulators, EuIn<sub>2</sub>As<sub>2</sub> exhibits a layered structure and 2D AF order. It is found that the parent compound EuIn<sub>2</sub>As<sub>2</sub> exhibits metallic behavior instead of the predicted insulating feature. To pursuit the predicted non-trivial topological state and novel feature, in this paper, we use various elements to dope the system to adjust the Fermi level. It is found that only Ca is successfully doped into the EuIn<sub>2</sub>As<sub>2</sub> system. The systematic transport and magnetization studies are performed on the single crystal of Eu<sub>1–<i>x</i></sub>Ca<i><sub>x</sub></i>In<sub>2</sub>As<sub>2</sub>. The long-range AF order is revealed to be similar to the parent compound. Above the AF transition, the magnetization violated Curie-Weiss behavior and magnetoresistance keeps negative, indicating the ferromagnetic order. With doping nearly 20% non-magnetic Ca, the magnetic properties of the system barely change, which is favorable to keeping the former predicted nontrivial topological properties in EuIn<sub>2</sub>As<sub>2</sub>. Although Ca shares the same valence with Eu, the carrier density of Eu<sub>1–<i>x</i></sub>Ca<i><sub>x</sub></i>In<sub>2</sub>As<sub>2</sub> is one order lower than that of EuIn<sub>2</sub>As<sub>2</sub>. The Ca doping brings electrons in and lifts the Fermi level. The results enrich the 2D magnetic material candidate pool and provide useful information for realizing the nontrivial topological state in the 2D AF system.

Quasi-one-dimensional TaSe3: A New Topological Superconductor Candidate

Topological superconductors are a new type of quantum matter with the combination of superconductivity and nontrivial electronic topology. Such a unique class of material has become one of the hottest research topics in condensed matter physics, due to its rich scientific implications (predicted to host exotic emergent particles such as Majorana bound states) and considerable application potentials in fault-tolerant quantum computation. Up to date, only very few materials are experimentally verified as candidates of topological superconductors. Searching for new material system is always the focus in this intriguing field. Recently, Chen et al., for the first time, observed both nontrivial topological surface states and bulk superconductivity in a quasi-one-dimensional compound TaSe₃, suggesting a promising new candidate of topological superconductors. Moreover, unlike other existing candidates, the simultaneously combination of stoichiometric, exfoliable, and air-stable properties in TaSe₃ makes it an ideal platform for both fundamental studies and further applications.

Electron transport through Su-Schrieffer-Heeger chain with spin-orbit coupling

In the Su-Schrieffer-Heeger (SSH) chain, the nontrivial topological edge states will have different winding numbers when the intra-cell and inter-cell hopping amplitudes are spin-dependent ones. Consequently, how to detect the edge states with different winding numbers theoretically and experimentally has become one of important topics in condensed matter physics. In this paper, in the framework of the tight-binding approximation, we study the topological properties and the electron transport properties of the edge states of the SSH chain with the spin-orbit coupling. It is demonstrated that the winding numbers of the quadruple-degenerate and twofold-degenerate edge states are two and one, respectively. Importantly, the electron transport properties in the vicinity of the zero energy can characterize the energy spectra of the edge states, when the spin-polarized electrons tunnel into the SSH chain from the source lead, namely, the source lead is a ferromagnetic one. With increasing the tunneling coupling strengths between the SSH chain and the two leads from the weak coupling regime to the strong coupling one, the number of transmission resonance peaks of the quadruple-degenerate with the winding numbers being two and twofold-degenerate edge states with the winding numbers being one will be reduced by four and two, respectively. In other words, the transmission resonance peaks related to the edge states will disappear when the SSH chain is strongly coupled to the two leads. Therefore, these results suggest an alternative way of detecting the nontrivial topological ones with different winding numbers by changing the number of transmission resonance peaks of edge states.

Quantum-confinement-induced periodic surface states in two-dimensional metal-organic frameworks

Recently, a series of single-layer metal–organic frameworks (MOFs) was theoretically predicted to be two-dimensional organic topological materials. However, the experimental evidence of their nontrivial topological states has not been found. Here, combining the use of angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we report the electronic structure studies on a single-layer Cu-coordinated 2,4,6-tri(4-pyridyl)-1,3,5-triazine (Cu-T4PT) MOF supported by a Cu(111) substrate and identify periodic surface states with the period of the Cu-T4PT reciprocal lattice. These periodic surface states, which have identical features to the Cu(111) Shockley surface states, can be attributed to the quantum confinement of the surface states of the underlying Cu(111) substrate by the network lattices of the Cu-T4PT MOF. Our work indicates that the surface states of the metal substrate can be tailored in a controlled manner by the network structures of MOFs with different periodic lattices. The lack of intrinsic bands and the possible topological properties of the single-layer Cu-T4PT MOF may be attributed to the strong electronic coupling between the Cu-T4PT MOF and the Cu(111) substrates. In order to exploit organic topological materials predicted in MOFs, it is necessary to grow them on weak van der Waals interaction substrates in the future.

Effect of antiferromagnetic order on topological electronic structure in Eu-substituted Bi2Se3 single crystals

Topological antiferromagnetic spintronics is an emerging field due to advantages such as no stray field effect and high-speed dynamics. In bismuth chalcogenide topological insulators, the coexistence of long-range antiferromagnetic order and topologically protected states has scarcely been observed. Here, an antiferromagnetic order, which sets in the direction of magnetic moments perpendicular to the c axis, is introduced by Eu substitution in Bi2Se3, and therefore it influences the topological electronic properties of Bi2Se3. Despite Eu substitution, Shubnikov–de Haas (SdH) oscillations are observed. The angle dependence of SdH oscillations shows a signature of anisotropic 3D Fermi surfaces with a nontrivial Berry phase by Eu substitution, and the temperature dependence of SdH oscillations reveals that the effective mass is comparable to the pristine Bi2Se3. These results suggest that the nontrivial topological state can survive in the antiferromagnetic order of Eu-substituted Bi2Se3. Our work expands the base of topological materials available for antiferromagnetic spintronics applications.

Observation of Topological Electronic Structure in Quasi-1D Superconductor TaSe3

Topological superconductors (TSCs), with the capability to host Majorana bound states that can lead to non-Abelian statistics and application in quantum computation, have been one of the most intensively studied topics in condensed matter physics recently. Up to date, only a few compounds have been proposed as candidates of intrinsic TSCs, such as doped topological insulator CuxBi2Se3 and iron-based superconductor FeTe0.55Se0.45. Here, by carrying out synchrotron and laser based angle-resolved photoemission spectroscopy (ARPES), we systematically investigated the electronic structure of a quasi-1D superconductor TaSe3, and identified the nontrivial topological surface states. In addition, our scanning tunneling microscopy (STM) study revealed a clean cleaved surface with a persistent superconducting gap, proving it suitable for further investigation of potential Majorana modes. These results prove TaSe3 as a stoichiometric TSC candidate that is stable and exfoliable, therefore a great platform for the study of rich novel phenomena and application potentials.

Magnetotransport and Berry phase in magnetically doped Bi0.97−xSb0.03 single crystals

We report large magnetoresistance (MR) and Shubnikov-de Haas (SdH) oscillations in single crystals of magnetically (M= Ni and Fe) doped M$_x$Bi$_{0.97-x}$Sb$_{0.03}$ ($x=$ 0, 0.02) topological insulators. The R$\bar{3}$m symmetry and phase have been confirmed by the Rietveld refinement of x-ray diffraction data. Interestingly, a magnetic field induced phase transition from semi-metallic to semi-conducting type is found with the energy gap around 80 meV at 15 Tesla in the $x=$ 0 sample. Moreover, we observe linear behavior of MR up to 15 Tesla in transverse mode and SdH oscillations in longitudinal mode where the field direction is with respect to the current and crystal plane. For the parent sample, we found the coherence length L$_\phi=$ 12.7 nm through the fitting of MR data in transverse mode with modified H-L-N equation. The extracted frequencies of SdH oscillations using the fast Fourier transform method and Landau level (LL) fan diagram are found to be consistent for the parent and Ni doped samples. The determined Fermi surface area is found to be slightly larger in Ni doped as compared to the parent sample possibly due to change in the Fermi energy. The Kohler's plot indicates a single scattering mechanism below 100 K. More importantly, the analysis with the help of LL fan diagram reveals the non-zero Berry phase $\phi_{\rm B}= -$(1$\pm$0.1)$\pi$, which demonstrates the non-trivial topological states near the Dirac point in the parent and Ni doped samples.

Pure Zirconium: Type II Nodal Line and Nodal Surface States.

Type II nodal line states have novel properties, such as direction-reliant chiral anomalies and high anisotropic negative magneto-resistance. These type II nodal line states have been widely investigated. Compared to nodal line materials, there are far fewer proposed nodal surface materials, and furthermore, a very recent challenge is to find a realistic material that co-exhibits both nodal line and nodal surface states. In this manuscript, we present the study of the electronic and topological states of pure zirconium within the density functional theory. We found that pure Zr is an interesting material that rarely exhibits both the type II nodal line state (in kz = 0 plane) and nodal surface state (in kz = π plane). The nontrivial topological states are explained based on the orbital-resolved band structures. Our study shows that pure Zr can serve as a new platform to investigate the interplay between the nodal line state and the nodal surface state.

Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling

Motivated by recent developments in the experimental study of ultracold atoms in graphene-like honeycomb optical lattices, we investigate superconductivity of the attractive Kane-Mele-Habbard (KMH) model with the next-nearest-neighbor (NNN) hoping at half filling. The mean-field approximation is used to study the phase diagram which interpolates the trivial and the non-trivial topological states. It is shown that: (a) when the NNN hoping is taken into account, one has to introduce two mean-field gap equations for the two sublattices, instead of a single gap when the NNN hopping is neglected, and (b) in the non-trivial topological region the phase diagram with the NNN hopping is significantly different compared to the phase diagram calculated previously, but without the NNN term. We also discuss the superconducting instability of the attractive KMH model that is driven by condensation of Cooperons.

Evolution and reversal of topological edge states at optical frequencies from a two-dimensional photonic crystal

The nonreciprocal, defect-immune and backscatter suppression of topological waveguides will play an important role in future optical communication systems. For a long time, researchers have studied such waveguides through magneto-optical media. On one hand, for gyromagnetic media, they have a large magneto-optical effect, but also have large losses at high frequencies; on the other hand, for gyroelectric media, they have small losses at optical frequencies, but their magneto-optical effect is too small. In this paper, we study a magneto-optical photonic crystal (PC) based on a metamaterial design with gyroelectric media, ordinary media and metal. The PC not only can work at optical frequencies, but it also has a large magneto-optical effect. From the PC, we have found some unique properties of non-trivial topological edge states. Different from the ordinary topological edge states that result from the broken band gap from the band degeneration, the topological edge states in the current structure can directly occur in the lowest band gap. For a small magneto-optical effect, the topological edge state and ordinary edge state can coexist in the lowest gap. Through adjusting the external magnetic field, the first trivial band leaves off the zero-frequency point at the center of the first Brillouin zone and becomes non-trivial. With the increase of the external magnetic field, the first and second bands undergo a process of separation–intersection–separation. Following the process, the reversal of modes and Chern number from the two bands occurs. The direction of the topological edge states have also been reversed by the band reversal. The design in this paper has not only realized a topological waveguide working at optical frequencies, but it has also achieved dynamical control of topological edge states.

Nontrivial topological states in the tantalum dipnictides TaX2 (X = As, P)

The intriguing quasiparticles in solids, known as Dirac, Weyl, and Majorana fermions, etc. with properties akin to those theoretically predicted but never realized in high-energy physics, have excited intensive research activities in recent years. The transition metal dipnictides are attractive because of their extremely large magnetoresistance that is usually attributed to the carrier compensation effect. We briefly review herein the crystal growth, magneto-transport measurements, and theoretical studies of tantalum dipnictides TaAs2 and TaP2, with the emphasis being put on discussion of the nontrivial topological states in both materials. The analysis of quantum oscillations of the magnetoresistance unveils nonzero Berry phase. The chiral negative longitudinal magnetoresistance further points to possible Weyl state, which was recently theoretically suggested as the result of the magnetic field-induced Zeeman splitting effect no matter how large the field is. The analysis of these intriguing behaviors could brush up our understanding about the family of materials and would be valuable for future work on investigating the magnetic field-induced topological phase transition in such semimetals.

De Haas-van Alphen Quantum Oscillations in BaSn3 Superconductor with Multiple Dirac Fermions**Supported by the National Natural Science Foundation of China (Grant No. 11874264), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA18000000), the Starting Grant of ShanghaiTech University, the Shenzhen Peacock Team Plan (Grant No. KQTD20170809110344233), the Bureau of Industry and Information Technology of Shenzhen through

Characterization of Fermi surface of the BaSn3 superconductor (Tc ∼ 4.4 K) by de Haas–van Alphen (dHvA) effect measurement reveals its non-trivial topological properties. Analysis of non-zero Berry phase is supported by the ab initio calculations, which reveals a type-II Dirac point setting and tilting along the high symmetric K–H line of the Brillouin zone, about 0.13 eV above the Fermi level, and other two type-I Dirac points on the high symmetric Γ–A direction, but slightly far below the Fermi level. The results demonstrate BaSn3 as an excellent example hosting multiple Dirac fermions and an outstanding platform for studying the interplay between nontrivial topological states and superconductivity.