Large-gap quantum spin Hall insulator in single layer bismuth monobromide Bi4Br4

Robust Weak Topological Insulator in the Bismuth Halide Bi_{4}Br_{2}I_{2}

We apply a topological material design concept for selecting a bulk topology of 3D crystals by different van der Waals stackings of 2D topological insulator layers, and find a bismuth halide Bi_{4}Br_{2}I_{2} to be an ideal weak topological insulator (WTI) with the largest band gap (∼300  meV) among all the WTI candidates, by means of angle-resolved photoemission spectroscopy (ARPES), density functional theory (DFT) calculations, and resistivity measurements. Furthermore, we reveal that the topological surface state of a WTI is not "weak" but rather robust against external perturbations against the initial theoretical prediction by performing potassium deposition experiments. Our results vastly expand future opportunities for fundamental research and device applications with a robust WTI.

Large-Gap Quantum Spin Hall Insulators in Two-Dimensional Hafnium Halides: Unraveling the Impact of Strain and Substrate

Two-dimensional (2D) topological insulators (TIs) or quantum spin Hall (QSH) insulators, characterized by insulating 2D electronic band structures and metallic helical edge states protected by time-reversal symmetry, offer a platform for realizing the quantum spin Hall effect, making them promising candidates for future spintronic devices and quantum computing. However, observing a high-temperature quantum spin Hall effect requires large-gap 2D TIs, and only a few 2D systems have been experimentally confirmed to possess this property. In this study, we employ first-principles calculations, combined with a structural search based on an evolutionary algorithm, to predict a class of 2D QSH insulators in hafnium halides, namely, HfF, HfCl, and HfBr with sizable band gaps of 0.12, 0.19, and 0.38 eV. Their topological nontrivial nature is confirmed by a Z2 invariant which equals to 1 and the presence of gapless edge states. Furthermore, the QSH effect in these materials remains robust under biaxial tensile strain of up to 10%, and the use of h-BN as a substrate effectively preserves the QSH states in these materials. Our findings pave the way for future theoretical and experimental investigations of 2D hafnium halides and their potential for realizing the QSH effect.

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.

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.

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.

Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4

The notion of topological insulators (TIs), characterized by an insulating bulk and conducting topological surface states, can be extended to higher-order topological insulators (HOTIs) hosting gapless modes localized at the boundaries of two or more dimensions lower than the insulating bulk. In this work, by performing high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements with submicron spatial and spin resolution, we systematically investigate the electronic structure and spin texture of quasi-one-dimensional (1D) HOTI candidate Bi4Br4. In contrast to the bulk-state-dominant spectra on the (001) surface, we observe gapped surface states on the (100) surface, whose dispersion and spin-polarization agree well with our ab-initio calculations. Moreover, we reveal in-gap states connecting the surface valence and conduction bands, which is a signature of the hinge states inside the (100) surface gap. Our findings provide compelling evidence for the HOTI phase of Bi4Br4. The identification of the higher-order topological phase promises applications based on 1D spin-momentum locked current in electronic and spintronic devices.

Engineering topological states in a two-dimensional honeycomb lattice

In this work, we use first-principles calculations to determine the interplay between spin-orbit coupling (SOC) and magnetism which can not only generate a quantum anomalous Hall state but can also result in topologically trivial states although some honeycomb systems host large band gaps. By employing tight-binding model analysis, we have summarized two types of topologically trivial states: one is due to the coexistence of quadratic non-Dirac and linear Dirac bands in the same spin channel that act together destructively in magnetic materials (such as, CrBr3, CrCl3, and VBr3 monolayers); the other one is caused by the destructive coupling effect between two different spin channels due to small magnetic spin splitting in heavy-metal-based materials, such as, BaTe(111)-supported plumbene. Further investigations reveal that topologically nontrivial states can be realized by removing the Dirac band dispersion of the magnetic monolayers for the former case (such as in alkali metal doped CrBr3), while separating the two different spin channels from each other by enhancing the magnetic spin splitting for the latter case (such as in half-iodinated silicene). Thus, our work provides a theoretical guideline to manipulate the topological states in a two-dimensional honeycomb lattice.

Towards layer-selective quantum spin hall channels in weak topological insulator Bi4Br2I2

Weak topological insulators, constructed by stacking quantum spin Hall insulators with weak interlayer coupling, offer promising quantum electronic applications through topologically non-trivial edge channels. However, the currently available weak topological insulators are stacks of the same quantum spin Hall layer with translational symmetry in the out-of-plane direction-leading to the absence of the channel degree of freedom for edge states. Here, we study a candidate weak topological insulator, Bi4Br2I2, which is alternately stacked by three different quantum spin Hall insulators, each with tunable topologically non-trivial edge states. Our angle-resolved photoemission spectroscopy and first-principles calculations show that an energy gap opens at the crossing points of different Dirac cones correlated with different layers due to the interlayer interaction. This is essential to achieve the tunability of topological edge states as controlled by varying the chemical potential. Our work offers a perspective for the construction of tunable quantized conductance devices for future spintronic applications.

Oxygen functionalized InSe and TlTe two-dimensional materials: transition from tunable bandgap semiconductors to quantum spin Hall insulators

From first-principles calculations, we found that oxygen functionalized InSe and TlTe two-dimensional materials undergo the following changes with the increased concentrations of oxygen coverage, transforming from indirect bandgap semiconductors to direct bandgap semiconductors with tunable bandgap, and finally becoming quantum spin hall insulators. The maximal nontrivial bandgap are 0.121 and 0.169 eV, respectively, which occur at 100% oxygen coverage and are suitable for applications at room temperature. In addition, the topological phases are derived from SOC induced p-p bandgap opening, which can be further determined by Z₂ topological invariants and topologically protected gapless edge states. Significantly, the topological phases can be maintained in excess of 75% oxygen coverage and are robust against external strain, making the quantum spin hall effect easy to achieve experimentally. Thus, the oxygen functionalized InSe and TlTe are fine candidate materials for the design and fabrication of topological devices.

Gate-tunable transport in van der Waals topological insulator Bi4Br4nanobelts

Bi₄Br₄is a quasi-one-dimensional van der Waals topological insulator with novel electronic properties. Several efforts have been devoted to the understanding of its bulk form, yet it remains a challenge to explore the transport properties in low-dimensional structures due to the difficulty of device fabrication. Here we report for the first time a gate-tunable transport in exfoliated Bi₄Br₄nanobelts. Notable two-frequency Shubnikov-de Haas oscillations oscillations are discovered at low temperatures, with the low- and high-frequency parts coming from the three-dimensional bulk state and the two-dimensional surface state, respectively. In addition, ambipolar field effect is realized with a longitudinal resistance peak and a sign reverse in the Hall coefficient. Our successful measurements of quantum oscillations and realization of gate-tunable transport lay a foundation for further investigation of novel topological properties and room-temperature quantum spin Hall states in Bi₄Br₄.

Optical bulk-boundary dichotomy in a quantum spin Hall insulator

The bulk-boundary correspondence is a critical concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z₂ topology. However, the bulk-boundary dichotomy and distinction are rarely explored in optical experiments, which can provide unique information about topological charge carriers beyond transport and electronic spectroscopy techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses of Bi₄Br₄, a recently discovered room-temperature quantum spin Hall insulator. Benefiting from the low energy of infrared photons and the high spatial resolution, we unambiguously resolve a strong absorption from the boundary states while the bulk absorption is suppressed by its insulating gap. Moreover, the boundary absorption exhibits strong polarization anisotropy, consistent with the one-dimensional nature of the topological boundary states. Our infrared pump-probe microscopy further measures a substantially increased carrier lifetime for the boundary states, which reaches one nanosecond scale. The nanosecond lifetime is about one to two orders longer than that of most topological materials and can be attributed to the linear dispersion nature of the helical boundary states. Our findings demonstrate the optical bulk-boundary dichotomy in a topological material and provide a proof-of-principal methodology for studying topological optoelectronics.

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics^1,2. The quantum spin Hall phase^3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi₄Br₄. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z₂ topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

Designing SnS/MoS2 van der Waals heterojunction for direct Z-scheme photocatalytic overall water-splitting by DFT investigation

Construction of direct Z-scheme photocatalytic heterojunctions with an internal electric field has been proposed as an outstanding method to achieve efficient utilization of solar energy for photocatalytic overall water-splitting. In this work, the properties of van der Waals (vdW) heterojunctions formed by group-IV mono-chalcogenides (MXs) (M = Ge, Sn; X = S, Se, Te) and MoS₂ are systematically studied by first-principles calculations, including the vdW binding energy, the direction of an internal electric field and the electronic structure. The results predict that GeS/MoS₂, GeSe/MoS₂ and SnS/MoS₂ vdW heterojunctions are potential direct Z-scheme water-splitting photocatalysts with appropriate band alignments, a wide light absorption range and low effective charge-carrier mass. Furthermore, the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) activities of the heterojunctions as photocatalysts are predicted. The results indicate that SnS/MoS₂ with the Sn vacancy has a low Gibbs free energy of the HER (0.06 eV), and MoS₂ with the S edge can offer OER active sites. This study provides a theoretical basis for the further design and preparation of a new two-dimensional overall water-splitting photocatalyst, which is conducive to the development of efficient two-dimensional photocatalysts in the field of clean energy.

A piezoelectric quantum spin Hall insulator VCClBr monolayer with a pure out-of-plane piezoelectric response

The combination of piezoelectricity with a nontrivial topological insulating phase in two-dimensional (2D) systems, namely piezoelectric quantum spin Hall insulators (PQSHI), is intriguing for exploring novel topological states toward the development of high-speed and dissipationless electronic devices. In this work, we predict a PQSHI Janus monolayer VCClBr constructed from VCCl₂, which is dynamically, mechanically and thermally stable. In the absence of spin orbital coupling (SOC), VCClBr is a narrow gap semiconductor with a gap value of 57 meV, which is different from Dirac semimetal VCCl₂. The gap of VCClBr is due to a built-in electric field caused by asymmetrical upper and lower atomic layers, which is further confirmed by the external-electric-field induced gap in VCCl₂. When including SOC, the gap of VCClBr is increased to 76 meV, which is larger than the thermal energy of room temperature (25 meV). The VCClBr is a 2D topological insulator (TI), which is confirmed by Z₂ topological invariant and nontrivial one-dimensional edge states. It is proved that the nontrivial topological properties of VCClBr are robust against strain (biaxial and uniaxial cases) and external electric fields. Due to broken horizontal mirror symmetry, only an out-of-plane piezoelectric response can be observed, when a biaxial or uniaxial in-plane strain is applied. The predicted piezoelectric strain coefficients d₃₁ and d₃₂ are -0.425 pm V^-1 and -0.219 pm V^-1, respectively, and they are higher than or compared with those of many 2D materials. Finally, Janus monolayer VCFBr and VCFCl (dynamically unstable) are also constructed, and they are still PQSHIs. Moreover, the d₃₁ and d₃₂ of VCFBr and VCFCl are higher than those of VCClBr, and the d₃₁ (absolute value) of VCFBr is larger than one. According to out-of-plane piezoelectric coefficients of VCXY (X ≠ Y = F, Cl and Br), CrX_1.5Y_1.5 (X = F, Cl and Br; Y = I) and NiXY (X ≠ Y = Cl, Br and I), it is concluded that the size of the out-of-plane piezoelectric coefficient has a positive relation with the electronegativity difference of X and Y atoms. Our studies enrich the diversity of Janus 2D materials, and open a new avenue in the search for PQSHI with a large out-of-plane piezoelectric response, which provides a potential platform in nanoelectronics.

Spin-valley-coupled quantum spin Hall insulator with topological Rashba-splitting edge states in Janus monolayer CSb1.5Bi1.5

Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer CSb_1.5Bi_1.5with dynamic, mechanical and thermal stabilities. Calculated results show that the CSb_1.5Bi_1.5is a direct band gap semiconductor with and without spin-orbit coupling, and the conduction-band minimum and valence-band maximum are at valley point. The inequivalent valleys have opposite Berry curvature and spin moment, which can produce a spin-valley Hall effect. In the center of Brillouin zone, a Rashba-type spin splitting can be observed due to missing horizontal mirror symmetry. The topological characteristic of CSb_1.5Bi_1.5is confirmed by theZ₂invariant and topological protected conducting helical edge states. Moreover, the CSb_1.5Bi_1.5shows unique Rashba-splitting edge states. Both energy band gap and spin-splitting at the valley point are larger than the thermal energy of room temperature (25 meV) with generalized gradient approximation level, which is very important at room temperature for device applications. It is proved that the spin-valley-coupling and nontrivial quantum spin Hall state are robust again biaxial strain. Our work may provide a new platform to achieve integration of topological physics, spintronics and valleytronics.

Large-Gap Quantum Spin Hall State and Temperature-Induced Lifshitz Transition in Bi4Br4

Searching for quantum spin Hall insulators with large fully opened energy gap to overcome the thermal disturbance at room temperature has attracted tremendous attention because of the robustness of one-dimensional (1D) spin-momentum locked topological edge states in the practical applications of electronic devices and spintronics. Here, we report the investigation of topological nature of monolayer Bi₄Br₄ by the techniques of angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy. The possible topological nontriviality of 1D edge state integrals within the large energy gap (∼0.2 eV) is revealed by the first-principle calculations. The ARPES measurements at different temperatures show a temperature-induced Lifshitz transition, corresponding to the resistivity anomaly evoked by the chemical potential shift. The connection between the emergency of superconductivity and the Lifshitz transition is discussed.

Gate-Tunable Transport in Quasi-One-Dimensional α-Bi4I4 Field Effect Transistors

Bi₄I₄ belongs to a novel family of quasi-one-dimensional (1D) topological insulators (TIs). While its β phase was demonstrated to be a prototypical weak TI, the α phase, long thought to be a trivial insulator, was recently predicted to be a rare higher order TI. Here, we report the first gate tunable transport together with evidence for unconventional band topology in exfoliated α-Bi₄I₄ field effect transistors. We observe a Dirac-like longitudinal resistance peak and a sign change in the Hall resistance; their temperature dependences suggest competing transport mechanisms: a hole-doped insulating bulk and one or more gate-tunable ambipolar boundary channels. Our combined transport, photoemission, and theoretical results indicate that the gate-tunable channels likely arise from novel gapped side surface states, two-dimensional (2D) TI in the bottommost layer, and/or helical hinge states of the upper layers. Markedly, a gate-tunable supercurrent is observed in an α-Bi₄I₄ Josephson junction, underscoring the potential of these boundary channels to mediate topological superconductivity.

Generalization of piezoelectric quantum anomalous Hall insulator based on monolayer Fe2I2: a first-principles study

To easily synthesize a piezoelectric quantum anomalous Hall insulator (PQAHI), the Janus monolayer Fe₂IBr (FeI_0.5Br_0.5) as a representative PQAHI, is generalized to monolayer FeI_1-xBr_x (x = 0.25 and 0.75) with α and β phases. By first-principles calculations, it is proved that monolayer FeI_1-xBr_x (x = 0.25 and 0.75) are dynamically, mechanically and thermally stable. They are excellent room-temperature PQAHIs with high Curie temperatures, sizable gaps and high Chern number (C = 2). Because the considered crystal structures of α and β phases possess M_x and M_y mirror symmetries, the topological properties of monolayer FeI_1-xBr_x (x = 0.25 and 0.75) are maintained. Namely, if the constructed structures have M_x and M_y mirror symmetries, the mixing ratio of Br and I atoms can be generalized for other proportions. It is also found that different crystal phases have important effects on the out-of-plane piezoelectric response, and the piezoelectric strain coefficient, d₃₂, of the β phase is higher than or comparable with those of other known two-dimensional (2D) materials. To further confirm this idea, the physical and chemical properties of monolayer LiFeSe_0.75S_0.25 with α and β phases, as a generalization of PQAHI LiFeSe_0.5S_0.5, is investigated, as it has a similar electronic structure, magnetic and topological properties as LiFeSe_0.5S_0.5. Our work provides a practical guide to achieve PQAHIs experimentally, and the combination of piezoelectricity, topological and ferromagnetic (FM) orders makes Fe₂I₂-based monolayers a potential platform for multi-functional spintronics and piezoelectric electronics.

Observation of Topological Edge States on α-Bi4Br4 Nanowires Grown on TiSe2 Substrates

A time-reversal invariant two-dimensional (2D) topological insulator (TI) is characterized by the gapless helical edge states propagating along the perimeter of the system. However, the small band gap in the 2D TIs discovered so far hinders their applications. Recently, we predicted that single-layer Bi₄Br₄ is a 2D TI with a remarkable band gap and that α-Bi₄Br₄ crystals can host topological edge states at the step edges. Here we report the growth of α-Bi₄Br₄ nanowires with (102)-oriented top surfaces on the TiSe₂ substrates and the direct observation of the predicted topological edge states at the step edges of the nanowires using scanning tunneling microscopy. The coupling between the edge states leads to the formation of surface states at the (102) top surfaces of the nanowires. Our work demonstrates the existence of topological edge states in α-Bi₄Br₄ and paves the way for developing α-Bi₄Br₄-based devices for a high-temperature quantum spin Hall effect.

Epitaxial Growth of Quasi-One-Dimensional Bismuth-Halide Chains with Atomically Sharp Topological Non-Trivial Edge States

Quantum spin Hall insulators (QSHIs) have one-dimensional (1D) spin-momentum locked topological edge states (ES) inside the bulk band gap, which can serve as dissipationless channels for the practical applications in low consumption electronics and high performance spintronics. However, obtaining the clean and atomically sharp ES which serves as ideal 1D spin-polarized nondissipative conducting channels is demanding and still a challenge. Here, we report the formation of the quasi-1D Bi₄I₄ nanoribbons on the surface of Bi(111) with the support of the graphene-terminated 6H-SiC(0001) and the direct observation of the topological ES at the step edges by the scanning tunneling microscopy (STM) and spectroscopic-imaging results. The ES reside surround the edge of Bi₄I₄ nanoribbons and exhibits noteworthy robustness against nontime reversal symmetry (non-TRS) perturbations. The theoretical simulations verify the topological nontriviality of 1D ES, which is retained after considering the presence of the underlying Bi(111). Our study supports the existence of topological ES in Bi₄I₄ nanoribbons, benefiting to engineer the topological features by using the 1D nanoribbons as building blocks.

Selective Substrate-Orbital-Filtering Effect to Realize the Large-Gap Quantum Spin Hall Effect

Although Pb harbors a strong spin-orbit coupling effect, pristine plumbene (the last group-IV cousin of graphene) hosts topologically trivial states. Based on first-principles calculations, we demonstrate that epitaxial growth of plumbene on the BaTe(111) surface converts the trivial Pb lattice into a quantum spin Hall (QSH) phase with a large gap of ∼0.3 eV via a selective substrate-orbital-filtering effect. Tight-binding model analyses show the p_z orbital in half of the Pb overlayer is selectively removed by the BaTe substrate, leaving behind a p_z-p_x,y band inversion. Based on the same working principle, the gap can be further increased to ∼0.5-0.6 eV by surface adsorption of H or halogen atoms that filters out the other half of the Pb p_z orbitals. The mechanism of selective substrate-orbital-filtering is general, opening an avenue to explore large-gap QSH insulators in heavy-metal-based materials. It is worth noting that plumbene has already been widely grown on various substrates experimentally.

Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains

Low-dimensional van der Waals materials have been extensively studied as a platform with which to generate quantum effects. Advancing this research, topological quantum materials with van der Waals structures are currently receiving a great deal of attention. Here, we use the concept of designing topological materials by the van der Waals stacking of quantum spin Hall insulators. Most interestingly, we find that a slight shift of inversion centre in the unit cell caused by a modification of stacking induces a transition from a trivial insulator to a higher-order topological insulator. Based on this, we present angle-resolved photoemission spectroscopy results showing that the real three-dimensional material Bi₄Br₄ is a higher-order topological insulator. Our demonstration that various topological states can be selected by stacking chains differently, combined with the advantages of van der Waals materials, offers a playground for engineering topologically non-trivial edge states towards future spintronics applications.

Families of asymmetrically functionalized germanene films as promising quantum spin Hall insulators

Topological insulators (TIs), exhibiting the quantum spin Hall (QSH) effect, are promising for developing dissipationless transport devices that can be realized under a wide range of temperatures. The search for new two-dimensional (2D) TIs is essential for TIs to be utilized at room-temperature, with applications in optoelectronics, spintronics, and magnetic sensors. In this work, we used first-principles calculations to investigate the geometric, electronic, and topological properties of GeX and GeMX (M = C, N, P, As; X = H, F, Cl, Br, I, O, S, Se, Te). In 26 of these materials, the QSH effect is demonstrated by a spin-orbit coupling (SOC) induced large band gap and a band inversion at the Γ point, similar to the case of an HgTe quantum well. In addition, engineering the intra-layer strain of certain GeMX species can transform them from a regular insulator into a 2D TI. This work demonstrates that asymmetrical chemical functionalization is a promising method to induce the QSH effect in 2D hexagonal materials, paving the way for practical application of TIs in electronics.

Pressure-induced phase transitions and superconductivity in a quasi-1-dimensional topological crystalline insulator α-Bi4Br4

Great progress has been achieved in the research field of topological states of matter during the past decade. Recently, a quasi-1-dimensional bismuth bromide, Bi₄Br₄, has been predicted to be a rotational symmetry-protected topological crystalline insulator; it would also exhibit more exotic topological properties under pressure. Here, we report a thorough study of phase transitions and superconductivity in a quasihydrostatically pressurized α-Bi₄Br₄ crystal by performing detailed measurements of electrical resistance, alternating current magnetic susceptibility, and in situ high-pressure single-crystal X-ray diffraction together with first principles calculations. We find a pressure-induced insulator-metal transition between ∼3.0 and 3.8 GPa where valence and conduction bands cross the Fermi level to form a set of small pockets of holes and electrons. With further increase of pressure, 2 superconductive transitions emerge. One shows a sharp resistance drop to 0 near 6.8 K at 3.8 GPa; the transition temperature gradually lowers with increasing pressure and completely vanishes above 12.0 GPa. Another transition sets in around 9.0 K at 5.5 GPa and persists up to the highest pressure of 45.0 GPa studied in this work. Intriguingly, we find that the first superconducting phase might coexist with a nontrivial rotational symmetry-protected topology in the pressure range of ∼3.8 to 4.3 GPa; the second one is associated with a structural phase transition from monoclinic C2/m to triclinic P-1 symmetry.

Topological phase transition induced by px,y and pz band inversion in a honeycomb lattice

The search for more types of band inversion-induced topological states is of great scientific and experimental interest. Here, we proposed that the band inversion between p_x,y and p_z orbitals can produce a topological phase transition in honeycomb lattices based on tight-binding model analyses. The corresponding topological phase diagram was mapped out in the parameter space of orbital energy and spin-orbit coupling. Specifically, the quantum anomalous Hall (QAH) effect could be achieved when ferromagnetism was introduced. Moreover, our first-principles calculations demonstrated that the two systems of half-iodinated silicene (Si₂I) and one-third monolayer of bismuth epitaxially grown on the Si(111)-√3 ×√3 surface are ideal candidates for realizing the QAH effect with Curie temperatures of ∼101 K and 118 K, respectively. The underlying physical mechanism of this scheme is generally applicable, offering broader opportunities for the exploration of novel topological states and high-temperature QAH effect systems.

Oxygen-functionalized TlTe buckled honeycomb from first-principles study

A sizable band gap is crucial for the applications of topological insulators at room temperature. By first-principles calculations, we found that oxygen-functionalized TlTe buckled honeycomb, namely TlTeO, possessed quantum spin Hall (QSH) state with a sizable band gap of 0.17 eV, which owns potential applications at the room temperature. The QSH phase of TlTeO arose from the SOC-induced p-p band gap opening. In addition, the QSH phase was further confirmed by the topological invariant Z2 and gapless edge state in the bulk gap. Significantly, the QSH phase is robustly against the external strain and possesses more than 75% oxygen coverage, making the QSH effect of TlTeO easy to be achieved experimentally. Thus, the oxygen-functionalized TlTeO film is a fine candidate material for the topological device design and fabrication.

Spin valley and giant quantum spin Hall gap of hydrofluorinated bismuth nanosheet

Spin-valley and electronic band topological properties have been extensively explored in quantum material science, yet their coexistence has rarely been realized in stoichiometric two-dimensional (2D) materials. We theoretically predict the quantum spin Hall effect (QSHE) in the hydrofluorinated bismuth (Bi₂HF) nanosheet where the hydrogen (H) and fluorine (F) atoms are functionalized on opposite sides of bismuth (Bi) atomic monolayer. Such Bi₂HF nanosheet is found to be a 2D topological insulator with a giant band gap of 0.97 eV which might host room temperature QSHE. The atomistic structure of Bi₂HF nanosheet is noncentrosymmetric and the spontaneous polarization arises from the hydrofluorinated morphology. The phonon spectrum and ab initio molecular dynamic (AIMD) calculations reveal that the proposed Bi₂HF nanosheet is dynamically and thermally stable. The inversion symmetry breaking together with spin-orbit coupling (SOC) leads to the coupling between spin and valley in Bi₂HF nanosheet. The emerging valley-dependent properties and the interplay between intrinsic dipole and SOC are investigated using first-principles calculations combined with an effective Hamiltonian model. The topological invariant of the Bi₂HF nanosheet is confirmed by using Wilson loop method and the calculated helical metallic edge states are shown to host QSHE. The Bi₂HF nanosheet is therefore a promising platform to realize room temperature QSHE and valley spintronics.

Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal

A variety of monolayer crystals have been proposed to be two-dimensional topological insulators exhibiting the quantum spin Hall effect (QSHE), possibly even at high temperatures. Here we report the observation of the QSHE in monolayer tungsten ditelluride (WTe₂) at temperatures up to 100 kelvin. In the short-edge limit, the monolayer exhibits the hallmark transport conductance, ~e²/h per edge, where e is the electron charge and h is Planck's constant. Moreover, a magnetic field suppresses the conductance, and the observed Zeeman-type gap indicates the existence of a Kramers degenerate point and the importance of time-reversal symmetry for protection from elastic backscattering. Our results establish the QSHE at temperatures much higher than in semiconductor heterostructures and allow for exploring topological phases in atomically thin crystals.

Bismuth oxide film: a promising room-temperature quantum spin Hall insulator

Two-dimensional (2D) bismuth films have attracted extensive attention due to their nontrivial band topology and tunable electronic properties for achieving dissipationless transport devices. The experimental observation of quantum transport properties, however, are rather challenging, limiting their potential application in nanodevices. Here, we predict, based on first-principles calculations, an alternative 2D bismuth oxide, BiO, as an excellent topological insulator (TI), whose intrinsic bulk gap reaches up to 0.28 eV. Its nontrivial topology is confirmed by topological invariant Z ₂ and time-reversal symmetry protected helical edge states. The appearance of topological phase is robust against mechanical strain and different levels of oxygen coverage in BiO. Since the BiO is naturally stable against surface oxidization and degradation, these results enrich the topological materials and present an alternative way to design topotronics devices at room temperature.

Topological Insulator in Two-Dimensional SiGe Induced by Biaxial Tensile Strain

Strain-engineered two-dimensional (2D) SiGe is predicted to be a topological insulator (TI) based on first-principle calculations. The dynamical and thermal stabilities were ascertained through phonon spectra and ab initio molecular dynamics simulations. 2D SiGe remains dynamically stable under tensile strains of 4 and 6%. A band inversion was observed at the Γ-point with a band gap of 25 meV for 6% strain due to spin-orbit coupling interactions. Nontrivial of the TI phase was determined by its topological invariant (υ = 1). For SiGe nanoribbon with edge states, the valence band and conduction band cross at the Γ-point to create a topologically protected Dirac cone inside the bulk gap. We found that hexagonal boron nitride (h-BN) with high dielectric constant and band gap can be a very stable support to experimentally fabricate 2D SiGe as the h-BN layer does not alter its nontrivial topological character. Unlike other heavy-metal-based 2D systems, because SiGe has a sufficiently large gap, it can be utilized for spintronics and quantum spin Hall-based applications under ambient condition.

Recent progress in 2D group-VA semiconductors: from theory to experiment

This review provides recent theoretical and experimental progress in the fundamental properties, electronic modulations, fabrications and applications of 2D group-VA materials.

Two-dimensional transition-metal dichalcogenides-based ferromagnetic van der Waals heterostructures

The lack of ferromagnetic (FM) van der Waals (vdW) heterostructures hinders the application of two-dimensional (2D) materials in spintronics, information memories and storage devices. Herein, we find theoretically that 2D transition-metal dichalcogenides-based vdW heterostructures, such as MoS₂/VS₂ and WS₂/VS₂, possess excellent characteristics of stable stacking configurations, FM semiconducting ground states, high Curie temperatures, staggered band alignment and a large band offset. Fortunately, 100% spin-polarized currents at the Fermi level can be achieved under certain positive external electric fields, which can filter the current into a single spin channel. Moreover, the majority channel undergoes the transition from type-II to type-I (type-III) band alignment under the negative (positive) electric field; while the band alignment of the minority channel is robust to the electric field. Our results provide a feasible way to realize 2D TMDs-based FM semiconducting heterostructures for spintronic devices.

Nanostructured topological state in bismuth nanotube arrays: inverting bonding-antibonding levels of molecular orbitals

We demonstrate a new class of nanostructured topological materials that exhibit a topological quantum phase arising from nanoscale structural motifs. Based on first-principles calculations, we show that an array of bismuth nanotubes (Bi-NTs), a superlattice of Bi-NTs with periodicity in the order of tube diameter, behaves as a nanostructured two-dimensional (2D) quantum spin Hall (QSH) insulator, as confirmed from the calculated band topology and 1D helical edge states. The underpinning mechanism of the QSH phase in the Bi-NT array is revealed to be inversion of bonding-antibonding levels of molecular orbitals of constituent nanostructural elements in place of atomic-orbital band inversion in conventional QSH insulators. The quantized edge conductance of the QSH phase in a Bi-NT array can be more easily isolated from bulk contributions and their properties can be highly tuned by tube size, representing distinctive advantages of nanostructured topological phases. Our finding opens a new avenue for topological materials by extending topological phases into nanomaterials with molecular-orbital-band inversion.

First-principles prediction on bismuthylene monolayer as a promising quantum spin Hall insulator

Two-dimensional (2D) large band-gap topological insulators (TIs) with highly stable structures are imperative for achieving dissipationless transport devices. However, to date, only very few materials have been experimentally observed to host the quantum spin Hall (QSH) effect at low temperature, thus obstructing their potential application in practice. Using first-principles calculations, herein, we predicted a new 2D TI in the porous allotrope of a bismuth monolayer, i.e. bismuthylene, its geometrical stability was confirmed via phonon spectrum and molecular dynamics simulations. Analysis of the electronic structures reveals that bismuthylene is a native QSH state with a band gap as large as 0.28 eV at the Γ point, which is smaller than that (0.50 eV) of the buckled Bi (111) and suitable for room temperature applications. Notably, it has a much lower energy than flattened Bi and a higher energy than buckled Bi (111)…” [corrected] and flattened Bi films; thus, bismuthylene is feasible for experimental realization. Interestingly, the topological properties can be retained under strains within the range of -6%-3% and electrical fields up to 0.8 eV Å^-1. A heterostructure was constructed by sandwiching bismuthylene between BN sheets, and the non-trivial topology of bismuthylene was retained with a sizable band gap. These findings provide a platform to design a large-gap QSH insulator based on the 2D bismuthylene films, which show potential applications in spintronic devices.

Monolayer AgBiP2Se6: an atomically thin ferroelectric semiconductor with out-plane polarization

Using first-principles calculations, we designed a two-dimensional material, monolayer AgBiP₂Se₆, with the thickness of only 6 Å, which exhibited out-plane ferroelectricity. The ground state of the monolayer AgBiP₂Se₆ was not purely ferroelectric since the out-plane ferroelectricity originated from the compensated ferrielectric state: the off-centering antiparallel displacements of Ag⁺ and Bi³⁺ ions. The compensated ferrielectric ordering has superiority on reducing the depolarization field to stabilize the ferroelectricity. Furthermore, together with strong visible-light adsorption and suitable band edge alignments, we proposed the monolayer AgBiP₂Se₆ as a visible-light photocatalyst for water-splitting as the out-plane polarization could enhance the electron-hole separation. Our results offer a new way to overcome the critical thickness limitation of nanoscale ferroelectrics. The out-plane ferroelectricity in monolayer AgBiP₂Se₆ has great potential for developing various devices with desirable applications.

Antimonene Oxides: Emerging Tunable Direct Bandgap Semiconductor and Novel Topological Insulator

Highly stable antimonene, as the cousin of phosphorene from group-VA, has opened up exciting realms in the two-dimensional (2D) materials family. However, pristine antimonene is an indirect band gap semiconductor, which greatly restricts its applications for optoelectronics devices. Identifying suitable materials, both responsive to incident photons and efficient for carrier transfer, is urgently needed for ultrathin devices. Herein, by means of first-principles computations we found that it is rather feasible to realize a new class of 2D materials with a direct bandgap and high carrier mobility, namely antimonene oxides with different content of oxygen. Moreover, these tunable direct bandgaps cover a wide range from 0 to 2.28 eV, which are crucial for solar cell and photodetector applications. Especially, the antimonene oxide (18Sb-18O) is a 2D topological insulator with a sizable global bandgap of 177 meV, which has a nontrivial Z₂ topological invariant in the bulk and the topological states on the edge. Our findings not only introduce new vitality into 2D group-VA materials family and enrich available candidate materials in this field but also highlight the potential of these 2D semiconductors as appealing ultrathin materials for future flexible electronics and optoelectronics devices.

Two-Dimensional Topological Insulators: Progress and Prospects

Two-dimensional topological insulators (2D TIs) are a remarkable class of atomically thin layered materials that exhibit unique symmetry-protected helical metallic edge states with an insulating interior. Recent years have seen a tremendous surge in research of this intriguing new state of quantum matter. In this Perspective, we summarize major milestones and the most significant progress in the latest developments of material discovery and property characterization in 2D TI research. We categorize the large number and rich variety of theoretically proposed 2D TIs based on the distinct mechanisms of topological phase transitions, and we systematically analyze and compare their structural, chemical, and physical characteristics. We assess the current status and challenges of experimental synthesis and potential device applications of 2D TIs and discuss prospects of exciting new opportunities for future research and development of this fascinating class of materials.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z_{2} topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

New type of quantum spin Hall insulators in hydrogenated PbSn thin films

The realization of a quantum spin Hall (QSH) insulator working at high temperature is of both scientific and technical interest since it supports spin-polarized and dssipationless edge states. Based on first-principle calculations, we predicted that the two-dimensional (2D) binary compound of lead and tin (PbSn) in a buckled honeycomb framework can be tuned into a topological insulator with huge a band gap and structural stability via hydrogenation or growth on special substrates. This heavy-element-based structure is sufficiently ductile to survive the 18 ps molecular dynamics (MD) annealing to 400 K, and the band gap opened by strong spin-orbital-coupling (SOC) is as large as 0.7 eV. These characteristics indicate that hydrogenated PbSn (H-PbSn) is an excellent platform for QSH realization at high temperature.

Films based on group IV–V–VI elements for the design of a large-gap quantum spin Hall insulator with tunable Rashba splitting

Rashba spin–orbit coupling (SOC) in topological insulators (TIs) has recently attracted significant interest due to its potential applications in spintronics.

Large-Gap Quantum Spin Hall State in MXenes: d-Band Topological Order in a Triangular Lattice

MXenes are a large family of two-dimensional (2D) early transition metal carbides that have shown great potential for a host of applications ranging from electrodes in supercapacitors and batteries to sensors to reinforcements in polymers. Here, on the basis of first-principles calculations, we predict that Mo₂MC₂O₂ (M = Ti, Zr, or Hf), belonging to a recently discovered new class of MXenes with double transition metal elements in an ordered structure, are robust quantum spin Hall (QSH) insulators. A tight-binding (TB) model based on the d_z²-, d_xy-, and d_x²-y²-orbital basis in a triangular lattice is also constructed to describe the QSH states in Mo₂MC₂O₂. It shows that the atomic spin-orbit coupling (SOC) strength of M totally contributes to the topological gap at the Γ point, a useful feature advantageous over the usual cases where the topological gap is much smaller than the atomic SOC strength based on the classic Kane-Mele (KM) or Bernevig-Hughes-Zhang (BHZ) model. Consequently, Mo₂MC₂O₂ show sizable gaps from 0.1 to 0.2 eV with different M atoms, sufficiently large for realizing room-temperature QSH effects. Another advantage of Mo₂MC₂O₂ MXenes lies in their oxygen-covered surfaces which make them antioxidative and stable upon exposure to air.

A new kind of 2D topological insulators BiCN with a giant gap and its substrate effects

Based on DFT calculation, we predict that BiCN, i.e., bilayer Bi films passivated with -CN group, is a novel 2D Bi-based material with highly thermodynamic stability, and demonstrate that it is also a new kind of 2D TI with a giant SOC gap (~1 eV) by direct calculation of the topological invariant Z₂ and obvious exhibition of the helical edge states. Monolayer h-BN and MoS₂ are identified as good candidate substrates for supporting the nontrivial topological insulating phase of the 2D TI films, since the two substrates can stabilize and weakly interact with BiCN via van der Waals interaction and thus hardly affect the electronic properties, especially the band topology. The topological properties are robust against the strain and electric field. This may provide a promising platform for realization of novel topological phases.

Exploring Ag(111) Substrate for Epitaxially Growing Monolayer Stanene: A First-Principles Study

Stanene, a two-dimensional topological insulator composed of Sn atoms in a hexagonal lattice, is a promising contender to Si in nanoelectronics. Currently it is still a significant challenge to achieve large-area, high-quality monolayer stanene. We explore the potential of Ag(111) surface as an ideal substrate for the epitaxial growth of monolayer stanene. Using first-principles calculations, we study the stability of the structure of stanene in different epitaxial relations with respect to Ag(111) surface, and also the diffusion behavior of Sn adatom on Ag(111) surface. Our study reveals that: (1) the hexagonal structure of stanene monolayer is well reserved on Ag(111) surface; (2) the height of epitaxial stanene monolayer is comparable to the step height of the substrate, enabling the growth to cross the surface step and achieve a large-area stanene; (3) the perfect lattice structure of free-standing stanene can be achieved once the epitaxial stanene monolayer is detached from Ag(111) surface; and finally (4) the diffusion barrier of Sn adatom on Ag(111) surface is found to be only 0.041 eV, allowing the epitaxial growth of stanene monolayer even at low temperatures. Our above revelations strongly suggest that Ag(111) surface is an ideal candidate for growing large-area, high-quality monolayer stanene.

Topological phases in two-dimensional materials: a review

Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.

Quantum Phase Transition in Germanene and Stanene Bilayer: From Normal Metal to Topological Insulator

Two-dimensional (2D) topological insulators (TIs) that exhibit quantum spin Hall effects are a new class of materials with conducting edge and insulating bulk. The conducting edge bands are spin-polarized, free of back scattering, and protected by time-reversal symmetry with potential for high-efficiency applications in spintronics. On the basis of first-principles calculations, we show that under external pressure recently synthesized stanene and germanene buckled bilayers can automatically convert into a new dynamically stable phase with flat honeycomb meshes. In contrast with the active surfaces of buckled bilayer of stanene or germanene, the above new phase is chemically inert. Furthermore, we demonstrate that these flat bilayers are 2D TIs with sizable topologically nontrivial band gaps of ∼0.1 eV, which makes them viable for room-temperature applications. Our results suggest some new design principles for searching stable large-gap 2D TIs.

New quantum spin Hall insulator in two-dimensional MoS2 with periodically distributed pores

MoS2, one of the transition metal dichalcogenides (TMDs), has gained a lot of attention due to its excellent semiconductor characteristics and potential applications. Here, based on density functional theory methods, we predict a novel 2D QSH insulator in the porous allotrope of monolayer MoS2 (g-MoS2), consisting of MoS2 squares and hexagons. g-MoS2 has a nontrivial gap as large as 109 meV, comparable with previously reported 1T'-MoS2 (80 meV) and so-MoS2 (25 meV). We demonstrate that the origin of the 2D QSH effect in g-MoS2 originates from the pure d-d band inversion, different from the conventional band inversion between s-p, p-p or d-p orbitals. The new polymorph greatly enriches the TMD family and its stabilities are confirmed using phonon spectrum analysis. In particular, its porous structure endows it with the potential for efficient gas separation and energy storage applications.