Topological Invariant Z2 Research Articles

Emergence of topological phase and non-trivial surface states in rare-earth semimetal GdSb with pressure

Abstract We study the evolution of band topology under external pressure in rare-earth gadolinium mono-antimonide (GdSb) using first-principles calculations. This material crystallizes in a rocksalt-type structure and shows a structural phase transition (SPT) to a CsCl-type structure at 26.1 GPa. The phonon dispersions are analyzed to ascertain the dynamical stability of this material. We use hybrid density functional theory with the inclusion of spin–orbit coupling to investigate the structural, electronic, and topological phase transitions (TPTs). At ambient pressure, GdSb shows a topologically trivial state which is in agreement with existing experimental reports. The first TPT is observed at 6 GPa of hydrostatic pressure (at the high symmetry X-point) which is verified with the help of single-band inversion and surface state analysis along the (001) plane. The non-zero value of the first Z2 topological invariant and the presence of the Dirac cone also confirm the topological phase of this material. A further increase in pressure to 12 GPa results in two band inversions at Γ- as well as X-points, which corresponds to the trivial nature of GdSb. The same is also verified with (0; 000) values of Z2 topological invariants and a pair of Dirac cones in surface states. It is noted that the crystal symmetries are preserved throughout the study and the TPT values are much lower than the SPT pressure, i.e. 26.1 GPa.

Prediction of charge density wave, superconductivity and topology properties in two-dimensional Janus 2H/1T-WXH (X = S, Se)

The multiple properties in two-dimensional (2D) materials have attracted widespread attention. Utilizing first-principles calculations, we theoretically predict four 2D transition metal Janus sulfide hydrides, named 2H/1T-WXH (X = S, Se). The 2H-WSH and 2H–WSeH demonstrate superconductivity with critical temperatures (Tc) of 13.4 K and 11.4 K, respectively. Whereas 1T-WSH and 1T-WSeH display charge density wave (CDW) properties arising from electron-phonon coupling (EPC). It is noteworthy that the CDW can be suppressed through biaxial compressive strain, leading to the emergence of superconductivity with Tc of 12.2 K and 11.9 K for 1T-WSH (−2 %) and 1T-WSeH (−4 %), respectively. The superconductivity of the above materials originates from the coupling between W-3d electrons and the low-frequency vibrations of W. Interestingly, the 2H–WSeH and 1T-WSeH (−4 %) display nontrivial topological properties, as evidenced by topological invariant Z2 and the presence of edge states. Our research not only provides theoretical guidance for further exploring 2D Janus materials, but also provides ideas for the competition of multiple orders in 2D materials.

Topological Quantum Transport Characteristic by Three‐band Correlation Mechanism in 2D SnSe

AbstractUnderstanding electron quantum transport and their coupling interactions in 2D matrix is crucial for manipulating and designing more efficient energy conversion devices, especially in the context of spin transport. Here, we systematically calculate the electronic dispersion properties which the synergistic interaction of the three‐band accounted for the topological transport of edge correlated electrons. The helical state protected by the topology appears at the boundary, accompanied by the upward movement (∼0.2 eV) of the helical point caused by the excitation and the loop channel, which the weak braiding effect reveal local strongly correlated interactions between the boundary electrons. In addition, we also introduce spin Hall conductance and Z2 topological invariants to describe the election dispersion of the topological transport. This provides more possibilities for the realization of topological quantum computing application.

Topological phase transition and tunable surface states in YBi

A unique co-existence of extremely large magnetoresistance (XMR) and topological characteristics in non-magnetic rare-earth monopnictides has stimulated intensive research on these materials. Yttrium monobismuthide (YBi) has been reported to exhibit XMR up to 105% but its topological properties still need clarification. Here we use the hybrid density functional theory to probe the structural, electronic, and topological properties of YBi in detail. We observe that YBi is topologically trivial semimetal at ambient pressure which is in accordance with reported experimental results. The topological phase transitions i.e. trivial to non-trivial are obtained with volumetric pressure of 6.5 GPa and 3% of epitaxial strain. These topological phase transitions are well within the structural phase transition of YBi (24.5 GPa). The topological non-trivial state is characterized by band inversions among Y-d band and Bi-p band at Γ- and X-point which is further verified with the help of surface band structure along (001) plane. The Z2 topological invariants are calculated with the help of product of parities and evolution of Wannier charge centers. The occurrence of non-trivial phase in YBi with a relatively small epitaxial strain, which a thin film geometry can naturally have, make it an ideal candidate to probe inter-relationship between XMR and non-trivial topology.

The quantum spin Hall insulator with large bandgap in functionalized AlBi monolayer

The quantum spin Hall (QSH) insulator exhibits various interesting physical properties. Therefore, researchers have been seeking QSH insulators with large bandgaps suitable for room temperature applications. Here, based on first-principles calculations, we predict that the chlorine atom functionalized AlBi monolayer forms a topological insulator with a large bandgap (Eg = 0.215 eV). Chlorination and SOC effect induce AlBi(Cl)2 band inversion, and phonon spectra calculations demonstrate excellent dynamic stability for AlBi(Cl)2. The Z2 topological invariants, as well as the topological nontrivial edge states further confirm these findings. In addition, we applied the biaxial strains ranging from −5% to 5% to the monolayer, revealing a topological phase transition at −3%, resulting in the emergence of a normal insulator. These interesting features suggest that chlorinated AlBi is a promising material for room temperature spintronic devices.

Honeycomb Sb layers on Cu(111) and parities of the surface states

The performed DFT study of the electronic structure of honeycomb Sb monolayer adsorbed on the Cu(111) surface has confirmed previous observations of significant role of tensile strain and related reduced buckling of adsorbed layer. The simulated STM pictures are perfectly consistent with those observed in experiment. We show that a significant band mixing with the substrate, which leads to an absence of occupied surface states at M point, questions applicability of the method of determination of the topological invariant Z2 by means of estimates of the products of the parity eigenvalues. Hence, since the adsorption interaction with a metal surface is rather strong, the transformations of the bands of free honeycomb Sb layers with increasing lattice constants, which was recently suggested to cause the transition to the topological insulator state for certain range of the tensile strain, do not directly correspond to the changes which occur for adsorbed layers.

Software implementation for calculating Chern and [formula omitted] topological invariants of crystalline solids with WIEN2k all-electron density functional package

We present two modules that expand functionalities of the all-electron full-potential density functional theory package WIEN2k for computation of the Chern and Z2 topological invariants. Characterization of topological properties relies on two methods: computing an evolution of hybrid Wannier charge centers for Z2 topological insulators (construction of maximally localized Wannier functions is not needed) and computing the Berry phase for a multitude of Wilson loops that discretize a 2D Brillouin zone for Chern insulators as well as for mapping the Berry curvature. The implementation is validated by testing on well-known materials that feature topologically non-trivial electronic states.

Topological nature of large bulk band gap materials Sr3Bi2 and Ca3Bi2

Topological materials are an emerging class of materials attracting the attention of the scientific community due to their potential applications in the fields of spintronics and quantum computing. Using first-principles calculations, the structural, electronic, and topological properties of Sr3Bi2 and Ca3Bi2 compounds without and with spin–orbit coupling are investigated. In the absence of spin–orbit coupling, the projected bulk band structure revealed that the Sr3Bi2 compound host a type-I Dirac point along the F-Γ direction. Since the compound possesses time-reversal and space-inversion symmetries, this Dirac point is associated with the nodal line. The existence of a type-I nodal ring around the Γ-point in the kz = 0 planes, as well as a drumhead-like surface state within the nodal ring, suggested that Sr3Bi2 is a type-I nodal-line semimetal with no spin–orbit coupling. The inclusion of spin–orbit coupling introduced an energy gap of 0.36 eV between the valence band and conduction band at Dirac point. The topological surface states forming a Dirac cone between the bulk bandgap for (001) surface of Sr3Bi2 compound is calculated with spin–orbit coupling. The Z2 topological invariants (1;000), as calculated by using parity product criteria, suggested that Sr3Bi2 is a strong topological insulator. Ca3Bi2, another compound with a similar crystal structure, is also predicted to behave similarly to Sr3Bi2 compound without and with spin–orbit coupling. This research broadens the application of topological insulators and existing platforms for developing novel spintronic devices.

Topological properties of MoP[formula omitted]N[formula omitted] (x = 0, 0.25, 0.5, 0.75, 1) compounds: A density functional approach

Triply Degenerate Point (TDP) fermions in tungsten–carbide-type materials such as MoP which represent new topological states of quantum matter, have generated great interest recently. However, the TDPs in these materials are found to be far below the Fermi level (∼ −1.5eV) leading to the TDP fermions having less contribution to low-energy quasiparticle excitations. Here, we theoretically investigate the existence of TP fermions with TDPs close to the Fermi level in MoN, which has the same structure as MoP, and the ternary MoP1−xNx ordered alloys which their crystal structure is defined by replacing P atoms by N atoms in MoP compound. The topological properties of MoP1−xNx (x = 0, 0.25, 0.5, 0.75, 1) ordered alloys are systematically investigated by combining first-principles calculations and Wannier tight-binding analysis. The obtained Wannier Charge Centers (WCCs) are applied to calculate the topological invariant Z2 number. Our calculations show that hexagonal MoP, MoP0.75N0.25, MoP0.25N0.75, and MoN compounds are topological semimetals hosting triply degenerate nodal points resulting from band crossing between degenerate and nondegenerate bands along the high-symmetry directions of the Brillouin Zone, being protected by crystalline symmetries. Among these compounds, the triple degenerate points in MoP0.75N0.25 are much closer to the Fermi level. MoP0.75N0.25 hosts some points slightly above (42 meV, 73 meV and 87 meV) the Fermi energy. On the other hand, our ab initio calculations suggest that the MoP0.5N0.5 compound with orthorhombic structure does not host any triple degenerate point. It hosts a multitude of topological features including Weyl Points and nodal lines. The calculations indicate that these nodal lines are located in the vicinity of Fermi level.

Two-dimensional dual topological insulator in hexagonal IrO

Double topological insulators (DTIs) are systems with two kinds of nontrivial topological indexes. Three-dimensional materials with dual-topological character (DTC) have received extensive research, whereas two-dimensional (2D) DTIs have received less attention. In this paper, we propose a new 2D DTI IrO material by using first-principles calculations. Further calculation reveal it is energetically, dynamically, and mechanically stable. There is a direct band gap in the electronic band structures with and without spin–orbit coupling (SOC), and a SOC-induced band inversion occurs at the M point. Based on the symmetry analysis and the k · p model, the topological invariant Z2 and mirror Chern number C m are determined to be nontrivial. The DTC is supported further by the different behavior of the edge states with and without the mirror symmetry breaking. Our theoretical prediction broadens the domain of candidate 2D DTIs in terms of topological manifestations as well as material realization.

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.

First-principles study on the electronic structures and topological properties of Bi(110)/IV-VI and Bi(110)/V-V van der Waals heterostructures

Based on the first-principles calculations, numerous theoretical research efforts have been made to exploit electronic structures and topological properties in Bi(110) and IV-VI groups (Sn0.5Se0.5, Sn0.5Se0.25Te0.25, Sn0.5Te0.5), V-V groups (Sb0.5As0.5, Bi0.5As0.5, α-Bi0.5Sb0.5, α2-Bi0.5Sb0.5) substrates heterostructures. Molecular dynamics confirmed that the proposed bilayer heterostructures are stable. The electronic analysis results show that the valence and conduction bands near the Fermi level are mainly contributed by Bi(110). More importantly, Bi(110)/Sn0.5Te0.5 and Bi(110)/Sn0.5Se0.25Te0.25 have non-topological properties. However, when applying 20% biaxial tensile strain, both of them have nontrivial Z2 topological invariants and topological edge states. Our findings not only breathe new power into the family of 2D materials but also highlight these 2D semiconductors as attractive materials potential for future electronics and topological devices.

New room-temperature 2D hexagonal topological insulator OsC: First Principle Calculations

The structural, electronic and topological characteristics of the two-dimensional (2D) binary compound OsC are investigated using DFT simulations. Phonon dispersion and molecular dynamics calculations confirm a strong structural, dynamic and thermal stability of the osmium carbide monolayer in hexagonal planar geometry where C−Os hybridization is sp2. Electronic band structures attest that OsC is a zero-gap semiconductor with the valence band coming mainly from osmium d orbitals and some contributions from carbon p orbitals. By tuning on the spin orbit coupling (SOC), the gap ΔSOC of 141 meV, corrected to 220 meV using HSE approximations, opens in the vicinity of the Γ point with the occurrence of a band inversion between d32−Os and d52−Os revealing that our system is a nontrivial QSH insulator with topological invariant Z2=1 and topological edge states. Our study shows that the room-temperature 2D topological insulator OsC is a potential material for possible applications in nanoelectronic and spintronic devices.

Topological phase transitions on the square-octagon lattice driven by the Rashba spin-orbit coupling and staggered potential

We propose that the topological phase transitions can occur in the square-octagon lattice, when the Rashba spin-orbit coupling and the staggered potential are taken into account. By means of the Fukui-Hatsugai method, topological invariant Z2 is evaluated and the phase diagram is presented as a function of the Rashba spin-orbit coupling and the staggered potential. We find that the square-octagon lattice can support different phases, such as semimetal, normal insulator and topological insulator. Particularly, the competition between the Rashba spin-orbit coupling and staggered potential can lead to the topological phase transition for all the filling fractions. To clearly support the identification of topological nontrivial phase, helical edge states are given numerically, the number of which is demonstrated by the spin chern number. Finally, we analyze and discuss the density distribution and spin polarization to further confirm the topological properties of the system.

Prediction of tetragonal monolayer CuN with a quantum spin Hall state

Abstract Two-dimensional (2D) quantum spin Hall (QSH) insulator are promising candidates for miniaturized electronic and dissipationless transport devices. The bottleneck preventing applications from QSH phase, however, is lack of feasible 2D materials in experiments so far. By using first-principles calculations, here we propose a realistic 2D QSH phase in tetragonal CuN, which is dynamically and mechanically stable. Band structure analysis reveals that it is a nontrivial QSH phase robust against external strains. The origin of QSH effect can be identified by a px-pz band inversion, topological invariant Z2, and helical edge states within the bulk gap. Also, a heterostructure composed of CuN deposited on semiconducting AlAs substrate remains topologically nontrivial with a sizable gap. These findings provide a promising platform to design new QSH insulators in tetragonal lattices, which show potential applications in multifunctional spintronics devices.

Insight into the topological phase and elastic properties of halide perovskites CsSnX3 (X = l, Br, Cl) under hydrostatic pressures

Topological materials are considered as a novel quantum state of matter, which can be characterized by symmetry-protected Dirac interfacial states, and exhibit an exotic phenomenon when combined with the other phases. The topological phase in the perovskite structures is important since it can provide various heterostructure interfaces with multifunctional properties. Alpha-(α-) phase cesium-based halide perovskites CsSnX3 (X = I, Br, Cl) can be considered as a promising candidate for topological semiconductors under hydrostatic pressures. The narrow bandgap of these compounds (≤1.83 eV) has made them interesting materials for the electronic, optoelectronic, and photovoltaic applications. In the current research, we systematically carry out first-principles density functional theory (DFT) to study the effects of hydrostatic pressure on the electronic structure of CsSnX3 (X = I, Br, Cl) compounds. The topological phase of these compositions is investigated using the Fu–Kane and Wilson loop methods in order to identify the Z2 topological invariants for each structure. The topological surface states (TSSs) of the (001) plane of these compounds are investigated using the semi-infinite Green's function. These TSSs guarantee the nontrivial nature of CsSnX3 compounds under pressure. With respect to the engineering applications, three important mechanical properties of these compounds including elastic anisotropy, ductility, and hardness are also investigated.

Discovery of Superconductivity in 2M WS2 with Possible Topological Surface States.

Recently the metastable 1T'-type VIB-group transition metal dichalcogenides (TMDs) have attracted extensive attention due to their rich and intriguing physical properties, including superconductivity, valleytronics physics, and topological physics. Here, a new layered WS2 dubbed "2M" WS2 , is constructed from 1T' WS2 monolayers, is synthesized. Its phase is defined as 2M based on the number of layers in each unit cell and the subordinate crystallographic system. Intrinsic superconductivity is observed in 2M WS2 with a transition temperature Tc of 8.8 K, which is the highest among TMDs not subject to any fine-tuning process. Furthermore, the electronic structure of 2M WS2 is found by Shubnikov-de Haas oscillations and first-principles calculations to have a strong anisotropy. In addition, topological surface states with a single Dirac cone, protected by topological invariant Z2 , are predicted through first-principles calculations. These findings reveal that the new 2M WS2 might be an interesting topological superconductor candidate from the VIB-group transition metal dichalcogenides.

Oxygenation‐Induced Two‐Dimensional Topological Insulators in Antimony Arsenide

This study investigates the stability, electronic structure, and topological property of a fully oxygenated blue‐antimony arsenide system based on first principle calculations. Our results demonstrate that the functionalized system is energetically, dynamically, and mechanically stable. Without the inclusion of spin–orbit coupling (SOC), a semimetal nature is observed with the degenerate valence and conduction bands at the Γ point. The SOC opens a large bulk gap of 252 meV, which makes it possible to work at room temperature. The nontrivial topological feature is confirmed by the Z2 topological invariant Z2 = 1 and the gapless edge states inside the bulk gap. This finding enriches the family of 2D topological insulators, deepens the insight into the quantum Hall effect, and provides some theoretical ideas for preparing high‐speed and dissipationless spintronic devices.

Quantum fluctuation in thermopower at the topological phase transition in CaSrX (X: Si, Ge, Sn, Pb) studied from first principles theory

The present density functional calculations propose the compounds CaSrX (X: Si, Ge, Sn, Pb) as strong topological insulators, with appreciable thermoelectric properties. Emergence of Dirac semi-metallic states has been observed in CaSrX (X: Si, Ge, Sn, Pb), which is induced by uni-axial strain along ‘b’ axis. CaSrSi and CaSrGe evolved as normal semiconductors with uni-axial strain. The trivial and non-trivial topological phases are evaluated by band inversion and Z2 topological invariants. A comprehensive analysis of thermopower, electrical conductivity scaled by relaxation time at these Dirac semi-metallic states exposes the highly oscillating behaviour, which gives insight to quantum oscillations driven by uni-axial strain. Further the thermoelectric properties at strong topological insulating states and normal insulating states have been summarized, which reveals the potential thermoelectric properties of these materials.

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.