Band Inversion Mechanism Research Articles

Topologically nontrivial phase in Na2CuX (X= As, Sb, Sn and Bi) full Heusler compounds: Insights from DFT-based computer simulation

The inspection of materials supporting topological excitations is one of the prospective areas of condensed matter physics. This paper is devoted to studying the possibility of the existence of topological phases in Na2CuX (X= As, Sb, Sn and Bi) full Heusler compounds using the FP-LMTO (Full-Potential Linear Muffin-Tin Orbital) method with and without spin-orbit coupling (SOC). The study of structural properties has found that these materials are energetically stable in the Hg2CuTi type structure. Also, formation energy calculations have shown that these materials are convenient to manufacture. Otherwise, band structure calculations show that these materials exhibit the behavior of non-trivial topological materials with a semi-metallic nature. The obtained results in this study, generally, showed that SOC is not a primary cause of the band inversion mechanism.

Band inversion induced large-gap quantum spin Hall states in III-Bi-monolayer/ SiO2

We extend the ${p}_{x}\ensuremath{-}{p}_{y}$ large-gap scenario to the band inversion systems and exemplify the mechanism with a family of III-Bi honeycomb monolayers on $\mathrm{Si}{\mathrm{O}}_{2}$, which can be the next generation of large-gap quantum spin Hall (QSH) systems. First, it suggests a topological gap of the same order as the current record kept of bismuthene/SiC(0001). Second, the band inversion mechanism in which these QSH insulators originate is qualitatively distinct from the Kane-Mele paradigm. Our work demonstrates that the ${p}_{x}\text{\ensuremath{-}}{p}_{y}$ scenario can be utilized to promote large-gap QSH states with both Kane-Mele and band inversion mechanisms, providing an efficient building principle for future topological device construction.

Angular momentum invoked band inversions in mirror symmetry protected topological states

The notion of a band inversion provides an intuitive physical paradigm for understanding the electronic band topology. Here we study the general band inversion mechanism, which exploits local atomic orbitals and lattice symmetry, in mirror protected topological crystalline insulators (TCIs). Based on low-energy effective theory analysis, we find that for these mirror protected TCIs, the topological invariant (i.e., the mirror Chern number ${\mathcal{C}}_{M}$) is determined by the difference of total magnetic quantum numbers ${m}_{j}$ of orbitals involved in the band inversion: $|{\mathcal{C}}_{M}|=|\mathrm{\ensuremath{\Delta}}{m}_{j}|$. This angular-momentum criterion is further verified by the atomic tight-binding model calculations in two-dimensional (2D) crystalline, quasicrystalline, and disordered lattices. Moreover, such an angular momentum invoked band inversion (AMBI) is also extendable to 3D lattices and gives rise to topological semimetals with Dirac points in the bulk and double Fermi arcs on surfaces. As a concrete material example, we further predict that the Ba monolayer is an AMBI-induced TCI by first-principles calculations. In addition, we also show that a large number of previously proposed TCI materials satisfy the AMBI mechanism. Our findings not only provide an alternative understanding of mirror protected band topology but also offer useful guidance for designing or engineering mirror protected TCI materials.

Generic Orbital Design of Higher-Order Topological Quasicrystalline Insulators with Odd Five-Fold Rotation Symmetry.

In addition to crystals, topological phases in quasicrystals and disorder systems have drawn increasing attention lately. Here, we propose a generic double band-inversion mechanism underlying the higher-order topological phase in quasicrystals, that is.,"higher-order topological quasicrystalline insulator" (HOTQI), which exploits local atomic orbital and lattice symmetries. It is generally applicable to both quasicrystals and crystals with either odd-rotational (OR) or even-rotational symmetry (ERS), different from previous HOTI mechanisms whose applicability is limited by symmetry types. The HOTQI is characterized by topological corner states at the nonordinary corners of pentagonal (octagonal) samples of five-fold (eight-fold) quasicrystals, which violate the translational invariance and ordinary crystalline symmetries. The role of quasicrystalline symmetry, the robustness against symmetry breaking, and possible experimental realizations are discussed. Our findings not only provide a concrete example of HOTQIs that is incompatible with classical crystallographic symmetry but also offer useful guidance to the search of higher-order topological materials and metamaterials.

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.

Insight View of Topological Nontrivial Nature in the Novel Alkali Metal–Based Quaternary Heusler Compounds via Ab Initio Calculations

In this paper, we have highlighted a first-principles study of the structural stability and electronic behavior of the novel alkali metal–based quaternary Heusler compounds (LiNaCuAs, LiKCuAs, NaKCuAs, LiRbCuAs, NaRbCuAs, and KRbCuAs), using the full-potential linear muffin-tin orbital (FP-LMTO) method. The obtained results show that our compounds are energetically more stable in the Hg2CuTi-type structure. The calculated electronic properties with and without spin-orbit coupling (SOC) effects indicate that the majority of compounds naturally present a band inversion order which confirmed the topological nontrivial behavior of these materials. In addition, our results show that SOC is not a primary cause of the band inversion mechanism. The obtained values of the calculated formation energy confirm the physical stability of these compounds against decomposition, and they can be passed in fabrication level.

Aperiodic topological crystalline insulators

Topological crystalline insulators (TCIs) are usually described with topological protection imposed by the crystalline symmetry. In general, however, the existence of TCI states does not necessitate the periodicity of crystals as long as an essential lattice symmetry can be identified. Here we demonstrate the compatibility of TCIs with aperiodic systems, as exemplified by an octagonal quasicrystal. The aperiodic TCIs we proposed are attributed to a band inversion mechanism, which inverts states with the same parity but opposite eigenvalues of a specific symmetry (such as mirror reflection). The nontrivial topology is characterized by a nonzero integer ``mirror Bott index.'' Moreover, we demonstrate that the topological edge states and quantized conductance of the aperiodic TCI, which are robust against disorder, can be effectively manipulated by external electric fields. Our findings not only provide a better understanding of electronic topology in relation to symmetry but also extend the experimental realization of topological states to much broader material categories beyond crystals.

Turning copper metal into a Weyl semimetal

A search for new topological quantum systems is challenging due to the requirement of nontrivial band connectivity that leads to protected surface states of electrons. Progress in this field was primarily due to a realization of a band inversion mechanism between even and odd parity states that was proven to be very useful in both predicting many such systems and our understanding of their topological properties. Despite many proposed materials that assume the band inversion between $s$ and $p$ (or $p/d$, $d$/$f$) electrons, here, we explore a different mechanism where the occupied $d$ states subjected to a tetrahedral crystal field produce an active ${t}_{2g}$ manifold behaving as a state with an effective orbital momentum equal to $\ensuremath{-}1$, and pushing ${j}_{\mathrm{eff}}=1/2$ doublet at a higher energy. Via hybridization with nearest-neighbor orbitals realizable, e.g., in a zinc-blende structural environment, this allows a formation of odd parity state whose subsequent band inversion with an unoccupied $s$ band becomes possible, prompting us to look for the compounds with ${\mathrm{Cu}}^{+1}$ ionic state. Chemical valence arguments coupled to a search in the materials database of zinc-blende-like lattice space groups ${T}_{d}^{2}$ ($F\overline{4}3m$) lead us to systematically investigate electronic structures and topological properties of CuY ($Y=\text{F}$, Cl, Br, I) and $\mathrm{Cu}X\mathrm{O}$ ($X=\text{Li}$, Na, K, Rb) families of compounds. Our theoretical results show that CuF displays a behavior characteristic of an ideal Weyl semimetal with 24 Weyl nodes at the bulk Brillouin zone. We also find that other compounds, CuNaO and CuLiO, are the $s\text{\ensuremath{-}}d$ inversion-type topological insulators. Results for their electronic structures and corresponding surfaces states are presented and discussed in the context of their topological properties.

Unconventional band inversion and intrinsic quantum spin Hall effect in functionalized group-V binary films

Adequately understanding band inversion mechanism, one of the significant representations of topological phase, has substantial implications for design and regulation of topological insulators (TIs). Here, by identifying an unconventional band inversion, we propose an intrinsic quantum spin Hall (QSH) effect in iodinated group-V binary (ABI2) monolayers with a bulk gap as large as 0.409 eV, guaranteeing its viable application at room temperature. The nontrivial topological characters, which can be established by explicit demonstration of Z2 invariant and gapless helical edge states, are derived from the band inversion of antibonding states of px,y orbitals at the K point. Furthermore, the topological properties are tunable under strain engineering and external electric field, which supplies a route to manipulate the spin/charge conductance of edge states. These findings not only provide a new platform to better understand the underlying origin of QSH effect in functionalized group-V films, but also are highly desirable to design large-gap QSH insulators for practical applications in spintronics.

Acoustic topological insulator and robust one-way sound transport

Discovery of novel topological orders of condensed matters is of a significant interest in both fundamental and applied physics due to the associated quantum conductance behaviors and unique symmetry-protected backscattering-immune propagation against defects, which inspired similar fantastic effects in classical waves system, leading to the revolution of the manipulation of wave propagation. To date, however, only few theoretical models were proposed to realize acoustic topological states. Here, we theoretically and experimentally demonstrate a two dimensional acoustic topological insulators with acoustic analogue of quantum spin Hall Effect. Due to the band inversion mechanism near the double Dirac cones, acoustic one-way pseudospin dependent propagating edge states, corresponding to spin-plus and spin-minus, can be observed at the interface between two graphene-like acoustic crystals. We have also experimentally verified the associated topological immunity of such one-way edge states against the different lattice defects and disorders, which can always lead to inherent propagation loss and noise. We show that this unique acoustic topological phenomenon can offer a new promising application platform for the design of novel acoustic devices, such as one-way sound isolators, acoustic mode switchers, splitters, filters etc.

Interface orbital engineering of large-gap topological states: Decorating gold on a Si(111) surface

Intensive effort has recently been made in search of topological insulators (TIs) that have great potential in spintronics applications. In this paper, a novel concept of overlayer induced interfacial TI phase in conventional semiconductor surface is proposed. The first-principles calculations demonstrate that a $p$-band-element $X$ $(X=\text{In}$, Bi, and Pb) decorated $d$-band surface, such as Au/Si(111) surface $[X$/Au/Si(111)] of an existing experimental system, offers a promising prototype for TIs. Specifically, Bi/Au/Si(111) and Pb/Au/Si(111) are identified to be large-gap TIs. A $p\text{\ensuremath{-}}d$ band inversion mechanism induced by growth of $X$ in the Au/Si(111) surface is revealed to function at different coverage of $X$ with different lattice symmetries, suggesting a general approach of interface orbital engineering of large-gap TIs via tuning the interfacial atomic orbital position of $X$ relative to Au.

Band inversion at critical magnetic fields in a silicene quantum dot

We have found out that the band inversion in a silicene quantum dot (QD), in perpendicular magnetic B and electric fields, drastically depends on the strength of the magnetic field. We study the energy spectrum of the silicene QD where the electric field provides a tunable band gap Δ. Boundary conditions introduce chirality, so that negative and positive angular-momentum m zero Landau level (ZLL) edge states show a quite different behavior regarding the band-inversion mechanism underlying the topological insulator transition. We show that, whereas some ZLLs suffer band inversion at for any B > 0, other ZLLs only suffer band inversion above critical values of the magnetic field at nonzero values of the gap.

Quantum anomalous Hall effect and related topological electronic states

Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically-doped topological insulator completed a quantum Hall trio---quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). On the theoretical front, it was understood that intrinsic AHE is related to Berry curvature and U(1) gauge field in momentum space. This understanding established connection between the QAHE and the topological properties of electronic structures characterized by the Chern number. With the time reversal symmetry broken by magnetization, a QAHE system carries dissipationless charge current at edges, similar to the QHE where an external magnetic field is necessary. The QAHE and corresponding Chern insulators are also closely related to other topological electronic states, such as topological insulators and topological semimetals, which have been extensively studied recently and have been known to exist in various compounds. First-principles electronic structure calculations play important roles not only for the understanding of fundamental physics in this field, but also towards the prediction and realization of realistic compounds. In this article, a theoretical review on the Berry phase mechanism and related topological electronic states in terms of various topological invariants will be given with focus on the QAHE and Chern insulators. We will introduce the Wilson loop method and the band inversion mechanism for the selection and design of topological materials, and discuss the predictive power of first-principles calculations. Finally, remaining issues, challenges and possible applications for future investigations in the field will be addressed.

Exploration and prediction of topological electronic materials based on first-principles calculations

Abstract

Topological insulators with unexpectedly HgTe-like band inversion in hexagonal wurtzite-type binary compounds

By using first-principles calculations, we propose a new topological insulator family in hexagonal wurtzite-type binary compounds. As a result, we found that two compounds AuI and strained-AgI are three-dimensional topological insulators with a naturally opened band gap at the Fermi level. By considering the band inversion mechanism, this new family of topological insulators shows an unexpectedly HgTe-like, i.e., band inversion. These findings suggest that, in these wurtzite-type compounds, the spin-orbit coupling may not play a crucial role in the band inversion mechanism; on the contrary, it is mainly responsible for the formation of the global band gaps. We further theoretically explore the feasibility of tuning the topological order of the wurtzite compounds AuI and AgI with two types of strains (hydrostatic and uniaxial). The results indicate that the uniaxial strain can significantly influence the band inversion behavior and the underlying physical mechanism is discussed.

Band inversion mechanism in topological insulators: A guideline for materials design

Alteration of the topological order by band inversion is a key ingredient of a topologically nontrivial material. Using first-principles calculations for HgTe, PtScBi, and Bi${}_{2}$Se${}_{3}$, we argue that it is not accurate to ascribe the band inversion to the spin-orbit coupling. Instead, scalar relativistic effects and/or lattice distortions are found to be essential. Therefore, the search for topologically nontrivial materials should focus on band shifts due to these mechanisms rather than spin-orbit coupling. We propose an effective scheme to search for new topological insulators.