Nontrivial Topological Insulator Research Articles

Stability of 2D Crystals from Tessellation

AbstractReticular chemistry has been a cornerstone in the design of novel 2D materials. Despite numerous possibilities for topological arrangements, only a few with high symmetry can form stable networks. Here, starting from 2D carbons, four types of highly stable tessellations are discovered, which consist of chains of non‐hexagonal rings separated by hexagonal ribbons. A modified Read–Shockley model is established to perfectly describe the stability of these highly stable frameworks, which is based on the interaction between non‐hexagonal rings. Moreover, these four types of tessellations and the modified Read–Shockley model are found to be of general validity in designing highly stable 2D materials, which is verified by the calculations on polymorphs of boron nitride and molybdenum disulfide. Besides, among the studied 2D carbon allotropes, two semi‐metallic structures with highly anisotropic Dirac cones and one semimetal with a Dirac nodal line at the Fermi level are discovered, as protected by their D2h symmetry. Spin‐orbital coupling is further found to open small bandgaps for these three Dirac structures, making them nontrivial topological insulators. The in‐depth understanding of the stability of 2D crystals in this study provides a new way for rational design of 2D crystals that may show peculiar electronic structures.

Exploring interacting topological insulator in the extended Su-Schrieffer-Heeger model

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.

Magnetic field switching of Weyl semimetal associated with quantum criticality in one-dimensional extended Su-Schrieffer-Heeger chain

Graphene/silicon nanoribbons (G/SiNRs) provide low-dimensional platforms to engineer the topological characters for carbon/silicon-based electronics. Herein, we propose a one-dimensional (1D) extended Su-Schrieffer-Heeger (SSH) model to describe the G/SiNRs with a superlattice consisting of two interacting dimers, in which the topological quantum phase transition (QPT) and quantum criticality are investigated. The trivial band insulator transition into a nontrivial topological insulator via a critical Dirac semimetal is revealed, the self-duality of which is manifested by the zero value of Grüneisen ratio (GR) irrelevant of temperature. In a magnetic field, the time-reversal symmetry is broken such that the Weyl semimetal appears and is switched by a critical quadratic contact point semimetal with gap closing, at which the quantum criticality is not self-dual with GR Γ∼±T−1. Furthermore, the quantum critical scaling is done to analyze the quantum criticality, which provides a new clue to detect the QPT. The low-temperature specific heat demonstrates the low-lying excitation of gapped and gapless topological quantum phases explicitly.

Rashba Splitting and Electronic Valley Characteristics of Janus Sb and Bi Topological Monolayers.

Janus Sb and Bi monolayers as a new class of 2D topological insulator materials, which could be fulfilled by asymmetrical functionalizations with methyl or hydroxyl, are demonstrated by first-principles spin–orbit coupling (SOC) electronic structure calculations to conflate nontrivial topology, Rashba splitting and valley-contrast circular dichroism. Cohesive energies and phonon frequency dispersion spectra indicate that all Janus Sb and Bi monolayers possess a structural stability in energetic statics but represent virtual acoustic phonon vibrations of the hydrogen atoms passivating on monolayer surfaces. Band structures of Janus Sb and Bi monolayers and their nanoribbons demonstrate they are nontrivial topological insulators. Rashba spin splitting at G point in Brillouin zone of Janus Bi monolayers arises from the strong SOC px and py orbitals of Bi bonding atoms together with the internal out-of-plane electric field caused by asymmetrical functionalization. Janus Sb and Bi monolayers render direct and indirect giant bandgaps, respectively, which are derived from the strong SOC px and py orbitals at band-valley Brillouin points K and K′ where valley-selective circular dichroism of spin valley Hall insulators is also exhibited.

Half-topological state in magnetic topological insulators

We predict a novel topological state, half-topological state, in magnetic topological insulators. The topological state is characterized by different topologies of electrons with different spin orientations, i.e., electrons with one spin orientation occupy a nontrivial topological insulating state, while electrons with opposite orientation occupy another insulating state with trivial topology. We demonstrate the occurrence of the half-topological state in magnetic topological insulators by employing a minimal model. The minimal model is a combination of the spinful Haldane and the double-exchange models. The double-exchange processes maintain a spontaneous magnetic ordering, while the next-nearest-neighbor hopping in the Haldane model gives rise to a nontrivial topological insulator. The minimal model is studied by applying the dynamical mean field theory. It is found that the long-range antiferromagnetic ordering drives the system from either topological or topologically trivial antiferromagnetic insulator to the half-topological state, and finally to topologically trivial antiferromagnetic insulator. The equations for the topological phase transitions are also explicitly derived.

Topological Properties in Strained Monolayer Antimony IodideSupported by the National Natural Science Foundation of China (Grant Nos. 11974076 and 61804030), and the Key Project of Natural Science Foundation of Fujian Province (Grant No. 2021J02012).

Two-dimensional (2D) topological insulators present a special phase of matter manifesting unique electronic properties. Till now, many monolayer binary compounds of Sb element, mainly with a honeycomb lattice, have been reported as 2D topological insulators. However, research of the topological insulating properties of the monolayer Sb compounds with square lattice is still lacking. Here, by means of the first-principles calculations, a monolayer SbI with square lattice is proposed to exhibit the tunable topological properties by applying strain. At different levels of the strain, the monolayer SbI shows two different structural phases: buckled square structure and buckled rectangular structure, exhibiting attracting topological properties. We find that in the buckled rectangular phase, when the strain is greater than 3.78%, the system experiences a topological phase transition from a nontrivial topological insulator to a trivial insulator, and the structure at the transition point actually is a Dirac semimetal possessing two type-I Dirac points. In addition, the system can achieve the maximum global energy gap of 72.5 meV in the topological insulator phase, implying its promising application at room temperature. This study extends the scope of 2D topological physics and provides a platform for exploring the low-dissipation quantum electronics devices.

Topological classification of the single-wall carbon nanotube

The single-wall carbon nanotube (SWNT) can be a one-dimensional topological insulator, which is characterized by a $\mathbb{Z}$-topological invariant, winding number. Using the analytical expression for the winding number, we classify the topology for all possible chiralities of SWNTs in the absence and presence of a magnetic field, which belongs to the topological categories of BDI and AIII, respectively. We find that the majority of SWNTs are nontrivial topological insulators in the absence of a magnetic field. In addition, the topological phase transition takes place when the band gap is closed by applying a magnetic field along the tube axis, in all the SWNTs except armchair nanotubes. The winding number determines the number of edge states localized at the tube ends by the bulk-edge correspondence, the proof of which is given for SWNTs in general. This enables the identification of the topology in experiments.

Flexible quantum spin Hall insulator in O-functionalized GaSe monolayer

The quantum spin Hall (QSH) insulators possess potential applications in dissipationless spintronics. With the rapid development of flexible electronics, it is highly desirable to search or design high-performance QSH insulators with excellent flexibility and large bandgap, which is still a huge challenge. Here, using first-principles calculations, we report that surface oxygen functionalization can transform two-dimensional (2D) GaSe monolayer from a trivial insulator to a nontrivial topological insulator with superior stretchability. The fully O-functionalized GaSe monolayer, GaSeO, exhibits a sizable QSH gap of 178 meV, in which the topological nature is characterized by the nontrivial Z2 topological invariant and the topological edge states. The nontrivial band topology originates from the s-p band inversion in the crystal field. Remarkably, the GaSeO monolayer shows isotropic mechanical flexibility and can sustain large strains of up to 26%, beyond graphene and 2D flexible Ti2C. Furthermore, the QSH state of GaSeO is robust against small elastic strains. The discovery of this 2D flexible and large-gap QSH insulator opens up new opportunities for developing stretchable and low-power electronic devices.

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z2 Topological Insulator**Supported by the Major State Basic Research Development Program of China under Grant No 2016YFB0700700, and the National Natural Science Foundation of China (NSFC) under Grants Nos 11634003, 11474273, 61121491 and U1530401. J. W. L. was also supported by the National Young 1000 Talents Plan. H. X. D. was

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases. It is a fundamental challenge to realize quantum transition between Z2 nontrivial topological insulator (TI) and topological crystalline insulator (TCI) in one material because Z2 TI and TCI have different requirements on the number of band inversions. The Z2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.

Evidence of topological insulator state in the semimetal LaBi

By employing angle-resolved photoemission spectroscopy combined with first-principles calculations, we performed a systematic investigation on the electronic structure of LaBi, which exhibits extremely large magnetoresistance (XMR), and is theoretically predicted to possess band anticrossing with nontrivial topological properties. Here, the observations of the Fermi-surface topology and band dispersions are similar to previous studies on LaSb [Phys. Rev. Lett. 117, 127204 (2016)], a topologically trivial XMR semimetal, except the existence of a band inversion along the $\Gamma$-$X$ direction, with one massless and one gapped Dirac-like surface state at the $X$ and $\Gamma$ points, respectively. The odd number of massless Dirac cones suggests that LaBi is analogous to the time-reversal $Z_2$ nontrivial topological insulator. These findings open up a new series for exploring novel topological states and investigating their evolution from the perspective of topological phase transition within the family of rare-earth monopnictides.

Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings

The doubly-connected polygonal geometry of planar graphene rings is found to bring forth topological configurations for accessing nontrivial relativistic quantum field (RQF) theory models that carry beyond the constant-mass Dirac-fermion theory. These include generation of sign-alternating masses, solitonic excitations, and charge fractionization. The work integrates a RQF Lagrangian formulation with numerical tight-binding Aharonov-Bohm electronic spectra and the generalized position-dependent-mass Dirac equation. In contrast to armchair graphene rings (aGRGs) with pure metallic arms, certain classes of aGRGs with semiconducting arms, as well as with mixed metallic-semiconducting ones, are shown to exhibit properties of one-dimensional nontrivial topological insulators. This further reveals an alternative direction for realizing a graphene-based nontrivial topological insulator through the manipulation of the honeycomb lattice geometry, without a spin-orbit contribution.

Pressure-induced topological quantum phase transition in Sb2Se3

Based on the first-principles band structure calculations, we investigate the effects of hydrostatic pressure on the conventional insulator (CI) Sb_2Se_3 and predict that it undergoes a topological quantum phase transition from a CI to a nontrivial topological insulator at a critical pressure value. The pressure-induced topological quantum phase transition is confirmed by calculating the evolution of the bulk energy gap as a function of pressure, the inversion of energy band structure, and the Z_2 topological invariant, as well as the existence of the Dirac-like topological surface states. Our predictions can be tested by both spectroscopy and transport experiments.

Quantum spin Hall effect in a disordered hexagonal SixGe1−xalloy

We show that the Si${}_{x}$Ge${}_{1\ensuremath{-}x}$ random alloys in the honeycomb monolayer structure are nontrivial topological insulators with the same topological classification ${Z}_{2}=1$ as pristine silicene and germanene. The application of an external electric field decreases the band gap up to its closure at a critical value of the field, $|{E}_{c}|$. For absolute values of the field larger than $|{E}_{c}|$ the band gap increases again, and the systems are now trivial insulators. Thus, similarly to what happens for zinc-blend Si${}_{x}$Ge${}_{1\ensuremath{-}x}$ alloys, these materials will bring new possibilities in the design of devices, such as band gap and mobility engineering, with the added feature that they will exhibit a quantum spin Hall effect due to the gap generated by the spin-orbit coupling.

Classification of topological insulators and superconductors in the presence of reflection symmetry

We discuss a topological classification of insulators and superconductors in the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using the structure of bulk Dirac Hamiltonians of minimal matrix dimensions and explicit constructions of topological invariants, we provide the complete classification, which still has the same dimensional periodicities with the original Altland-Zirnbauer classification. The classification of reflection-symmetry-protected topological insulators and superconductors depends crucially on the way reflection symmetry operation is realized. When a boundary is introduced, which is reflected into itself, these non-trivial topological insulators and superconductors support gapless modes localized at the boundary.

A new class of (2 + 1)-dimensional topological superconductors with topological classification

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors, the topological classification is obtained systematically and non-trivial topological insulators are classified by either integer or Z2. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in (2 + 1) dimensions which has time-reversal symmetry and a spin conservation symmetry. We demonstrate that the superconductors in this class are classified by when electron interaction is considered, while the classification is without interaction.

Adiabatic transformation as a search tool for new topological insulators: Distorted ternary Li2AgSb-class semiconductors and related compounds

We demonstrate that first-principles based adiabatic continuation approach is a very powerful and efficient tool for constructing topological phase diagrams and locating non-trivial topological insulator materials. Using this technique, we predict that the ternary intermetallic series Li$_2M'X$ where $M'$=Cu, Ag, Au, or Cd, and $X$=Sb, Bi, or Sn, hosts a number of topological insulators with remarkable functional variants and tunability. We also predict that several III-V semimetallic compounds are topologically non-trivial. We construct a topological phase diagram in the parameter space of the atomic numbers of atoms in Li$_2M'X$ compounds, which places a large number of topological materials presented in this work as well as in earlier studies within a single unified topological framework. Our results demonstrate the efficacy of adiabatic continuation as a useful tool for exploring topologically nontrivial alloying systems and for identifying new topological insulators even when the underlying lattice does not possess inversion symmetry, and the approaches based on parity analysis are not viable.

Topological electronic structure and Weyl semimetal in the TlBiSe2class of semiconductors

We present an analysis of bulk and surface electronic structures of thallium based ternary III-V-VI$_2$ series of compounds TlMQ$_2$, where M=Bi or Sb and Q=S, Se or Te, using the ab initio density functional theory framework. Based on parity analysis and (111) surface electronic structure, we predict TlSbSe$_2$, TlSbTe$_2$, TlBiSe$_2$ and TlBiTe$_2$ to be non-trivial topological insulators with a single Dirac cone at the $\Gamma$-point, and TlSbS$_2$ and TlBiS$_2$ to be trivial band insulators. Our predicted topological phases agree well with available angle-resolved photoemission spectroscopy (ARPES) measurements, in particular the topological phase changes between TlBiSe$_2$ and TlBiS$_2$. Moreover, we propose that Weyl semimetal can be realized at the topological critical point in TlBi(S$_{1-x}$Se$_x$)$_2$ and TlBi(S$_{1-x}$Te$_x$)$_2$ alloys by breaking the inversion symmetry in the layer by layer growth in the order of Tl-Se(Te)-Bi-S, yielding six Dirac cones centered along the $\Gamma-L$ directions in the bulk band structure.

Candidates for topological insulators: Pb-based chalcogenide series

We theoretically predict that the series of Pb-based layered chalcogenides, Pb${}_{n}$Bi${}_{2}$Se${}_{n+3}$and Pb${}_{n}$Sb${}_{2}$Te${}_{n+3}$, are possible new candidates for topological insulators, and the topological phases are changed from a topological insulator to a band insulator with increasing $n$. Among the new topological insulators, we found a large bulk band gap of 0.40 eV in PbBi${}_{2}$Se${}_{4}$, and that of Pb${}_{2}$Sb${}_{2}$Te${}_{5}$ is located near the phase boundary between a trivial and a nontrivial topological insulator, which raises the possibility of tuning the topological phase by changing the external parameters.