Trivial Band Insulator Research Articles

Alternative Structure Model of Correlated Charge Density Wave in Monolayer 1T-Nb(Ta)Se2.

The putative Mott charge density wave (CDW) phases of monolayer 1T-NbSe2 and 1T-TaSe2 have attracted a lot of recent interest due to the unexpected orbital texture of their Mott-Hubbard states and the superstructure related to an exotic possibility of a quantum spin liquid with a spinon Fermi surface. The origins of the orbital texture and the superstructure have been, however, elusive. We find by using density functional theory calculations that these CDW phases can have an alternative metastable structure, an anion (Se) centered cluster, in contrast to the prevailing model of a cation (Nb or Ta) centered David star cluster. This structure can be stabilized by the charge transfer from the bilayer graphene/SiC substrate used commonly in the experiments. The anion-centered structure has a similar electronic band structure of a charge transfer insulator to that of DS clusters but naturally explains the orbital texture of the upper Hubbard band from simply its atomic structure. Moreover, this band structure exhibits a Fermi surface nesting to possibly break the symmetry spontaneously into a -R30° superstructure observed experimentally. The resulting ground state of the superstructure is shown to be a trivial band insulator, in contrast to exotic proposals. This result emphasizes the huge structural flexibility of these heteroexpitaxial monolayers, for which careful studies on atomic structures and interactions with substrates are highly requested.

Effect of the spin–orbit interaction in nanotubes

In this work, we study the electronic properties of nanotubes with spin–orbit interaction that exhibit a spin Hall effect. Nanoribbons made of these materials are expected to have topologically protected states. The lack of edge states in a seamless tube eliminates the possibility of finding a topological edge state. The spin–orbit interaction breaks the degeneracy of Dirac’s cones and eliminates the chance of finding a metal nanotube. As a consequence, this makes all nanotubes with spin–orbit interaction trivial band insulators. We focus our attention on two features. First, we study the energy band gap as a function of the diameter of the nanotubes. Then, we concentrate on controlling the bandgap of a nanotube by applying an external radial electric field. Finally, we discuss the possibility of using one of these tubes as a field-effect transistor.

Surface enhanced electron correlation on the trivial quasi-two-dimensional bulk insulator 1T−TaS2

While the prototypical quasi-two-dimensional charge density wave system of $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ has been known as a Mott insulator with a possibility of quantum spin liquid, recent band-structure calculations and spectroscopic works in parallel suggested a metallic system or a spin-singlet insulator due to the interlayer coupling. Here, we carefully reinvestigate the out-of-plane electron dispersion, which reflects the interlayer electronic coupling, with angle-resolved photoelectron spectroscopy. We identify two distinct branches for the topmost valence band, which can be unambiguously related to the surface and the bulk layers with different band gaps. Density functional theory calculations clearly indicate a trivial band insulator due to the interlayer coupling for the bulk but the surface band gap affected substantially by the electron correlation. The surface-bulk electronic dichotomy consistently incorporates most of the theoretical and spectroscopic results reported so far and has wide implications for van der Waals materials with nontrivial interlayer interactions.

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.

C3 symmetry breaking metal-insulator transitions in a flat band in the half-filled Hubbard model on the decorated honeycomb lattice

We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the noninteracting theory at half filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states---a dimer valence bond solid Mott insulator when intertriangle correlations dominate, and a broken ${C}_{3}$-symmetry antiferromagnet that arises from frustration when intratriangle correlations dominate. The metal-insulator transitions into these two phases have very different characters. The metal-broken ${C}_{3}$ antiferromagnetic transition is driven by spontaneous ${C}_{3}$ symmetry breaking that lifts the topologically required degeneracy at the Fermi energy and opens an energy gap in the quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no symmetries of the Hamiltonian. It is caused by strong correlations renormalizing the electronic structure into a phase that is adiabatically connected to both the trivial band insulator and the ground state of the spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither of these metal-insulator transitions can be understood in either the Brinkmann-Rice or Slater paradigms.

Connecting topological Anderson and Mott insulators in disordered interacting fermionic systems

The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivial band insulator by the combination of disorder and interaction, as the generalization of topological Anderson insulators to the many-body interacting regime. The phase diagram is determined by computing various topological properties and confirmed by unsupervised and automated machine learning. We develop an approach to provide a unified and clear description of topological phase transitions driven by interaction and disorder. The topological phases can be detected from disorder/interaction induced edge excitations and charge pumping in optical lattices.

Distinguishing a Mott Insulator from a Trivial Insulator with Atomic Adsorbates.

In an electronic system with various interactions intertwined, revealing the origin of its many-body ground state is challenging and a direct experimental way to verify the correlated nature of an insulator has been lacking. Here we demonstrate a way to unambiguously distinguish a paradigmatic correlated insulator, a Mott insulator, from a trivial band insulator based on their distinct chemical behavior for a surface adsorbate using 1T-TaS_{2}, which has been debated between a spin-frustrated Mott insulator or a spin-singlet trivial insulator. We start from the observation of different sizes of spectral gaps on different surface terminations and show that potassium adatoms on these two surface layers behave in totally different ways. This can be straightforwardly understood from distinct properties of Mott and band insulators due to the fundamental difference of the half- and full-filled orbitals involved, respectively. This work not only solves an outstanding problem in this particularly interesting material but also provides a simple touchstone to identify the correlated ground state of electrons experimentally.

Interacting Chern Insulator in Infinite Spatial Dimensions.

We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension D and demonstrate that the model remains well defined and nontrivial in the D→∞ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a continuum of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semimetal states, which are unconventional already in the noninteracting case. Topological phases are characterized by a nonquantized Chern density replacing the Chern number as D→∞.

Nondiagonal anisotropic quantum Hall states

We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $\nu=p/2q$ for bosonic systems and $\nu=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers. Non-diagonal quantum Hall states are constructed in a coupled wire model, which shows an intimate relation to the non-diagonal conformal field theory and has a constrained pattern of motion for bulk quasiparticles, featuring a non-trivial interplay between charge symmetry and translation symmetry. The non-diagonal state is established as a distinctive symmetry-enriched topological order. Aside from the usual $U(1)$ charge sector, there is an additional symmetry-enriched neutral sector described by the quantum double model $\mathcal{D}(\mathbb{Z}_p)$, which relies on the presence of both the $U(1)$ charge symmetry and the $\mathbb{Z}$ translation symmetry of the wire model. Translation symmetry distinguishes non-diagonal states from Laughlin states, in a way similar to how it distinguishes weak topological insulators from trivial band insulators. Moreover, the translation symmetry in non-diagonal states can be associated to the $\mathbf{e}\leftrightarrow\mathbf{m}$ anyonic symmetry in $\mathcal{D}(\mathbb{Z}_p)$, implying the role of dislocations as two-fold twist-defects. The boundary theory of non-diagonal states is derived microscopically. For the edge perpendicular to the direction of wires, the effective Hamiltonian has two components: a chiral Luttinger liquid and a generalized $p$-state clock model. Importantly, translation symmetry in the bulk is realized as self-duality on the edge. The symmetric edge is thus either gapless or gapped with spontaneously broken symmetry. For $p=2,3$, the respective electron tunneling exponents are predicted for experimental probes.

Excitonic insulator phase and condensate dynamics in a topological one-dimensional model

We employ mean-field approximation to investigate the interplay between the nontrivial band topology and the formation of excitonic insulator (EI) in a one-dimensional chain of atomic $s-p$ orbitals in the presence of repulsive inter-orbital Coulomb interaction. We find that our model, in a non-interacting regime, admits topological and trivial insulator phases, whereas, in strong Coulomb interaction limit, the chiral symmetry is broken and the system undergoes a topological-excitonic insulator phase transition. The latter phase transition stems from an orbital pseudomagnetization and band inversion around $k=0$. Our findings show that contrary to the topological insulator phase, electron-hole bound states do not form exciton condensate in the trivial band insulator phase due to lack of band inversion. Interestingly, the EI phase in low $s-p$ hybridization limit hosts a Bardeen-Cooper-Schrieffer (BCS)/Bose-Einstein condensation (BEC) crossover. Irradiated by a pump pulse, our findings reveal that the oscillations of exciton states strongly depend on the frequency of the laser pulse. We further explore the signatures of dynamics of the exciton condensate in optical measurements.

Partial flux ordering and thermal Majorana metals in higher-order spin liquids

In frustrated quantum magnetism, chiral spin liquids are a particularly intriguing subset of quantum spin liquids in which the fractionalized parton degrees of freedom form a Chern insulator. Here we study an exactly solvable spin-3/2 model which harbors not only chiral spin liquids but also spin liquids with higher-order parton band topology -- a trivial band insulator, a Chern insulator with gapless chiral edge modes, and a second-order topological insulator with gapless corner modes. With a focus on the thermodynamic precursors and thermal phase transitions associated with these distinct states, we employ numerically exact quantum Monte Carlo simulations to reveal a number of unconventional phenomena. This includes a heightened thermal stability of the ground state phases, the emergence of a partial flux ordering of the associated $\mathbb{Z}_2$ lattice gauge field, and the formation of a thermal Majorana metal regime extending over a broad temperature range.

Topological Dirac Semimetal Phase in Bismuth Based Anode Materials for Sodium-Ion Batteries

Bismuth has recently attracted interest in connection with Na-ion battery anodes due to its high volumetric capacity. It reacts with Na to form Na 3 Bi which is a prototypical Dirac semimetal with a nontrivial electronic structure. Density-functional-theory based first-principles calculations are playing a key role in understanding the fascinating electronic structure of Na 3 Bi and other topological materials. In particular, the strongly-constrained-and-appropriately-normed (SCAN) meta-generalized-gradient-approximation (meta-GGA) has shown significant improvement over the widely used generalized-gradient-approximation (GGA) scheme in capturing energetic, structural, and electronic properties of many classes of materials. Here, we discuss the electronic structure of Na 3 Bi within the SCAN framework and show that the resulting Fermi velocities and s-band shift around the Γ point are in better agreement with experiments than the corresponding GGA predictions. SCAN yields a purely spin-orbit-coupling (SOC) driven Dirac semimetal state in Na 3 Bi in contrast with the earlier GGA results. Our analysis reveals the presence of a topological phase transition from the Dirac semimetal to a trivial band insulator phase in Na 3 Bi x Sb 1 − x alloys as the strength of the SOC varies with Sb content, and gives insight into the role of the SOC in modulating conduction properties of Na 3 Bi.

Topological phase transition of Bi2–xInxTe3

Compared with Bi2Se3 with its Dirac point in the bulk gap, the Dirac point of Bi2Te3 is in the valence band, then it is generally considered that it is difficult to observe the topological phase transition course in the Bi2Te3 system via nonmagnetic lighter element doping. Here, we report the phase transition of Bi2–xInxTe3, from a topological insulator to a trivial band insulator observed by angle-resolved photoemission spectroscopy. The robust surface state exists in the range of . At , the surface state completely disappears and only the bulk gap exists, suggesting a sudden gap closure and topological phase transition around .

Bilayer Haldane model: From trivial band insulator to fractionalized quantum anomalous Hall insulator

Motivated by work on the bulk topological proximity effect and the topological bootstrap, we consider two coupled layers of quantum anomalous Hall (QAH) insulators with opposite signs of time-reversal breaking, which leads to a trivial band insulator at half-filling. We study the impact of interactions in this model within slave rotor theory, which leads to a layer-selective Mott transition, resulting in a fractionalized quantum anomalous Hall insulator QAH$^*$ where a Chern band insulator coexists with a chiral spin liquid. We also compute the edge electron spectral function in the vicinity of the QAH$^*$ phase.

Optical properties of (Bi1-xInx)2Se3 thin films

Bi2Se3 is a topological insulator with unique optical properties, including linearly-dispersing surface states. Many of the proposed device applications for Bi2Se3 require a lattice-matched trivially-insulating component. It is known that (Bi1-xInx)2Se3 is a trivial band insulator for moderate indium concentrations. In this paper, we grow and characterize the optical properties of (Bi1-xInx)2Se3 films with varying indium concentrations. We find that the lattice constant and optical bandgap for (Bi1-xInx)2Se3 varies linearly with concentration. We perform infrared reflection measurements as a function of polarization and angle, enabling us to model the permittivity for these materials. Again, we find that most parameters vary linearly with concentration. Our results for the pure end members are consistent with the literature values. This is the first report of optical values for the intermediate compounds, which are likely to be integral components of future topological insulator optical 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.

Linear AC transport in T-stub and crossed silicene nanosystems

In this work, we theoretically study the linear AC transport properties in T-stub and crossed zigzag silicene nanosystems. The DC conductance and AC emittance are numerically calculated based on the tight-binding approach and AC transport theory, by considering the nearest-neighbor hopping, second-nearest-neighbor spin-orbit interaction (SOI) and external electric field. The relatively strong SOI of silicene was demonstrated to induce a topological quantum edge state in the nanosystems by the local density of states, which eliminates the AC emittance response at the Dirac point. Further investigations suggest that the SOI-induced AC transport is topologically protected from the changes of geometrical size. Moreover, the AC transport properties of these nanosystems can be tuned by the external electric field, which would open an energy gap and destroy the topological quantum state, making them trivial band insulators.

Interface induced quantized spin Hall response in three-dimensional topological insulator/normal insulator heterostructures

We report analytic investigation of the electronic properties of heterostructures comprised by films of three-dimensional topological insulator (TI) and normal insulator (NI) revealing strong interface and size effects on their spin transport characteristics. Imposing at the TI/NI interfaces the natural boundary conditions within a continual scheme, we show that the intrinsic spin Hall response of the NI/TI/NI trilayer can be controlled by tuning the interface potential (IP) together with the TI film thickness. We predict a series of interface induced quantum transitions between topological insulating phase and trivial band insulator phase. We calculate the phase diagram of the NI/TI/NI trilayer and establish an appropriate range of the IP strength and the TI film thickness to realize the regime of quantum spin Hall effect. Our results can provide a useful guide in choosing the relevant material parameters to facilitate the detection of quantum spin Hall conductivity in the TI/NI heterostructures.

Two- and three-dimensional topological phases in BiTeX compounds

Recently, it was shown that quantum spin Hall insulator phase with a gap wide enough for practical applications can be realized in the ultrathin films constructed from two inversely stacked structural elements of trivial band insulator BiTeI. Here, we study the edge states in nanoribbons made of the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{I}}_{2}$ sextuple layer (SL) and the electronic structure of the SL deposited on the natural BiTeI substrate as well as sandwiched between two thick BiTeI films. We show that the ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{I}}_{2}$ SL keeps nontrivial topological properties. We also demonstrate that ultrathin centrosymmetric films constructed in a similar manner from related material BiTeBr are trivial band insulators up to five-SL film thickness. In contrast to ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{I}}_{2}$ for which the stacking of nontrivial SLs in a three-dimensional (3D) limit results in a strong topological insulator (TI) phase, a 3D TI ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}{\mathrm{Br}}_{2}$ is formed by trivial SLs. For the last material of the $\mathrm{BiTe}X$ ($X=\text{I}$,Br,Cl) series, BiTeCl, both 2D and 3D centrosymmetric phases are characterized by topologically trivial band structure.

Topologically Protected AC Transport Induced by Spin–Orbit Interaction in H-Shaped Silicene Nanojunction

The linear ac transport properties are theoretically studied in H-shaped zigzag silicene nanojunction. We numerically calculated the dc conductance and ac emittance by considering the nearest-neighbor hopping, the second-nearest-neighbor spin–orbit interaction (SOI), and external electric field, based on the tight-binding approach and the ac transport theory. It is found that the relatively large SOI induces a topological quantum edge state in the nanojunction, which eliminates the ac emittance response at the Dirac point. Further investigations indicate that the SOI-induced ac transport is topologically protected, despite the changes of geometric size. Moreover, the external electric field would open an energy gap, and destroy the topological quantum state, making the nanojunction a trivial band insulator.