Trivial Band Insulator Research Articles

Electronic structure of SrSn2As2 near the topological critical point

Topological materials with exotic quantum properties are promising candidates for quantum spin electronics. Different classes of topological materials, including Weyl semimetal, topological superconductor, topological insulator and Axion insulator, etc., can be connected to each other via quantum phase transition. For example, it is believed that a trivial band insulator can be twisted into topological phase by increasing spin-orbital coupling or changing the parameters of crystal lattice. With the results of LDA calculation and measurement by angle-resolved photoemission spectroscopy (ARPES), we demonstrate in this work that the electronic structure of SrSn2As2 single crystal has the texture of band inversion near the critical point. The results indicate the possibility of realizing topological quantum phase transition in SrSn2As2 single crystal and obtaining different exotic quantum states.

Dynamic conductance in double-bend silicene nanosystem

In this work, dynamic conductance transport properties are theoretically investigated in the zigzag silicene nanosystem with a double-bend structure. We numerically study the dc conductance and ac emittance in the nanosystem based on the tight-binding approach, Green's function method and ac transport theory, by considering the second-nearest-neighbor spin–orbit interaction (SOI) and external electric field. The numerical results suggest that the nanosystem undergoes a quantum phase transition driven by the relatively strong SOI, which results in a large dc conductance and a vanishing ac emittance around the Dirac point despite the interface scattering. The distribution of the local density of states in the real space reveals that the SOI induces the quantum edge state by establishing transport paths at the edge of the nanosystem. Further investigation indicates that the dynamic conductance related to the quantum edge state are topologically protected from the geometrical size change of the nanosystem. Finally, the nanosystem can be tuned to be a trivial band insulator without any dc or ac response by applying external electric field.

Quantum phases of disordered three-dimensional Majorana-Weyl fermions

The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three dimensional spinless $p_x+ip_y$ superconductor provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions in class D of the Altland-Zirnbauer symmetry classification; such a phase can support a large anomalous thermal Hall conductivity and protected surface Majorana-Fermi arcs at zero energy. We study the effect of quenched disorder on such a topological phase with both numerical and analytical methods. Using the kernel polynomial method, we compute the average and typical density of states for the BdG quasiparticles; based on this, we construct the disordered phase diagram. We show for infinitesimal disorder, the ThSM is converted into a diffusive thermal Hall metal (ThDM) due to rare statistical fluctuations. Consequently, the phase diagram of the disordered model only consists of ThDM and thermal insulating phases. Nonetheless, there is a cross-over at finite energies from a ThSM regime to a ThDM regime, and we establish the scaling properties of the avoided quantum critical point which marks this cross-over. Additionally, we show the existence of two types of thermal insulators: (i) a trivial thermal band insulator (ThBI) [or BEC phase] supporting only exponentially localized Lifshitz states (at low energy), and (ii) a thermal Anderson insulator (AI) at large disorder strengths. We determine the nature of the two distinct localization transitions between these two types of insulators and ThDM.We also discuss the experimental relevance of our results for three dimensional, time reversal symmetry breaking, triplet superconducting states.

Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers

The quantum spin Hall insulators predicted ten years ago and now experimentally observed are instrumental for a break- through in nanoelectronics due to non-dissipative spin-polarized electron transport through their edges. For this transport to persist at normal conditions, the insulators should possess a sufficiently large band gap in a stable topological phase. Here, we theoretically show that quantum spin Hall insulators can be realized in ultra-thin films constructed from a trivial band insulator with strong spin-orbit coupling. The thinnest film with an inverted gap large enough for practical applications is a centrosymmetric sextuple layer built out of two inversely stacked non-centrosymmetric BiTeI trilayers. This nontrivial sextuple layer turns out to be the structure element of an artificially designed strong three-dimensional topological insulator Bi2Te2I2. We reveal general principles of how a topological insulator can be composed from the structure elements of the BiTeX family (X = I, Br, Cl), which opens new perspectives towards engineering of topological phases.

Topological phase transition coupled with spin-valley physics in ferroelectric oxide heterostructures

The possibility to engineer the coupling of spin and valley physics is explored in ferroelectric oxide heterostructures with ${e}_{g}^{2}$ electronic configuration. We show that the polar structural distortion induces the appearance of spin-valley coupled properties, at the same time as being responsible for a topological transition from a quantum spin-Hall insulating phase to a trivial band insulator. The coupled spin-valley physics is affected by the topological band inversion in a nontrivial way; while the valley-dependent spin polarization of both conduction and valence bands is preserved, a change of the Berry curvature and of spin-valley selection rules is predicted, leading to different circular dichroic response as well as valley and spin Hall effects.

Dynamics of Weyl quasiparticles in an optical lattice

We investigate the dynamics of the Weyl quasiparticles emerged in an optical lattice where the topological Weyl semimental and trivial band insulator phases can be adjusted with the on-site energy. The evolution of the density distribution is demonstrated to have an anomalous velocity in Weyl semimental but a steady Zitterbewegung effect in the band insulator. Our analysis demonstrates that the topological Chern number and the chirality of the system can be directly determined from the positions of the atomic center-of-mass. Furthermore, the amplitude and the period of the relativistic Zitterbewegung oscillations are shown to be observable with the time-of-flight experiments.

Tunable spin-charge conversion through topological phase transitions in zigzag nanoribbons

We study spin-orbit torques and charge pumping in magnetic quasi-one dimensional zigzag nanoribbons with hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences topological phase transition from a trivial band insulator to a quantum spin Hall insulator either by tuning the magnetization direction or the intrinsic spin-orbit coupling. We find that spin-charge conversion efficiency (i.e. spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.

Strong correlation effects on topological quantum phase transitions in three dimensions

We investigate the role of short-ranged electron-electron interactions in a paradigmatic model of three dimensional topological insulators, using dynamical mean-field theory and focusing on non magnetically ordered solutions. The non-interacting band-structure is controlled by a mass term M, whose value discriminates between three different insulating phases, a trivial band insulator and two distinct topologically non-trivial phases. We characterize the evolution of the transitions between the different phases as a function of the local Coulomb repulsion U and find a remarkable dependence of the U -M phase diagram on the value of the local Hund's exchange coupling J. However, regardless the value of J, following the evolution of the topological transition line between a trivial band insulator and a topological insulator, we find a critical value of U separating a continuous transition from a first-order one. When the Hund's coupling is significant, a Mott insulator is stabilized at large U . In proximity of the Mott transition we observe the emergence of an anomalous "Mott-like" strong topological insulating state.

Topological states in two-dimensional hexagon lattice bilayers

We investigate the topological states of the two-dimensional hexagon lattice bilayer. The system exhibits a quantum valley Hall (QVH) state when the interlayer interaction t⊥ is smaller than the nearest neighbor hopping energy t, and then translates to a trivial band insulator state when t⊥/t>1. Interestingly, the system is found to be a single-edge QVH state with t⊥/t=1. The topological phase transition also can be presented via changing bias voltage and sublattice potential in the system. The QVH states have different edge modes carrying valley current but no net charge current. The bias voltage and external electric field can be tuned easily in experiments, so the present results will provide potential application in valleytronics based on the two-dimensional hexagon lattice.

Electronic structure and topological features of tin-based binary nanosheets and their hydrogenated/fluorinated derivatives: A first-principles study

Utilizing first-principles calculations, we have investigated the structural, electronic and topological properties of binary SnSi and SnGe nanosheets as well as their H-/F-derivatives. It is found that all these systems have chair-like buckled configurations with robust structural stabilities. Unlike the elemental group-IV sheets, SnSi and SnGe sheets are narrow-band-gap semiconductors, which have a gapped Dirac cone with massive Fermions. Under the strains, a direct-to-indirect band gap transition and a semiconductor-to-metal transition would occur in these systems. Although these binary systems are trivial band insulators with ℤ2=0, their topological features can be altered by the surface decorations. Particularly, the fluorinated SiGe sheet becomes a topological insulator with ℤ2=1, and such non-trivial state can also be found in the strained fluorinated SnSi and hydrogenated SnGe sheets. Large non-trivial SOC band gaps of 0.09–0.17eV are obtained in these 2D topological insulating systems, which will be beneficial for realizing the room-temperature quantum spin Hall effect. Our study demonstrates that binary Sn-based nanomaterials possess tunable electronic and topological properties, which have potential applications in low-power nano-electrics and devices.

Competing magnetic orderings and tunable topological states in two-dimensional hexagonal organometallic lattices

The exploration of topological states is of significant fundamental and practical importance in contemporary condensed matter physics, for which the extension to two-dimensional (2D) organometallic systems is particularly attractive. Using first-principles calculations, we show that a 2D hexagonal triphenyl-lead lattice composed of only main group elements is susceptible to a magnetic instability, characterized by a considerably more stable antiferromagnetic (AFM) insulating state rather than the topologically nontrivial quantum spin Hall state proposed recently. Even though this AFM phase is topologically trivial, it possesses an intricate emergent degree of freedom, defined by the product of spin and valley indices, leading to Berry curvature-induced spin and valley currents under electron or hole doping. Furthermore, such a trivial band insulator can be tuned into a topologically nontrivial matter by the application of an out-of-plane electric field, which destroys the AFM order, favoring instead ferrimagnetic spin ordering and a quantum anomalous Hall state with a non-zero topological invariant. These findings further enrich our understanding of 2D hexagonal organometallic lattices for potential applications in spintronics and valleytronics.

Electric control of topological phase transitions in Dirac semimetal thin films.

Dirac semimetals host three-dimensional (3D) Dirac fermion states in the bulk of crystalline solids, which can be viewed as 3D analogs of graphene. Owing to their relativistic spectrum and unique topological character, these materials hold great promise for fundamental-physics exploration and practical applications. Particularly, they are expected to be ideal parent compounds for engineering various other topological states of matter. In this report, we investigate the possibility to induce and control the topological quantum spin Hall phase in a Dirac semimetal thin film by using a vertical electric field. We show that through the interplay between the quantum confinement effect and the field-induced coupling between sub-bands, the sub-band gap can be tuned and inverted. During this process, the system undergoes a topological phase transition between a trivial band insulator and a quantum spin Hall insulator. Consequently, one can switch the topological edge channels on and off by purely electrical means, making the system a promising platform for constructing topological field effect transistors.

Sudden gap closure across the topological phase transition inBi2−xInxSe3

The phase transition from a topological insulator to a trivial band insulator is studied using angle-resolved photoemission spectroscopy on ${\mathrm{Bi}}_{2\ensuremath{-}x}{\mathrm{In}}_{x}{\mathrm{Se}}_{3}$ single crystals. We first report the complete evolution of the bulk band structures throughout the transition. The robust surface state and the bulk-gap size ($\ensuremath{\sim}0.50\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$) show no significant change upon doping for $x=0.05$, 0.10, and 0.175. At $x\phantom{\rule{0.16em}{0ex}}\ensuremath{\ge}0.225$, the surface state completely disappears and the bulk-gap size increases, suggesting a sudden gap closure and topological phase transition around $x\ensuremath{\sim}0.175--0.225$. We discuss the underlying mechanism of the phase transition, proposing that it is governed by the combined effect of spin-orbit coupling and interactions upon band hybridization. Our study provides a venue to investigate the mechanism of the topological phase transition induced by nonmagnetic impurities.

First-order character and observable signatures of topological quantum phase transitions.

Topological quantum phase transitions are characterized by changes in global topological invariants. These invariants classify many-body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For noninteracting electrons, it is well understood that such transitions are continuous and always accompanied by a gap closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. Here, we demonstrate that a sufficiently strong electron-electron interaction can fundamentally change the situation: we discover a topological quantum phase transition of first-order character in the genuine thermodynamic sense that occurs without a gap closing. Our theoretical study reveals the existence of a quantum critical endpoint associated with an orbital instability on the transition line between a 2D topological insulator and a trivial band insulator. Remarkably, this phenomenon entails unambiguous signatures related to the orbital occupations that can be detected experimentally.

Magnetic properties of Dirac fermions in a buckled honeycomb lattice

We calculate the magnetic response of a buckled honeycomb lattice with intrinsic spin-orbit coupling (such as silicene) which supports valley-spin polarized energy bands when subjected to a perpendicular electric field $E_z$. By changing the magnitude of the external electric field, the size of the two band gaps involved can be tuned, and a transition from a topological insulator (TI) to a trivial band insulator (BI) is induced as one of the gaps becomes zero, and the system enters a valley-spin polarized metallic state (VSPM). In an external magnetic field ($B$), a distinct signature of the transition is seen in the derivative of the magnetization with respect to chemical potential ($\mu$) which gives the quantization of the Hall plateaus through the Streda relation. When plotted as a function of the external electric field, the magnetization has an abrupt change in slope at its minimum which signals the VSPM state. The magnetic susceptibility ($\chi$) shows jumps as a function of $\mu$ when a band gap is crossed which provides a measure of the gaps' variation as a function of external electric field. Alternatively, at fixed $\mu$, the susceptibility displays an increasingly large diamagnetic response as the electric field approaches the critical value of the VSPM phase. In the VSPM state, magnetic oscillations exist for any value of chemical potential while for the TI, and BI state, $\mu$ must be larger than the minimum gap in the system. When $\mu$ is larger than both gaps, there are two fundamental cyclotron frequencies (which can also be tuned by $E_z$) involved in the de-Haas van-Alphen oscillations which are close in magnitude. This causes a prominent beating pattern to emerge.

A new topological insulator built from quasi one-dimensional atomic ribbons

A novel topological insulator with orthorhombic crystal structure is demonstrated. It is characterized by quasi one-dimensional, conducting atomic chains instead of the layered, two-dimensional sheets known from the established Bi2(Se,Te)3 system. The Sb-doped Bi2Se3 nanowires are grown in a TiO2-catalyzed process by chemical vapor deposition. The binary Bi2Se3 is transformed from rhombohedral to orthorhombic by substituting Sb on ∼38% of the Bi sites. Pure Sb2Se3 is a topologically trivial band insulator with an orthorhombic crystal structure at ambient conditions, and it is known to transform into a topological insulator at high pressure. Angle-resolved photoemission spectroscopy shows a topological surface state, while Sb doping also tunes the Fermi level to reside in the bandgap. (© 2015 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim)

Get it strained

Stretching a sheet of graphene could induce a superconducting state. Similar strain-induced superconductivity may be realized at the interface between a topological crystalline insulator and a trivial band insulator.

Structurally unstableAIIIBiO3perovskites are predicted to be topological insulators but their stable structural forms are trivial band insulators

Structurally unstable compounds can be predicted to be topological insulators (TIs) but their stable structural forms are trivial band insulators. The authors illustrate the danger in such false positive predictions for the A${}^{I\phantom{\rule{0}{0ex}}I\phantom{\rule{0}{0ex}}I}$BiO${}_{3}$ bismuth oxides that have been recently proposed as TIs in a hypothetical ``perovskite'' crystal structure-type. They show that the inversion of anti-bonding with bonding electron levels may destabilize the material and argue that to predict new candidate TIs by quantum atomistic modeling, one should simultaneously test structural stability and topological character of the candidate materials.

Dynamics of tunneling into nonequilibrium edge states

Time-dependent perturbations can drive a trivial two-dimensional band insulator into a quantum Hall-like phase, with protected nonequilibrium states bound to its edges. We propose an experiment to probe the existence of these topological edge states which consists of passing a tunneling current through a small two-dimensional sample out of equilibrium. The signature is a nonquantized metallic conductance near the edges of the sample and, in contrast, an excitation gap in the bulk. This proposal is demonstrated for the case of a two-dimensional lattice model of Dirac electrons with tunable mass in a strong electromagnetic field. In addition, we also study the tunneling conductance of the driven resonant level model and find a phenomenon similar to dynamic localization in which certain transport channels are suppressed.

Topological and magnetic phases with strong spin-orbit coupling on the hyperhoneycomb lattice

We study the general phase diagram of correlated electrons for iridium-based (Ir) compounds on the hyperhoneycomb lattice---a crystal structure where the Ir$^{4+}$ ions form a three-dimensional network with three-fold coordination recently realized in the $\beta$-Li${}_{2}$IrO${}_{3}$ compound. Using a combination of microscopic derivations, symmetry analysis, and density functional calculations, we determine the general model for the electrons occupying the $j_{\text{eff}}=1/2$ orbitals at the Ir$^{4+}$ sites. In the non-interacting limit, we find that this model allows for both topological and trivial electronic band insulators along with metallic states. The effect of Hubbard-type electron-electron repulsion on the above electronic structure in stabilizing $\mathbf{q}=\mathbf{0}$ magnetic order reveals a phase diagram with continuous phase transition between a topological band insulator and a Neel ordered magnetic insulator.