Bulk Gap Research Articles

Coupled spin- 12 ladders as microscopic models for non-Abelian chiral spin liquids

We construct a two-dimensional (2D) lattice model that is argued to realize a gapped chiral spin liquid with (Ising) non-Abelian topological order. The building blocks are spin-1/2 two-leg ladders with $SU(2)$-symmetric spin-spin interactions. The two-leg ladders are then arranged on rows and coupled through SU(2)-symmetric interactions between consecutive ladders. The intra-ladder interactions are tuned so as to realize the c = 1/2 Ising conformal field theory, a fact that we establish numerically via Density Matrix Renormalization Group (DMRG) studies. Time-reversal breaking inter-ladder interactions are tuned so as to open a bulk gap in the 2D lattice system. This 2D system supports gapless chiral edge modes with Ising non-Abelian excitations but no charge excitations, in contrast to the Pfaffian non-Abelian fractional quantum Hall state.

Edge conduction in monolayer WTe2

A two-dimensional topological insulator (2DTI) is guaranteed to have a helical 1D edge mode in which spin is locked to momentum, producing the quantum spin Hall effect and prohibiting elastic backscattering at zero magnetic field. No monolayer material has yet been shown to be a 2DTI, but recently the Weyl semimetal WTe2 was predicted to become a 2DTI in monolayer form if a bulk gap opens. Here, we report that at temperatures below about 100 K monolayer WTe2 does become insulating in its interior, while the edges still conduct. The edge conduction is strongly suppressed by in-plane magnetic field and is independent of gate voltage, save for mesoscopic fluctuations that grow on cooling due to a zero-bias anomaly which reduces the linear-response conductance. Bilayer WTe2 also becomes insulating at low temperatures but does not show edge conduction. Many of these observations are consistent with monolayer WTe2 being a 2DTI. However, the low temperature edge conductance, for contacts spacings down to 150 nm, is below the quantized value,

Gallium bismuth halide GaBi-X2 (X = I, Br, Cl) monolayers with distorted hexagonal framework: Novel room-temperature quantum spin Hall insulators

Quantum Spin Hall (QSH) insulators with a large topologically nontrivial bulk gap are crucial for future applications of the QSH effect. Among these, group III-V monolayers and their halides with chair structure (regular hexagonal framework, RHF) were widely studied. Using first-principles calculations, we propose a new structure model for the functionalized group III-V monolayers, which consist of rectangular GaBi-X2 (X=I, Br, Cl) monolayers with a distorted hexagonal framework (DHF). These structures have a much lower energy than the GaBi-X2 monolayers with chair structure. Remarkably, the DHF GaBi-X2 monolayers are all QSH insulators, which exhibit sizeable nontrivial band gaps ranging from 0.17 eV to 0.39 eV. Those band gaps can be widely tuned by applying different spin-orbit coupling (SOC) strengths, resulting in a distorted Dirac cone.

Two-Dimensional Large Gap Topological Insulators with Tunable Rashba Spin-Orbit Coupling in Group-IV films

The coexistence of nontrivial topology and giant Rashba splitting, however, has rare been observed in two-dimensional (2D) films, limiting severely its potential applications at room temperature. Here, we through first-principles calculations to propose a series of inversion-asymmetric group-IV films, ABZ2 (A ≠ B = Si, Ge, Sn, Pb; Z = F, Cl, Br), whose stability are confirmed by phonon spectrum calculations. The analyses of electronic structures reveal that they are intrinsic 2D TIs with a bulk gap as large as 0.74 eV, except for GeSiF2, SnSiCl2, GeSiCl2 and GeSiBr2 monolayers which can transform from normal to topological phases under appropriate tensile strain of 4, 4, 5, and 4%, respectively. The nontrivial topology is identified by Z2 topological invariant together with helical edge states, as well as the berry curvature of these systems. Another prominent intriguing feature is the giant Rashba spin splitting with a magnitude reaching 0.15 eV, the largest value reported in 2D films so far. The tunability of Rashba SOC and band topology can be realized through achievable compressive/tensile strains (−4 ~ 6%). Also, the BaTe semiconductor is an ideal substrate for growing ABZ2 films without destroying their nontrivial topology.

Light-induced electron localization in a quantum Hall system

Picosecond pulses of terahertz radiation induce non-equilibrium electron dynamics in a GaAs quantum Hall system, suppressing the longitudinal resistivity, and giving rise to a quantized transverse component. An insulating bulk state is a prerequisite for the protection of topological edge states1. In quantum Hall systems, the thermal excitation of delocalized electrons is the main route to breaking bulk insulation2. In equilibrium, the only way to achieve a clear bulk gap is to use a high-quality crystal under high magnetic field at low temperature. However, bulk conduction could also be suppressed in a system driven out of equilibrium such that localized states in the Landau levels are selectively occupied. Here we report a transient suppression of bulk conduction induced by terahertz wave excitation between the Landau levels in a GaAs quantum Hall system. Strikingly, the Hall resistivity almost reaches the quantized value at a temperature where the exact quantization is normally disrupted by thermal fluctuations. The electron localization is realized by the long-range potential fluctuations, which are a unique and inherent feature of quantum Hall systems. Our results demonstrate a new means of effecting dynamical control of topology by manipulating bulk conduction using light.

Valley-filtered edge states and quantum valley Hall effect in gated bilayer graphene

Electron edge states in gated bilayer graphene in the quantum valley Hall (QVH) effect regime can carry both charge and valley currents. We show that an interlayer potential splits the zero-energy level and opens a bulk gap, yielding counter-propagating edge modes with different valleys. A rich variety of valley current states can be obtained by tuning the applied boundary potential and lead to the QVH effect, as well as to the unbalanced QVH effect. A method to individually manipulate the edge states by the boundary potentials is proposed.

Realization of quantum anomalous Hall effect in graphene from n−p codoping-induced stable atomic adsorption

Using first-principles calculation methods, we study the possibility of realizing quantum anomalous Hall effect in graphene from stable 3\textit{d}-atomic adsorption via charge-compensated \textit{n}-\textit{p} codoping scheme. As concrete examples, we show that long-range ferromagnetism can be established by codoping 3\textit{d} transition metal and boron atoms, but only the Ni codopants can open up a global bulk gap to harbour the quantum anomalous Hall effect. Our estimated ferromagnetic Curie transition temperature can reach over 10 Kelvin for various codoping concentrations.

From a normal insulator to a topological insulator in plumbene

Plumbene, similar to silicene, has a buckled honeycomb structure with a large band gap ($\sim 400$ meV). All previous studies have shown that it is a normal insulator. Here, we perform first-principles calculations and employ a sixteen-band tight-binding model with nearest-neighbor and next-nearest-neighbor hopping terms to investigate electronic structures and topological properties of the plumbene monolayer. We find that it can become a topological insulator with a large bulk gap ($\sim 200$ meV) through electron doping, and the nontrivial state is very robust with respect to external strain. Plumbene can be an ideal candidate for realizing the quantum spin Hall effect at room temperature. By investigating effects of external electric and magnetic fields on electronic structures and transport properties of plumbene, we present two rich phase diagrams with and without electron doping, and propose a theoretical design for a four-state spin-valley filter.

First-principles calculations for mechanical and electronic features of strained GaP nanowires

The mechanical and electronic properties of GaP nanowires are investigated by computing the Young’s modulus, Poisson’s ratio, energy band gap and effective carrier masses using first-principles calculations based on density functional theory. The wurtzite structural nanowires with diameters upper limited to [Formula: see text][Formula: see text]Å are strained by uniaxial strains in the range of [Formula: see text]–[Formula: see text]. The Young’s moduli of nanowires are found to be decreased with increase of the size in the direction of the Young’s modulus of the bulk GaP. The Poisson’s effect is determined to be stronger in GaP nanowires than in the bulk. The energy band gaps of the unstrained and strained nanowires are obtained to be enlarged with decrease of the size due to the quantum size effect. The confinement effect is found larger in the compressed nanowires than in the stretched ones. All the unstrained nanowires except the largest one are indirect band gap materials. Indirect to direct band gap transition is determined to be size and strain dependent. The effective carrier masses in all unstrained nanowires are found small compared to the ones in the bulk GaP. The effective electron and hole masses are obtained to be modulated in nanowires of this work by the compressive and both compressive/tensile strains, respectively.

Electronic transport in disordered MoS2 nanoribbons

We study the electronic structure and transport properties of zigzag and armchair monolayer molybdenum disulfide nanoribbons using an 11-band tight-binding model that accurately reproduces the material's bulk band structure near the band gap. We study the electronic properties of pristine zigzag and armchair nanoribbons, paying particular attention to the edges states that appear within the MoS$_2$ bulk gap. By analyzing both their orbital composition and their local density of states, we find that in zigzag-terminated nanoribbons these states can be localized at a single edge for certain energies independent of the nanoribbon width. We also study the effects of disorder in these systems using the recursive Green's function technique. We show that for the zigzag nanoribbons, the conductance due to the edge states is strongly suppressed by short-range disorder such as vacancies. In contrast, the local density of states still shows edge localization. We also show that long-range disorder has a small effect on the transport properties of nanoribbons within the bulk gap energy window.

Intrinsic coherent acoustic phonons in the indirect band gap semiconductors Si and GaP

We report on the intrinsic optical generation and detection of coherent acoustic phonons at (001)-oriented bulk Si and GaP without metallic phonon transducer structures. Photoexcitation by a 3.1-eV laser pulse generates a normal strain pulse within the $\ensuremath{\sim}100$-nm penetration depth in both semiconductors. The subsequent propagation of the strain pulse into the bulk is detected with a delayed optical probe as a periodic modulation of the optical reflectivity. Our theoretical model explains quantitatively the generation of the acoustic pulse via the deformation potential electron-phonon coupling and detection in terms of the spatially and temporally dependent photoelastic effect for both semiconductors. Comparison with our theoretical model reveals that the experimental strain pulses have finite buildup times of 1.2 and 0.4 ps for GaP and Si, which are comparable with the time required for the photoexcited electrons to transfer to the lowest X valley through intervalley scattering. The deformation potential coupling related to the acoustic pulse generation for GaP is estimated to be twice as strong as that for Si from our experiments, in agreement with a previous theoretical prediction.

Reduction of Z classification of a two-dimensional weak topological insulator: Real-space dynamical mean-field theory study

One of the remarkable interaction effects on topological insulators is the reduction of topological classification in free-fermion systems. We address this issue in a bilayer honeycomb lattice model by taking into account temperature effects on the reduction. Our analysis, based on the real-space dynamical mean field theory, elucidates the following results. (i) Even when the reduction occurs, the winding number defined by the Green's function can take a nontrivial value at zero temperature. (ii) The winding number taking the nontrivial value becomes consistent with the absence of gapless edge modes due to Mott behaviors emerging only at the edges. (iii) Temperature effects can restore the gapless edge modes, provided that the energy scale of interactions is smaller than the bulk gap. In addition, we observe the topological edge Mott behavior only in some finite temperature region.

Coexistence of topological Dirac fermions on the surface and three-dimensional Dirac cone state in the bulk of ZrTe5 single crystal

Although, the long-standing debate on the resistivity anomaly in ZrTe5 somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe5 to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe5 single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe5 hosts a novel electronic phase of material, having massless Dirac fermionic excitation in its bulk gap state, unlike earlier reported 3D topological insulators. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature (T < 2 K) by controlling impurity and defects.

On the origins of anomalous elastic moduli and failure strains of GaP nanowires

Previous reports suggest that Raman peaks in uniaxially loaded nanowires with diamond cubic and zinc blende crystal structures shift at rates that are significantly different from bulk specimens. We have investigated the first order Raman scattering from individual, free-standing, [111] oriented GaP nanowires ranging from 75 to 180 nm in diameter at uniaxial tensile stresses up to 5 GPa. All of the phonon modes were shifted to frequencies lower than previously reported for bulk GaP, and significant splitting of the degenerate transverse optical mode was observed. A general analysis method using single and double Lorentzian fits of the Raman peaks is presented and used to report more accurate values of the phonon deformation potentials (PDPs) that relate uniaxial strains to Raman peak shifts in GaP. A new set of PDPs determined from the nanowires revealed that the they have elastic moduli and failure strains that are consistent with bulk GaP. The analysis method eliminated the anomalous, inconsistent deformation behavior commonly reported in Raman-based strain measurements of nanowires, and can be extended to other materials systems with degenerate phonons.

Time-reversal-symmetry broken quantum spin Hall in Lieb lattice

In this paper, the time-reversal (TR) symmetry broken quantum spin Hall (QSH) in Lieb lattice is investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, and it has three different sites in each unit cell. The most distinctive feature of this model is that it contains only one Dirac-cone in the first Brillouin zone, where the upper dispersive band and the lower dispersive band touch the middle zero-energy band at M point and form a cone-like dispersion. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. When the intrinsic SOC is nonzero, all the band structures are separated everywhere in the Brillouin zone and can be characterized by some topological invariants. The exact QSH first put forward by Kane and Mele in 2005 is characterized by the z2 number. The protection from the TR symmetry ensures the gapless crossing in the surface state in the bulk gap. In our model, the presence of the exchange field breaks the TR symmetry, which results in opening a small gap in the crossing point and the z2 topological order is not suitable for the system. This kind of state is a TR symmetry broken QSH, which is characterized by the spin Chern numbers. The spin Chern numbers have a much wider scope of application than z2 index. It is suitable for both TR symmetry system and the TR symmetry broken system. For Lieb lattice ribbons, the spin polarization and the wave-function distributions are obtained numerically. There exists a weak scattering between the counter-propagating states in the TR symmetry broken QSH, and the spin transport along the boundary with a low dissipation replaces the dissipationless spin current in a TR symmetry system. In experiment, such a system can be realized by the two-dimensional Fermi gases in optical lattice with Lieb symmetry. The above conclusions are expected to give theoretical guidance in the spin device and the quantum information.

Emerging topological states in quasi‐two‐dimensional materials

Inspired by the discovery of graphene, various two‐dimensional (2D) materials have been experimentally realized, which exhibit novel physical properties and support promising applications. Exotic topological states in 2D materials (including quantum spin Hall and quantum anomalous Hall insulators), which are characterized by nontrivial metallic edge states within the insulating bulk gap, have attracted considerable attentions in the past decade due to their great importance for fundamental research and practical applications. They also create a surge of research activities and attract extensive efforts to search for new topological materials in realistic 2D/quasi‐2D systems. This review presents a comprehensive survey of recent progress in designing of topological states in quasi‐2D materials, including various quantum well heterostructures and 2D atomic lattice structures. In particular, the possibilities of constructing topological nontrivial states from commonly used materials are discussed and the ways of enlarging energy gaps of topological states and realizing different topological states in a single material are presented. WIREs Comput Mol Sci 2017, 7:e1296. doi: 10.1002/wcms.1296This article is categorized under: Structure and Mechanism &gt; Computational Materials Science

Phase transition and spin-resolved transport inMoS2nanoribbons

The electronic structure and transport properties of monolayer ${\mathrm{MoS}}_{2}$ are studied using a tight-binding approach coupled with the nonequilibrium Green's function method. A zigzag nanoribbon of ${\mathrm{MoS}}_{2}$ is conducting due to the intersection of the edge states with the Fermi level that is located within the bulk gap. We show that applying a transverse electric field results in the disappearance of this intersection and turns the material into a semiconductor. By increasing the electric field the band gap undergoes a two stage linear increase after which it decreases and ultimately closes. It is shown that in the presence of a uniform exchange field, this electric field tuning of the gap can be exploited to open low energy domains where only one of the spin states contributes to the electronic conductance. This introduces possibilities in designing spin filters for spintronic applications.

Effects of spin excitons on the surface states of SmB6 : A photoemission study

We present the results of high-resolution valence-band photoemission spectroscopic study of SmB6 which shows evidence for a V-shaped density of states of surface origin within the bulk gap. The spectroscopy data is interpreted in terms of the existence of heavy 4f surface states, which may be useful in resolving the controversy concerning the disparate surface Fermi-surface velocities observed in experiments. Most importantly, we find that the temperature dependence of the valence-band spectrum indicates that a small feature appears at a binding energy of about -9 meV at low temperatures. We attribute this feature to a resonance caused by the spin-exciton scattering in SmB6 which destroys the protection of surface states due to time-reversal invariance and spin-momentum locking. The existence of a low-energy spin-exciton may be responsible for the scattering which suppresses the formation of coherent surface quasi-particles and the appearance of the saturation of the resistivity to temperatures much lower than the coherence temperature associated with the opening of the bulk gap.

Disordered Chern insulator with a two-step Floquet drive

We explore the physics of a Chern insulator subjected to a two step Floquet drive. We analytically obtain the phase diagram and show that the system can exhibit different topological phases characterized by presence and chirality of edge-modes in the two bulk gaps of the Floquet quasienergy spectrum, around $0$ and $\pi$. We find that the phase of the system depends on the mean but not on the amplitude of the drive. The bulk topological invariants characterizing the phases can be extracted by mapping the unitary evolution within a time period to an energetically trivial but topologically non-trivial time evolution. An extensive numerical study of the bulk topological invariants in the presence of quenched disorder reveals new transitions induced by strong disorder (i) from the different topological to trivial insulator phases and (ii) from a trivial to a topological Anderson insulator phase at intermediate disorder strengths. Careful analysis of level statistics of the quasienergy spectrum indicates a `levitation-annihilation' mechanism near these transitions.

Edge states and quantum phase transition in graphene under in-plane effective exchange fields

We investigated the edge states and quantum phase transition in graphene under an in-plane effective exchange field. The result shows that the combined effects of the in-plane effective exchange field and a staggered sublattice potential can induce zero-energy flat bands of edge states. Such flat-band edge states can evolve into helical-like ones in the presence of intrinsic spin–orbit coupling, with a unique spin texture. We also find that the bulk energy gap induced by the spin–orbit coupling and staggered sublattice potential can be closed and reopened with the in-plane effective exchange field, and the reopened bulk gap can be even larger than that induced by only the spin–orbit coupling and staggered sublattice potential, which is different from the case of an out-of-plane effective exchange field. The calculated spin-dependent Chern numbers suggest that the bulk gap closing and reopening is accompanied by a quantum phase transition from a trivial insulator phase across a metal phase into a spin-dependent quantum Hall phase.