Quantum Valley Hall Effect Research Articles

Assessment of bilayer silicene to probe as quantum spin and valley Hall effect

Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.

Dial-in Topological Metamaterials Based on Bistable Stewart Platform

Recently, there have been significant efforts to guide mechanical energy in structures by relying on a novel topological framework popularized by the discovery of topological insulators. Here, we propose a topological metamaterial system based on the design of the Stewart Platform, which can not only guide mechanical waves robustly in a desired path, but also can be tuned in situ to change this wave path at will. Without resorting to any active materials, the current system harnesses bistablilty in its unit cells, such that tuning can be performed simply by a dial-in action. Consequently, a topological transition mechanism inspired by the quantum valley Hall effect can be achieved. We show the possibility of tuning in a variety of topological and traditional waveguides in the same system, and numerically investigate key qualitative and quantitative differences between them. We observe that even though both types of waveguides can lead to significant wave transmission for a certain frequency range, topological waveguides are distinctive as they support robust, back scattering immune, one-way wave propagation.

Tunable Acoustic Valley–Hall Edge States in Reconfigurable Phononic Elastic Waveguides

This study investigates the occurrence of acoustic topological edge states in a 2D phononic elastic waveguide due to a phenomenon that is the acoustic analogue of the quantum valley Hall effect. We show that a topological transition takes place between two lattices having broken space inversion symmetry due to the application of a tunable strain field. This condition leads to the formation of gapless edge states at the domain walls, as further illustrated by the analysis of the bulk-edge correspondence and of the associated topological invariants. Although time reversal symmetry is still intact in these systems, the edge states are topologically protected when inter-valley mixing is either weak or negligible. Interestingly, topological edge states can also be triggered at the boundary of a single domain if boundary conditions are properly selected. We also show that the static modulation of the strain field allows tuning the response of the material between the different supported edge states.

Topologically protected interface phonons in two-dimensional nanomaterials: hexagonal boron nitride and silicon carbide.

We perform both lattice dynamics analysis and molecular dynamics simulations to demonstrate the existence of topologically protected phonon modes in two-dimensional, monolayer hexagonal boron nitride and silicon carbide sheets. The topological phonon modes are found to be localized at an in-plane interface that divides these systems into two regions of distinct valley Chern numbers. The dispersion of this topological phonon mode crosses over the frequency gap, which is opened through analogy with the quantum valley Hall effect by breaking the inversion symmetry of the primitive unit cells. Consequently, vibrational energy with frequency within this gap is topologically protected, resulting in wave propagation that exhibits minimal backscattering, is robust with regard to structural defects such as sharp corners, and exhibits excellent temporal stability. Our findings open up the possibility of actuating and detecting topological phonons in two-dimensional nanomaterials.

Electronic structure and spin/valley transport properties of monolayer MoS2 under the irradiation of the off-resonant circularly polarized light

The new-type monolayer semiconductor material molybdenum disulfide (MoS2) is direct band gap semiconductor with a similar geometrical structure to graphene, and as it owns superior physical features such as spin/valley Hall effect, it should be more excellent than graphene from the viewpoint of device design and applications. The manipulation of the spin and valley transport in MoS2-based device has been an interesting subject in both experimental and theoretical researches. Experimentally, the photoninduced quantum spin and valley Hall effects may result in high on-off speed spin and/or valley switching based on MoS2. Theoretically, the off-resonant electromagnetic field induced Floquet effective energy should modulate effectively the electronic structure, spin/valley Hall conductance as well as the spin/valley polarization of the MoS2, through the virtual photon absorption and/or emission processes. Utilizing the low energy effective Hamilton model from the tight-binding approximation and Kubo linear response theorem, we theoretically investigate the electronic structure and spin/valley transport properties of the monolayer MoS2 under the irradiation of the off-resonant circularly polarized light in the present work. The band gaps around the K and K' point of the Brillouin region for monolayer MoS2 proves to increase linearly and decrease firstly and then increase, respectively with the increase of external off-resonant right-circularly polarized light induced effective coupling energy, and decrease firstly and then increase and increase linearly with the increase of left-circularly polarized light induced effective coupling energy, therefore, the interesting transition of semiconducting-semimetallic-semiconducting may be observable in monolayer MoS2. Furthermore, the spin and valley Hall conductance of the monolayer MoS2 for the case without off-resonant circularly polarized light are 0 and 2e2/h, respectively, and they will convert into -2e2/h and 0 when the absolute value of the off-resonant circularly polarized light induced effective coupling energy is in a range of 0.79-0.87 eV. Finally, the spin polarization for monolayer MoS2 increases up to a largest value and changes from positive to negative and/or negative to positive at the vicinity of the effective coupling energy ±0.79 eV of the off-resonant right/left circularly polarized light, while the valley polarization should increase firstly and then decrease with the off-resonant circularly polarized light, and goes up to 100% in the range of 0.79-0.87 eV of the absolute value for effective coupling energy. Therefore, the external off-resonant circularly polarized electromagnetic field should be an effective means in manipulating the electronic structure, spin/valley Hall conductance and spin/valley polarization of the monolayer MoS2, the two-dimensional MoS2 may be tuned into a brand bandgap material with excellent spin/valley and optoelectrical properties.

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit (RSO) interaction , and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.

Valley-polarized quantum transport generated by gauge fields in graphene

We report on the possibility to simultaneously generate in graphene a bulk valley-polarized dissipative transport and a quantum valley Hall effect by combining strain-induced gauge fields and real magnetic fields. Such unique phenomenon results from a ‘resonance/anti-resonance’ effect driven by the superposition/cancellation of superimposed gauge fields which differently affect time reversal symmetry. The onset of a valley-polarized Hall current concomitant to a dissipative valley-polarized current flow in the opposite valley is revealed by a Hall conductivity plateau. We employ efficient linear scaling Kubo transport methods combined with a valley projection scheme to access valley-dependent conductivities and show that the results are robust against disorder.

Quantum valley Hall effect and perfect valley filter based on photonic analogs of transitional metal dichalcogenides

We consider theoretically staggered honeycomb lattices for photons which can be viewed as photonic analogs of transitional metal dichalcogenides (TMD) monolayers. We propose a simple realization of a photonic Quantum Valley Hall effect (QVHE) at the interface between two TMD analogs with opposite staggering on each side. This results in the formation of valley-polarized propagating modes whose existence relies on the difference between the valley Chern numbers, which is a $\mathbb{Z}_2$ topological invariant. We show that the magnitude of the photonic spin-orbit coupling based on the energy splitting between TE and TM photonic modes allows to control the number and propagation direction of these interface modes. Finally, we consider the interface between a staggered and a regular honeycomb lattice subject to a non-zero Zeeman field, therefore showing Quantum Anomalous Hall Effect (QAHE). In such a case, the topologically protected one-way modes of the QAHE become valley-polarized and the system behaves as a perfect valley filter.

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.

Half-metallic quantum valley Hall effect in biased zigzag-edge bilayer graphene nanoribbons

We have investigated electron-electron interaction effects on gapless edge states in the antiferromagnetic phase of zigzag-edge bilayer graphene nanoribbons under a voltage bias between the layers by using a tight-binding model with on-site Coulomb interactions. We found that a zigzag-edge bilayer graphene nanoribbon can have gapless edge states corresponding to peculiar topologically nontrivial insulator phases, such as a half-metallic quantum valley Hall phase. The half-metallicity was found to be due to the on-site Coulomb interactions through which excess charges produced by the voltage bias between the layers give rise to the potential difference between the opposite edges. A topological phase diagram in the antiferromagnetic phase of a zigzag-edge bilayer graphene nanoribbon was determined as a function of the bias voltage and the ribbon width. The quantum confinement effect, which was found to be graphene-like for narrow ribbons and to be bilayer graphene-like for wide ribbons, was also confirmed to play an important role in determining the topologically nontrivial insulator phases.

Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect

We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry within the unit cell. Examples for discrete one and two-dimensional lattices elucidate the concept and illustrate parallels with the quantum valley Hall effect. The concept is implemented on an elastic plate featuring an array of resonators arranged according to a hexagonal topology. The resulting continuous structures have non-trivial bandgaps supporting edge waves at the interface between two media with different topological invariants. The topological properties of the considered configurations are predicted by unit cell and finite strip dispersion analyses. Numerical simulations demonstrate edge wave propagation for excitation at frequencies belonging to the bulk bandgaps. The considered plate configurations define a framework for the implementation of topological concepts on continuous elastic structures of potential engineering relevance.

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one- and two-dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the Pseudo quantum electrodynamics (PQED). The well known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.

Topological phase transition from trigonal warping in van der Waals multilayers

In van der Waals multilayers of triangular lattice, trigonal warping occurs universally due to the interlayer hopping. We theoretically investigate the effect of trigonal warping upon distinctive topological phases, like the quantum anomalous Hall effect (QAHE) and the quantum valley Hall effect (QVHE). Taking Bernal-stacked bilayer graphene as an example, we find that the trigonal warping plays a crucial role in the formation of QAHE in large exchange field and/or interlayer potential difference by inducing extra band inversion points at momentum further away from high symmetric point. The presence of trigonal warping shrinks the phase space of QAHE and QVHE, leading to the emergence of valley-polarized QAHE with high Chern numbers ranging from $ \mathcal{C}=-7 $ to $ 7 $. These results suggest that the universal trigonal warping may play important role when the Bloch states at momentum away from high-symmetric points are involved.

Mass inversion in graphene by proximity to dichalcogenide monolayer

Proximity effects resulting from depositing a graphene layer on a TMD substrate layer change the dynamics of the electronic states in graphene, inducing spin orbit coupling (SOC) and staggered potential effects. An effective Hamiltonian that describes different symmetry breaking terms in graphene, while preserving time reversal invariance, shows that an inverted mass band gap regime is possible. The competition of different perturbation terms causes a transition from an inverted mass phase to a staggered gap in the bilayer heterostructure, as seen in its phase diagram. A tight-binding calculation of the bilayer validates the effective model parameters. A relative gate voltage between the layers may produce such phase transition in experimentally accessible systems. The phases are characterized in terms of Berry curvature and valley Chern numbers, demonstrating that the system may exhibit quantum spin Hall and valley Hall effects.

Interfacial properties of stanene–metal contacts

Recently, two-dimensional buckled honeycomb stanene has been manufactured by molecular beam epitaxy growth. Free-standing stanene is predicted to have a sizable opened band gap of 100 meV at the Dirac point due to spin–orbit coupling (SOC), resulting in many fascinating properties such as quantum spin Hall effect, quantum anomalous Hall effect, and quantum valley Hall effect. In the first time, we systematically study the interfacial properties of stanene–metal interfaces (metals = Ag, Au, Cu, Al, Pd, Pt, Ir, and Ni) by using ab initio electronic structure calculations considering the SOC effects. The honeycomb structure of stanene is preserved on the metal supports, but the buckling height is changed. The buckling of stanene on the Au, Al, Ag, and Cu metal supports is higher than that of free-standing stanene. By contrast, a planar graphene-like structure is stabilized for stanene on the Ir, Pd, Pt, and Ni metal supports. The band structure of stanene is destroyed on all the metal supports, accompanied by a metallization of stanene because the covalent bonds between stanene and the metal supports are formed and the structure of stanene is distorted. Besides, no tunneling barrier exists between stanene and the metal supports. Therefore, stanene and the eight metals form a good vertical Ohmic contact.

Spin-polarized gapped Dirac spectrum of unsupported silicene

We study effects of the spin–orbit interaction and the atomic reconstruction of silicene on its electronic spectrum. As an example we consider unsupported silicene pulled off from Pb(111) substrate. Using first principles density functional theory we show that the inversion symmetry broken arrangement of atoms and the spin–orbit interaction generate a spin-polarized electronic spectrum with an energy gap in the Dirac cone. These findings are particularly interesting in view of the quantum anomalous and quantum valley Hall effects and should be observable in weakly interacting silicene-substrate systems.

First-principles investigations on the Berry phase effect in spin–orbit coupling materials

In recent years, the Berry phase as a fascinating concept has made a great success for interpreting many physical phenomena. In this paper, we review our past works on the Berry phase effect in solid materials with spin–orbit coupling. Firstly, we developed an exact method for directly evaluating the Berry curvature and anomalous Hall conductivity, then the intrinsic mechanism of anomalous Hall effect was quantitatively confirmed in bcc Fe and CuCr2Se4−xBrx. An effective method was proposed to decompose the anomalous Hall effect into the intrinsic and extrinsic contributions. We also developed computational methods for the spin Hall conductivity and anomalous Nernst conductivity. Secondly, we developed a powerful method for computing the Z2 topological invariant without consideration of special symmetry. We predicted many topological insulators in three-dimensions, including half-Heusler, chalcopyrite, strained InSb, core-holed Ge and InSb, Bi2Te3/BiTeI heterostructure, and in two-dimensions, including silicene, germanene, stanene, X-hydride/halide (X=N–Bi) monolayers and Bi4Br4. We also predicted the quantum anomalous Hall effect in magnetic atoms adsorbed graphene and half-passivated BiH, the quantum valley Hall effect and topological superconducting in silicene and n-dopped BiH. Finally, the summary of our past works and the further outlooks are discussed.

Valley Hall effect in silicene and hydrogenated silicene ruled by grain boundaries: Anab initioinvestigation

We have performed an ab initio theoretical study of the energetic stability and the electronic properties of pristine and hydrogen-adsorbed grain boundaries (GBs) in silicene. We find that GBs in silicene present lower formation energy when compared with their counterparts in graphene. Removing the inversion symmetry, by applying an external electric field perpendicular to the silicene sheet, we verify the formation of valley-indexed metallic states lying along the GBs, characterizing the quantum valley Hall effect (QVHE). Here, we find the maintenance of the QVHE upon the presence of disordered and asymmetric geometries along the GBs. Those metallic states are suppressed upon the adsorption of H adatoms along the GBs. The H adatoms promote an unbalance on the electronic occupation of the unsaturated $\ensuremath{\pi}$ electrons beside the hydrogenated GB rows, giving rise to (i) a net magnetic moment on the Si atoms along the edge sites of the hydrogenated GBs and (ii) an electronic band structure characterized by spin-polarized valley states protected against backscattering processes.

Tunable topological quantum states in three- and two-dimensional materials

We review our theoretical advances in tunable topological quantum states in three- and two-dimensional materials with strong spin-orbital couplings. In three-dimensional systems, we propose a new tunable topological insulator, bismuth-based skutterudites in which topological insulating states can be induced by external strains. The orbitals involved in the topological band-inversion process are the d- and p-orbitals, unlike typical topological insulators such as Bi2Se3 and BiTeI, where only the p-orbitals are involved in the band-inversion process. Owing to the presence of large d-electronic states, the electronic interaction in our proposed topological insulator is much stronger than that in other conventional topological insulators. In two-dimensional systems, we investigated 3d-transition-metal-doped silicene. Using both an analytical model and first-principles Wannier interpolation, we demonstrate that silicene decorated with certain 3d transition metals such as vanadium can sustain a stable quantum anomalous Hall effect. We also predict that the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition-metal-doped silicenes where the energy band inversion occurs. These findings provide realistic materials in which topological states could be arbitrarily controlled.

Topological valley transport at bilayer graphene domain walls.

Electron valley, a degree of freedom that is analogous to spin, can lead to novel topological phases in bilayer graphene. A tunable bandgap can be induced in bilayer graphene by an external electric field, and such gapped bilayer graphene is predicted to be a topological insulating phase protected by no-valley mixing symmetry, featuring quantum valley Hall effects and chiral edge states. Observation of such chiral edge states, however, is challenging because inter-valley scattering is induced by atomic-scale defects at real bilayer graphene edges. Recent theoretical work has shown that domain walls between AB- and BA-stacked bilayer graphene can support protected chiral edge states of quantum valley Hall insulators. Here we report an experimental observation of ballistic (that is, with no scattering of electrons) conducting channels at bilayer graphene domain walls. We employ near-field infrared nanometre-scale microscopy (nanoscopy) to image in situ bilayer graphene layer-stacking domain walls on device substrates, and we fabricate dual-gated field effect transistors based on the domain walls. Unlike single-domain bilayer graphene, which shows gapped insulating behaviour under a vertical electrical field, bilayer graphene domain walls feature one-dimensional valley-polarized conducting channels with a ballistic length of about 400 nanometres at 4 kelvin. Such topologically protected one-dimensional chiral states at bilayer graphene domain walls open up opportunities for exploring unique topological phases and valley physics in graphene.