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The complex nature of filling factor ν = 0 of monolayer graphene is studied in magnetotransport experiments. As a function of perpendicular magnetic field a metal-insulator transition is observed, which is attributed to disorder-induced Landau level broadening in the canted antiferromagnetic phase. In the metallic regime a separation of the zeroth Landau level appears and signs of the quantum spin Hall effect are seen near ν = 0. In addition to local transport, nonlocal transport experiments show results being consistent with helical edge transport.

A new model with analysis for the propagation of flexural waves in a phononic plate at nanoscale is developed. The Gurtin-Murdoch theory for surface elasticity is adopted to model the surface heterogeneity. The Mindlin (or first-order) plate theory is further generalized to establish the governing equations for flexural waves in a phononic plate with surface effect, for which the plane wave expansion method is applied to derive the dispersion relation. A numerical model is developed using the finite element method and very good consistency between theory and numerical solution is observed. It is found that the surface density and the surface residual stress play the main role that affects the band structures. The surface effect can be approximately regarded as the competition between frequency decrease due to surface density and frequency increase caused by surface residual stress, which effectively increases the low-frequency bands but decreases the high-frequency bands. The quantum spin Hall effect is observed in the phononic plate at nanoscale, and the surface effect is studied numerically. By applying the k.p perturbation method, a theoretical framework is established to calculate the spin Chern number, which is an important topological invariant that determines the quantum spin Hall effect. Based on the topological analysis, an efficient waveguide with a zig-zag path is designed, in which a topologically protected wave in the interface state can robustly propagate along the path against disorders. The theory and numerical study developed in this paper will help better understand the size-dependent quantum spin Hall effect in nanostructures and it may also provide guidance for the design of topological wave devices at nanoscale.

The completion of quantum Hall trio, namely the quantum Hall effect (QHE), the quantum spin Hall effect (QSHE), and the quantum anomalous Hall effect (QAHE), has greatly broadened our understandings about the electron movement in solids. Likewise, the discovered scale-invariant dissipationless conduction in these three quantum transport states has inspired us to the development of practical low-power-consumption electronics/spintronics applications. In this review article, we outline the fundamental physics and relations between different Hall effects. In general, QSHE is a result of band inversion due to the large spin-orbit coupling; since the time-reversal symmetry (TRS) is well-protected in such QSH insulators, helical edge states with both spin-up and spin-down electrons are allowed and the conduction is immune to non-magnetic impurities. On the other hand, when TRS is broken by either perpendicular magnetic field or magnetic order, helical edge states are reduced to the single chiral channel, which in turn gives rise to QHE and QAHE, and backscattering from any impurity is strictly forbidden owing to the nature of chirality. Moreover, the interplay between this quantum Hall trio in certain conditions unveils new ways to explore emerging chiral materials and related quantum phenomena.

General nonequilibrium quantum transport equations are derived for a coupled system of charge carriers, Dirac spin, isospin (or valley spin), and pseudospin, such as either one of the band, layer, impurity, and boundary pseudospins. Limiting cases are obtained for one, two or three different kinds of spin occurring in a system. We show that a characteristic integer number Ns determines the formal form of spin quantum transport equations, irrespective of the type of spins or pseudospins, as well as the maximal entanglement entropy. The results may shed a new perspective on the mechanism leading to zero modes and chiral/helical edge states in topological insulators, integer quantum Hall effect topological insulator (QHE-TI), quantum spin Hall effect topological insulator (QSHE-TI) and Kondo topological insulator (Kondo-TI). It also shed new light in the observed competing weak localization and antilocalization in spin-dependent quantum transport measurements. In particular, a novel mechanism of localization and delocalization, as well as the new mechanism leading to the onset of superconductivity in bilayer systems seems to emerge naturally from torque entanglements in nonequilibrium quantum transport equations of spin and pseudospins. Moreover, the general results may serve as a foundation for engineering approximations of the quantum transport simulations of spintronic devices based on graphene and other 2-D materials such as the transition metal dichalcogenides (TMDs), silicene, as well as based on topological materials exhibiting quantum spin Hall effects. The extension of the formalism to spincaloritronics and pseudo-spincaloritronics is straightforward.

The Dirac oscillator was initially introduced as a Dirac operator which is linear in momentum and coordinate variables. In contrast to the usual 2D Dirac oscillator, the 2D Kramers–Dirac oscillator admits the time-reversal symmetry, which is a reason for the present nomenclature. It is shown that there exists a family of eigenstates associated with an eigenvalue linear in the control parameter, and the eigenvalue in question goes down from positive values to negative values as the parameter varies in the positive direction. The other eigenvalues are broken up into two bands, positive and negative. The 2D Dirac and the 2D Kramers–Dirac oscillators are compared in their physical grounds and in their spectral structure from the viewpoint of the time-reversal symmetry.

We propose a computational methodology to perform inverse design of quantum spin hall effect (QSHE)-based phononic topological insulators. We first obtain two-fold degeneracy, or a Dirac cone, in the band structure using a level set-based topology optimization approach. Subsequently, four-fold degeneracy, or a double Dirac cone, is obtained by using zone folding, after which breaking of translational symmetry, which mimics the effect of strong spin-orbit coupling and which breaks the four-fold degeneracy resulting in a bandgap, is applied. We use the approach to perform inverse design of hexagonal unit cells of C6 and C3 symmetry. The numerical examples show that a topological domain wall with two variations of the designed metamaterials exhibit topologically protected interfacial wave propagation, and also demonstrate that larger topologically-protected bandgaps may be obtained with unit cells based on C3 symmetry.

Second-order phononic topological insulators (SPTIs) featured with topological edge and corner states offer promising ways for steering elastic waves. However, existing SPTIs were mainly designed with trial-and-error procedures, limiting the achievable width of topological bandgaps for tightly confining edge and corner states. Here, we develop a topology optimization approach for designing quantum spin Hall effect-based SPTIs. By simultaneously maximizing the powers emitted by the artificially selected body forces via topology optimization, the dipolar and quadrupolar modes are excited at the desirable frequencies. As a result, topologically nontrivial and trivial phononic crystals (PCs) with a record-breaking size of the overlapped bandgap (36.14%) are created. Thereafter, SPTIs arranged by hexagon and rhombus unit cells extracted from the optimized PCs are successfully created, validating the effectiveness of the optimization results. Additionally, the spatial decay of corner states is quantitatively characterized based on the complex band theory. Our work bridges topology optimization with SPTIs and, meanwhile, enriches the mechanism of corner states.

Surface-related properties of the three-dimensional topological insulators with/without considerable thickness are thought as the furthermost demandable in the field of condensed matter physics because of its rich technological applications. Motivated by these properties, we consider low energy effective Hamiltonian of three-dimensional topological insulators having a negligible thickness in the presence of irradiated off-resonant circularly polarized light to assess it's topological features. By evaluating the surface pseudo-spin Chern number analytically, we find that three dimensional topological insulator thin films pass through a phase transition from quantum pseudo spin Hall (QPSH) state to a photo-induced quantum Hall (P-QH) state when the effective energy induced by the circularly polarized light becomes greater in magnitude than the effective energy induced by the coupling between the top and bottom surfaces. We find that both the QPSH and P-QH states present a pronounced step-wise character. The phase-transition between these two topological states can be controlled by the degree of hybridization and off-resonant circularly polarized light. Additionally, we analyze the topological structure of QPSH and P-QH states by mapping the three-dimensional unit vector on a unit sphere and reveal that they display merons-like or anti-merons-like configurations in the real spin space.

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.

As a two-dimensional material with a low-buckling structure, germanene has attracted considerable interest because of its excellent physical properties, such as massless Dirac fermions and quantum spin Hall effect. The mechanical characteristics of germanene are of the utmost importance when one is assessing its viability for nanodevices, especially for ones with defects. In this work, the stabilities, mechanical properties, and changes in electronic properties under mechanical strain for both pristine and defective germanene sheets were studied and analyzed with use of density functional theory. The mechanical properties of defect-free germanene exhibited obvious anisotropy along different directions. The mechanical properties of germanene sheets exhibited high sensitivity to the defect parameters, such as the linear density of vacancies, the width of the cracks, and the inflection angles caused by the grain boundaries. In addition, the applied mechanical strain changed the electronic properties of germanene to a large extent. The information obtained will be useful for the understanding and potential application of germanene.

Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence. In this work, these techniques are implemented to study two-dimensional dirty superconductors described by Bogoliubov-de Gennes Hamiltonians. After a thorough presentation of the basic framework and the topological invariants, Kubo formulas for the thermal, thermoelectric and spin Hall conductance are analyzed together with the corresponding edge currents., published version in J Geo Phys

Dirac materials have received attracting attentions due to their intriguing properties and potential applications in advanced electronics. In this work, we reported 44 new two-dimensional Dirac materials, named ABX6 monolayers, by constructing group IVA, VA, and VIA elements with the same structural prototype. Our first principle calculations revealed that they show excellent dynamical stability, mechanical stability, and thermodynamics stability. Those monolayers possess the elastic constant from 23.93 to 245.57 N/m, attributing to broadly used mechanical strength materials. The electronic calculations show that the Dirac cones in all ABX6 monolayers are both located at K points in Brillouin zone and mainly contributed from the pz orbital of group IVA atoms and group VIA atoms. Their Fermi velocities are from 3.44 × 105 to 6.83 × 105 m/s, which is benefiting for the potential applications in high-speed electric devices. Moreover, it is interesting to notice that the ABX6 monolayers with heavy atoms, such as the ISbSn6 monolayer, exhibit a large band gap of ∼ 0.106 eV, due to the spin-orbital coupling effect. The further calculations reveal their nontrivial topological nature with topological edge states, indicating they could be used as potential dissipationless transport devices at room temperature.

We propose a topological photonic crystal (PC) with split hexagonal ring structure by removing six isosceles trapezoids on the ring. By changing the size of trapezoid and hexagonal ring, we realize Dirac point and multi topology transition of the quadruple accidental degenerate. We simulate the quantum spin Hall effect (QSHE) and find that the EM wave (from 149.9 THz to 155.96 THz) almost achieves lossless transmission in the system, and is immune to sharp bends, cavity and disorder. At the junction of trivial and nontrivial photonic crystals (PCs), the topological trivial is replaced with the ordinary honeycomb lattice to construct line defect. We prove that the line defect has a non-spin-mixing defect mode with topological protection. The PC with line defect mode has high transmission efficiency, robust unidirectionality, and high optical local performance, which can not only be used in lasers, all-optical integrated circuits, optical communication systems and semiconductor technologies, but also will enrich the exploration of topological physics.

Spin-orbit interaction (SOI) connecting an electronic spin with its momentum is crucial for numerous fundamental physical researches and their applications, including quantum spin Hall effect, Majorana Fermions and spin-orbit qubits. By breaking structural inversion symmetry, Rashba spin-orbit interaction (RSOI) provides an available method for the manipulation of spin by controlling electronic movement within external potential field. In this study, we demonstrate the RSOI of conduction electron modulated by stress-induced polarization field in ZnO/CdO quantum well (QW). The polarization field exactly triggers band inversion between the electron and light hole. The peak of RSOI coefficient can reach approximately up to 83 meV ⋅ nm, almost three orders of magnitude higher than the conventional GaAs-based QWs. This study can be beneficial to sufficient manipulation of spin qubits by strong RSOI quantum piezotronic effect, and will stimulate an intense researching interest in low-dimensional quantum piezotronic devices.

Topological photonic crystals (PCs) with unique optical performances have tremendous potential application in the realm of integrated photonic circuits. In this paper, we propose split-ring topological PCs manufactured by conventional silicon material, which hosts both topological transition and helical edge states mimicking the quantum spin Hall effect. A large nontrivial bandgap from 224.85 THz to 235.03 THz can be achieved. Non-spin-mixing defect modes with the nature of topological protection are demonstrated when line defects are introduced by fabricating the sectional columns with Al2O3 at the interface of two different topologies. A guide path for the non-spin-mixing defect modes reveals that light can propagate unidirectionally with high efficiency, powerful optical localization, and strong stability. This work provides a versatile method to improve the performances of optical transmission and reveals a novel mechanism to guide light transmission, which has vast application prospects in the all-optical integrated circuits.

Since the proposal of quantum spin Hall effect in graphene, there has been great progress made in exploration of various topological phases. Theoretical studies especially first-principles calculations have been playing a critical role in predicting material realizations and studying their novel properties. Here, we review some of our efforts in the prediction and study of gapped topological materials using various theoretical tools. We focus on WTe2-type quantum spin Hall insulators and SnTe-type topological crystalline insulators, both of which were predicted by first-principles calculations and soon confirmed in various experiments. In the end, we review the effect of strain on topological materials, which can generally induce a topological phase transition and manipulate electronic properties of topological materials for potential device applications.

A general study of [Tb2] molecular magnet is presented using the general spin Hamiltonian formalism. A spin-spin correlators determined for a spin wave functions in [Tb2] are analyzed numerically and compared in details with the results obtained by means of conventional quantum mechanics. It is shown that the various expectation values of the spin operators and a study of their corresponding probability distributions allow to have a novel understanding in spin dynamics of entangled qubits in quantum [Tb2] system. The obtained results reveal that the properties of spin-spin correlators are responsible for the entanglement of the spin qubit under a pulse magnetic field. It allows us to present some quantum circuits determined for quantum computing within SSNQ based on [Tb2] molecule, including the CNOT and SWAP gates.

In a Hall plate with finite size and contacts the Hall output voltage is given by the product of sheet resistance, input current, Hall mobility, magnetic flux density, and Hall geometry factor G H . G H ∈ [ 0 , 1 ] accounts for the loss in signal due to the contacts. At weak magnetic field G H → G H 0 is a function of geometrical parameters only, which makes it the crucial point for layout optimization. We show how to express G H 0 alternatively as a function of electrical parameters only, namely of input and output resistances over sheet resistance. This allows for an analytical optimization of signal-to-noise-ratio (SNR) without getting lost in the multitude of geometrical representations of equivalent Hall plates. In the course of this investigation we notice a hidden symmetry property of G H , which we prove rigorously in the limit of small magnetic fields. The physical meaning of this symmetry in the case of Hall plates with equal input and output resistances is also explained.

We investigate the electronic states of a zigzag graphene nanoribbon in the presence of mutually perpendicular electric and magnetic fields. We find that both edge and bulk states are localized in the vicinity of zero energy, leading to spin-polarized states and quantized transport in the system. A quantum spin Hall phase is characterized by helical edge and tilted bulk states. By tuning Fermi energy and in-plane electric field, a topological phase transition is also realized. The electronic states support the transport of spin and charge, and the corresponding spin and charge Hall conductivities are calculated in a four-terminal geometry.

A theoretical realization of the quantum magnetotransport properties for the surface states of ultrathin Floquet topological insulators (FTIs) is presented. Their band structure in the presence of an external perpendicular magnetic field is derived and discussed. Further, the longitudinal and Hall conductivities are evaluated using linear response theory. A new quantum Hall state of matter has been found in FTIs under the application of a magnetic field where the n =0 Landau level undergoes a quantum phase transition from a trivial insulator state to a Hall insulator state. In the former state the Hall conductivity is zero at zero Fermi energy ( EF=0) while in the latter the Hall conductivity is equal to e 2 / h . The proposed effects are accessible to experiments which open new possibilities to study FTIs for the realization of (i) non trivial quantum phase transitions, (ii) exchange of surface states, and (iii) unusual quantum Hall plateaus.

We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on $S^{2k-1}$ in the $SO(2k-1)$ monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold $S^{2k-1}$ to the one-dimension higher $SO(2k)$ gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed., Comment: 1+49 pages, 8 figures, 4 tables, typos corrected

Examination of the role of strain on the quantum spin hall (QSH) effect and band inversion for the monolayer of tin, stanene, is of interest. To this end, several uniaxial and biaxial strain loadings along the armchair (AC)- and zigzag (ZZ)-directions are applied using first principles calculations based on density functional theory (DFT). We observe QSH insulator as well as semi-metallic property associated with the strained stanene.

The study of ZrTe 5 is revived because theory predicts the quantum spin Hall effect in monolayer ZrTe 5 and topological phase in bulk ZrTe 5 . To study the topological property of ZrTe 5 , the growth of large size and high-quality single crystals is the first and crucial step. Here, by mean of iodine (I 2 ) transport agent, centimeter-sized ZrTe 5 single crystals were successfully grown by the chemical vapor transport technique. The microstructure characterization reveals that grown ZrTe 5 crystal has “stacking stripes of wood” morphology, and growth mechanism is proposed accordingly. The size of grown ZrTe 5 crystals can be reached as large as 35×2×0.5 mm 3 , which enable us to measure the a -, b - and c - axis anisotropic resistance. Large and single crystalline ZrTe 5 crystals provide a solid basis for exploring its topological phase.

The spin Hall effect of light originates from spin-orbit interaction of light, which manifests two types of geometric phases. In this paper, we report the observation of a geometric spin Hall effect by generating a light beam with inhomogeneous polarization distribution. Unlike the previously reported geometric spin Hall effect observed in a tilted beam-detector system, which is believed to result from an effective spin-redirection Berry geometric phase, the geometric spin Hall effect demonstrated here is attributed to an effective, spatially varying Pancharatnam-Berry geometric phase generated by the inhomogeneous polarization geometry. Our further experiments show that the geometric spin Hall effect can be tuned by tailoring the polarization geometry of light, demonstrating the spin states of photons can be steered with a great flexibility.

We investigate numerically the integer quantum Hall effect in a three-band triangular-lattice model. The three bands own the Chern number C=2,−1,−1, respectively. The lowest topological flat band carrying Chern number C=2, which leads to the Hall plateau σ H = 2 ( e 2 / h ) . This Hall plateau is sensitive to the disorder scattering and is rapidly destroyed by the weak disorder. Further increasing the strength of disorder, the gap of density of states always disappears before the vanishing of the corresponding Hall plateau. The scaling behavior of quantum phase transition between an insulator and a quantum Hall plateau is studied. We find that the insulator-plateau transition becomes sharper with increasing the size of system. Due to the different of edge states, the critical energy E c 1 gradually shifts to the center of Hall plateau while E c 2 is unaffected with increasing the disorder strength.

The intriguing discoveries of quantum spin Hall effect of electrons and its analogy in photon systems have renovated several concepts in condensed matter physics. Here we emulate topological edge states at microwave frequencies utilizing honeycomb photonic crystals with elliptical rods made of silicon material, and a novel topological beam splitter is implemented and analyzed. Robustness against perturbations provides the beam splitter with extremely strong transmission stability. Noticeably, suppressing the backward transmission of electromagnetic wave mitigates undesirable reflection interference. The numerical analysis results reveal that the splitting ratio obtained is in the range of 0.5–1.5 and the maximum transmittance value can reach up to 97% in this system. Besides, by appropriately adjusting the configuration parameters of photonic crystals, the location of operating frequency can be tuned to match different cases. The proposed structure has tremendous potential applications in the field of all-optical integrated circuits and will promote the practicability of photonic topological insulators in the communication domain

The analogy of quantum spin Hall effect in phononic fields has received enormous attentions these years. A significant hallmark of quantum spin Hall effect is that it can support interface modes that are protected by topology and robust to structural disturbance. However, researches on this topic are often limited to the passive structures that manifest topologically protected interface modes at fixed and narrow frequency ranges. In view of the shortage of non-passive topological metamaterial systems, this work has a primary motive to study the active control of quantum spin Hall effect in soft membrane-type metamaterials (MAM). After introducing sandwiched membrane-type acoustic metamaterials, the plane wave expansion method is adopted to analytically capture the system dispersion properties. A finite element model is further developed and a very good convergence with analytical result is presented. Further, by adjusting locations of spraying discs in the honeycomb lattice without violating the C 6 v symmetry, topological phase inversion is observed around a double Dirac cone at the center of the Brillouin zone, separating the topologically trivial state from the nontrivial counterpart. The topologically protected interface modes (TPIMs) around the interface between metamaterials of trivial and nontrivial states are observed. Additionally, to actively control working frequency of the TPIM, an electrical voltage that lies within the locking-up limit is applied to MAM. It is concluded that the topological interface state and the topological bandgaps are very sensitive to the applied voltage, while the system localization behavior is not influenced by the voltage. Utilizing this topologically protected interface state analysis, a straight path and a zig-zag path are designed to control wave propagation in the structure. Conclusively, a voltage-controlled topological metamaterial system is designed to broaden the working frequency range of TPIM.

We apply the non-equilibrium Green’s function (NEGF) method to study spin transport properties of graphene nanoribbons decorated with Gold (Au) and Thallium (Tl) adatoms.Both the enhanced intrinsic SOC and Rashba SOC induced by adatoms makes a huge impact and changes the spin-dependent transport properties such as spin relaxation, charge distribution, and electrical conductivity in the adatom armchair graphene nanoribbons (AGNR) system. Our results examine the Quantum Spin Hall phase in Tl adatom AGNR, and also supports that the Rashba effect which is induced by Au adatom is harmful for the stabilizing of QSH phase. Furthermore, a faster spin-relaxation in Au adatom AGNR system is also demonstrated in our study. The comparison of these spin-dependent effects in different adatoms systems would help us to clarify the influences of the enhanced intrinsic SOC and Rashba SOC in graphene, and pave the way for manipulating graphene-based spintronic devices. In the end, we summarized and discussed the spin-dependent transport properties of several heavy-metal decorated graphene systems.

Dirac point, the cornerstone of topological insulators, has been attracting ever-increasing attention due to its extraordinary properties. In this paper, a bottom-up topology optimization approach is established to systematically design the acoustic Dirac cones with customized double, triple and quadruple degeneracies at different wavelength scales. Using the proposed methodology, novel square-symmetric, chiral and orthogonal-symmetric sonic crystals (SCs) are constructed in a square lattice with tailored Dirac cones. The proposed design approach offers a unified framework to tailor SCs with exotic functionalities which are being widely researched in acoustic metamaterial community. As illustrative examples, zero-index acoustic cloaking and Talbot effect near the Dirac points of the optimized SCs are demonstrated numerically. Moreover, a novel acoustic pseudo-spin topological insulator is obtained, which entails a robust zigzag wave propagation and broadband, unidirectional, and topologically protected transport with a record-breaking relative bandwidth of 30.51%. The proposed design methodology shows promise and opens new horizons for customizing topological acoustics and conceiving high-efficiency wave devices.

For the realization of topologically protected wave propagation, engineering artificial structures of topological insulators (TIs) inspired by quantum mechanics has attracted extensive attention over the last few years. However, the existing structures commonly compose of a regular shape of inclusions for the limited arrangements in the unit cell. This paper develops a topology optimization approach for designing novel structures of acoustic TIs. With the mechanism of acoustic TIs based on the quantum spin Hall effect (QSHE), topology optimization first seeks sonic crystals (SCs) with double Dirac cones of dipolar and quadrupolar modes. Then, topology optimization creates topological trivial and non-trivial SCs by breaking the double Dirac cones, which freely assemble into acoustic TIs. The optimized structures exhibit the typical functionalities of acoustic TIs, the robust propagation and spin-locked unidirectional transmission of topological edge states, verifying the effectiveness of the proposed approach.

Two dimensional topological insulators with high feasibility and room-temperature band gaps are desirable at present. Here, kagome monolayers TMC6 (TM = Mo, W) are systematically investigated by density functional theory and molecular dynamics simulations. TMC6 lattice with one TM layer sandwiched between two trigonal carbon layers is proved to be stable. We identify that band inversion occurs in TMC6 with opened gaps up to 226 meV, making the system suitable for room temperature applications. By analyzing orbital resolved band structures and partial charge densities, we determine that the band inversion is mainly contributed by TM-d orbitals after introducing spin orbit coupling. The nontrivial topological feature is confirmed by direct calculation of Z2 invariant (Z2 = 1) indicating that TMC6 is quantum spin Hall (QSH) insulator. Distinct from previous QSH insulators, there is spin splitting along Γ→K direction (perpendicular to the mirror plane), while there is no splitting along Γ→M direction (parallel to the mirror plane). Further investigation unravels that the anisotropic spin splitting could be attributed to the in-plane structural inversion asymmetry. TMC6 kagome monolayers with nontrivial topology and anisotropic spin splitting could open up a way for new generation spintronic and electronic devices.

Silicene, a silicon analogue of graphene, has attracted increasing attention during the past few years. As early as in 1994, the possibility of stage corrugation in the Si analogs of graphite had already been theoretically explored. But there were very few studies on silicene until 2009, when silicene with a low buckled structure was confirmed to be dynamically stable by ab initio calculations. In spite of the low buckled geometry, silicene shares most of the outstanding electronic properties of planar graphene (e.g., the “Dirac cone”, high Fermi velocity and carrier mobility). Compared with graphene, silicene has several prominent advantages: (1) a much stronger spin–orbit coupling, which may lead to a realization of quantum spin Hall effect in the experimentally accessible temperature, (2) a better tunability of the band gap, which is necessary for an effective field effect transistor (FET) operating at room temperature, (3) an easier valley polarization and more suitability for valleytronics study. From 2012, monolayer silicene sheets of different superstructures were successfully synthesized on various substrates, including Ag(1 1 1), Ir(1 1 1), ZrB2(0 0 0 1), ZrC(1 1 1) and MoS2 surfaces. Multilayer silicene sheets have also been grown on Ag(1 1 1) surface. The experimental successes have stimulated many efforts to explore the intrinsic properties as well as potential device applications of silicene, including quantum spin Hall effect, quantum anomalous Hall effect, quantum valley Hall effect, superconductivity, band engineering, magnetism, thermoelectric effect, gas sensor, tunneling FET, spin filter, and spin FET, etc. Recently, a silicene FET has been fabricated, which shows the expected ambipolar Dirac charge transport and paves the way towards silicene-based nanoelectronics. This comprehensive review covers all the important theoretical and experimental advances on silicene to date, from the basic theory of intrinsic properties, experimental synthesis and characterization, modulation of physical properties by modifications, and finally to device explorations.

Experimental results show that the photoelectrons emitted from the gold substrate due to laser radiation, passe through DNA nanowires with spin-polarized nature. This study proposes the use of chiral DNA molecule in spintronics and information processing. To investigate the spin transfer in DNA molecules, we established a theoretical model based on a combined spin-polaronic Peyrard–Bishop–Holstein model. Accordingly, a nearly pure spin current is appeared. The simultaneous effects of the incident radiation and external magnetic field create characteristic islands corresponding to the pure spin currents, which can be predicted and detected using the multifractal dimensions spectrum. We can verify the spin Hall effect on DNA oligomers through spin–orbit coupling. As such, we can proceed to our significant purpose, which is to create a nearly pure spin current for information transfer and determine the regions of parameter values from which the maximal polarization in spin current emerges.

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 ℤ 2 = 0 , their topological features can be altered by the surface decorations. Particularly, the fluorinated SiGe sheet becomes a topological insulator with ℤ 2 = 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 0.09–0.17 eV 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.

We present a theory for quantum pump in a quantum spin Hall bar with two quantum point contacts (QPCs). The pump currents can be generated by applying harmonically modulating gate voltages at QPCs. The phase difference between the gate voltages introduces an effective gauge field, which breaks the time-reversal symmetry and generates pump currents. The pump currents display very different pump frequency dependence for weak and strong e–e interaction. These unique properties are induced by the helical feature of the edge states, and therefore can be used to detect and control edge state transport.

We study quantum Hall interferometers in which the interference loop encircles a quantum anti-dot. We base our study on thermodynamic considerations, which we believe reflect the essential aspects of interference transport phenomena. We find that similar to the more conventional Fabry–Perot quantum Hall interferometers, in which the interference loop forms a quantum dot, the anti-dot interferometer is affected by the electro-static Coulomb interaction between the edge modes defining the loop. We show that in the Aharonov–Bohm regime, in which effects of fractional statistics should be visible, is easier to access in interferometers based on anti-dots than in those based on dots. We discuss the relevance of our results to recent measurements on anti-dots interferometers.

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer–Buttiker theory. Scattering theory provides a microscopic derivation of the Landau–Lifshitz–Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.

A simple description of the Hall effect in the hopping regime of conductivity in semiconductors is presented. Expressions for the Hall coefficient and Hall mobility are derived by considering averaged equilibrium electron transport in a single triangle of localization sites in a magnetic field. Dependence of the Hall coefficient is analyzed in a wide range of temperature and magnetic field values. Our theoretical result is applied to our experimental data on temperature dependence of Hall effect and Hall mobility in ZnO.

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.

The fluctuation Hall conductivity and the Hall angle, describing the Hall effect, are calculated for arbitrary value of the imaginary part of the relaxation time in the frame of the time-dependent Ginzburg–Landau theory in type II-superconductor with thermal noise describing strong thermal fluctuations. The self-consistent Gaussian approximation is used to treat the nonlinear interaction term in dynamics. We obtain analytical expressions for the fluctuation Hall conductivity and the Hall angle summing all Landau levels without need to cutoff higher Landau levels to treat arbitrary magnetic field. The results are compared with experimental data on high- T c superconductor.

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.

The given report is devoted to the study of anomalous Hall resistance of donor electron system of hybridized states of transition element impurities of low concentration in quantum oscillation regime. There presented theoretical description of predicted specific behaviors on the base of the ideas about thermodynamic anomalous Hall effect. In experiments on mercury selenide crystals with cobalt impurities of low concentration one revealed the quantum oscillations of anomalous contribution to the Hall resistance corresponding to the developed concepts.

For an investigation of the quantum Hall effect on n-In0.85Ga0.18As/In0.82Al0.82As metamorphic nanoheterostructures with high InAs content the longitudinal and Hall magnetoresistances were measured in magnetic fields up to 9 T at T = ( 1.8 ÷ 30 ) K . The results for a temperature dependence of conductivity on the delocalized states at the center of Landau level were analysed within the scaling concept for a plateau-plateau transition in quantum Hall regime.

Graphene (Gr) has been demonstrated to be a two dimensional (2D) topological insulator (TI) with an opened spin–orbit coupling (SOC) energy gap at Dirac point. The extremely small energy gap, however, makes the predicted quantum spin Hall (QSH) effect difficult to be observed at room temperature. In present work, we propose an effective way to tune the energy gap of Gr by combining with GaSb. The intrinsic bulk gap of Gr reaches up to 125 meV and 116 meV in Gr/(Ga)Sb and Gr/Ga(Sb), respectively, which makes it available in practical applications. Moreover, the energy gap of Gr can be opened and increased to 147 meV in GaSb/Gr/GaSb by hydrogen passivation. The inverted band ordering and gapless edge states further demonstrate that our considered heterostructures possess QSH effect. Normal strain engineering leads to effective control and substantial enhancement of their energy gap and band inversion. Hexagonal boron nitride (h-BN) is also verified to be a suitable substrate to supporting films without destroying their QSH effect. Our results provide feasible platform to design Gr-based spintronics devices.

Using the tight-binding BHZ model and Landauer-B\"uttiker formalism, the topological invariant of the finite width of ribbons of HgTe/CdTe quantum well is studied in the absence and presence of an external transverse electric field. It will be recognized that a critical current changes topological invariant of ribbons of quantum well. This topological phase transition, which occurred by adjustment of the bias voltage, depends on the width of the sample and the gate voltage. The profound effects of an external transverse electric field are considered to the separation of spin-up and spin-down band structures, decreasing band gap and tuning the topological phase transition between ordinary and quantum spin Hall regime. These declares the transverse electric field amplifies the quantum spin Hall regime and causes inducing the topological phase transition in ribbons of quantum well. Our finding may instantly clear some practical aspects of the study in the field of spintronic for employment in spin-based devices., Comment: 21 pages, 8 figures

In this paper, we study the spin-orbit torques (SOTs) originated from the spin-orbit coupling (SOC) of intrinsic type in a periodically buckled honeycomb nanoribbon such as silicene. Using the Green function formalism with density matrix expressions, we analyze the SOT contributions from the Fermi-level and -sea electrons. We find that the intrinsic-SOC-induced inverse spin galvanic effect generates spin accumulations perpendicular to the honeycomb plane. The anti-damping torque results purely from the Fermi-level contribution, while the field-like torque from both the Fermi-level and -sea contributions. At zero bias voltage, the SOT is symmetric with respect to the Fermi energy (i.e., an even function of the Fermi energy), whereas the presence of bias further introduces the anti-symmetric torque components. When the ferromagnet magnetization lies in the honeycomb plane, all Fermi-sea contributions disappear. The maximum SOT among different Fermi energies is also inspected. For large enough in-plane magnetization compared to the staggered potential, the field-like torque has a maximum at zero Fermi energy. When the magnetization is smaller than some value characterized by the intrinsic SOC, the maximum of the anti-damping torque occurs at the cross point of the two Dirac linear bands in the leads. More importantly, we find that the anti-damping torques responsible for magnetic switching as well as the torkance require staggered potential from an applied out-of-plane electric field, i.e., lattice buckling is essential to the switching. When the electric field is reversed, the anti-damping torque and the torkance are also reversed. Accordingly, full electric control of the SOTs can be realized in this buckled system.

We study the edge-state band and transport property for a HgTe/CdTe quantum well Hall bar under the combined coupling of a transverse electric field and a perpendicular magnetic field. It is demonstrated that a weak magnetic field can protect one of the two edge states, open or enlarge a gap of the other edge state in the Hall bar. However, an appropriate electric field can remove the gap, restoring the quantum spin Hall effect. Using the scattering matrix method, we study the electronic transport of the system. We find that the electric field can not only make the switch from pure spin-up to spin-down current, but also open or close the edge-state channels in a narrow Hall bar under a weak magnetic field, which provides us with a new way to construct a topological insulator-based spin switch and charge switch.

We present the fractional quantum Hall (FQH) effect as a candidate emergent phenomenon. Unlike some other putative cases of condensed matter emergence (such as thermal phase transitions), the FQH effect is not based on symmetry breaking. Instead FQH states are part of a distinct class of ordered matter that is defined topologically. Topologically ordered states result from complex long-ranged correlations between their constituent parts, such that the system displays strongly irreducible, qualitatively novel properties.

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-B"uttiker theory. Scattering theory provides a microscopic derivation of the Landau-Lifshitz-Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics., 9 pages, 2 figures. Contribution to a special issue in Physica E on "Frontiers in quantum electronic transport" - in memory of Markus B"uttiker

We have developed a method of quantum hydrodynamics (QHD) that describes particles with spin-up and with spin-down in separate. We have derived the equation of the spin current evolution as a part of the set of the quantum hydrodynamics equations that treat particles with different projection of spin on the preferable direction as two different species. We have studied orthogonal propagation of waves in the external magnetic field and determined the contribution of quantum corrections due to the Bohm potential and to magnetization energy of particles with different projections of spin in the spin-current wave dispersion. We have analyzed the limits of weak and strong magnetic fields.