Spin Edge States Research Articles

Spin-dependent polarization and quantum Hall conductivity in decorated graphene: influence of locally induced spin–orbit-couplings and impurities

We study spin transport through graphene-like substrates in the presence of one or several, locally induced spin–orbit coupling (SOC) terms resulting from periodically placed strips, on their top and decorated with a random distribution of impurities. Intrinsic SOC, Rashba SOC and/or pseudo-spin-inversion-asymmetry coupling are considered. A systematic investigation of the spin conductance identifies the main SOC terms which lead to its energy dependence as well as the extent to which the impurity concentration and each SOC term can affect or tune it, In addition, the spin current flow is considered in the presence of different SOC impurities and their related group symmetry such C 6v , C 3v , D 6h and D 3h . Further, we show that the quantum spin-Hall effect (QSHE) related to the spin edge states depends only on the spin character when the PIA and ISO terms are not sublattice resolved, and on both the spin and sublattice character when they are. In addition, we show that the RSO term plays a major role in obtaining edge states that are either protected on both edges or only on one edge against backscattering. This Rashba term creates an anticrosing gap that affects the symmetry in the edge localizations and leads to half-topological states. The results can facilitate the experimental choice of appropriately decorated strips to (i) develop spin-transistor devices by tuning the Fermi energy, (ii) control the robustness of the QSHE against backscattering even in the presence of on-site sublattice asymmetry induced by a transverse electric field or functionalizations, and (iii) provide a strong theoretical support for spintronic quantum devices.

Full-electrostatic management of spin-valley transmission through topological edge states of the hexagonal materials

All-electrostatic generation and control of both spin and valley polarizations provides a highly promising route towards much smaller and energy-efficient nanoscale devices. However, the requirement of broken time reversal symmetry is a serious limitation in this procedure. Here, we show that the chiral spin-resolved topological edge states in each valley of the two-dimensional hexagonal materials, aid to get round this restriction. By topological analysis of the spin and valley dependent edge states, we demonstrate that bulk-to-edge transport in these materials allows all-electrostatic generation and control of fully polarized spin-valley data, preserved during a long enough time and distance. We also obtain an analytic relation for bulk-to-edge transmission and show that the perfect transmission is insensible to the applied electric fields which enables even more convenient implementation of this scheme in spin- and valley-based devices.

Topological phase transition based on structure reversal of two-dimensional photonic crystals and construction of topological edge states

Two kinds of two-dimensional photonic crystal with hexagonal honeycomb lattices are constructed in which the scatterer and the matrix materials are reversed. Due to the symmetry of special point group, the lattices have p and d orbitals in the center of Brillouin region, which are similar to those in the electronic system. With the structure reversal, the p and d orbitals are also directly inverted. Quantitative analysis shows that the orbital inversion is due to the inversion of air band and medium band because of the local resonance effect in the low frequency bands. Based on the parity properties of p and d orbitals, the pseudo spin states are constructed by analogy to the quantum spin Hall effect in electronic systems. The analysis of the effective Hamiltonian at <i>Γ</i> point shows that the topological phase transition caused by orbital inversion is revealed. The pseudo spin edge states construct an optimal structure. The electromagnetic wave simulations and energy flow vector analysis show that the structure edge takes on the properties of quantum spin Hall effect, namely, the propagation direction is locked by the spin direction and the propagation is topologically protected. The results also show that the quantum spin Hall effect can be realized without undergoing the closing of gap. The comparison among similar researches indicates that the realization of the pseudo spin states does not need the deformation of lattice, and the structure proposed in this work possesses the characteristics of simple design, wide band gap and strong edge localization.

Quantum spin–quantum anomalous Hall effect with tunable edge states in Sb monolayer-based heterostructures

A novel topological insulator with tunable edge states, called quantum spin-quantum anomalous Hall (QSQAH) insulator, is predicted in a heterostructure of a hydrogenated Sb (SbH) monolayer on a LaFeO3 substrate by using ab initio methods. The substrate induces a drastic staggered exchange field in the SbH film, which plays an important role to generate the QSQAH effect. A topologically nontrivial band gap (up to 35 meV) is opened by Rashba spin-orbit coupling, which can be enlarged by strain and electric field. To understand the underlying physical mechanism of the QSQAH effect, a tight-binding model based on px and py orbitals is constructed. With the model, the exotic behaviors of the edge states in the heterostructure are investigated. Dissipationless chiral charge edge states related to one valley are found to emerge along the both sides of the sample, while low-dissipation spin edge states related to the other valley flow only along one side of the sample. These edge states can be tuned flexibly by polarization-sensitive photoluminescence controls and/or chemical edge modifications. Such flexible manipulations of the charge, spin, and valley degrees of freedom provide a promising route towards applications in electronics, spintronics, and valleytronics.

Coupling site controlled spin transport through the graphene nanoribbon junction: A first principles investigation

A new type of nano-junctions based on Zigzag graphene nanoribbons (ZGNRs) has been proposed and investigated by first-principles calculations. The results show that large spin polarization of currents would be achieved when the junctions adopted the configuration that two ZGNR leads coupled each other along one edge. By virtue of spatial separation of the two spin edge states, only one spin channel is opened in those junctions at certain energy range, and spin polarized currents will be produced under a low bias. No more efforts are required to change ZGNR from the antiferromagnetic (AFM) ground states to the ferromagnetic (FM) states. Specially, this feature is stable, by changing the width of ZGNRs, modifying the edge morphology, and varying dihedral angle between two ZGNRs, spin polarization of currents are still observed. Our findings indicate that this approach is simple and efficient for spintronics design.

Topological Insulating States in Laterally Patterned Ordinary Semiconductors

We propose that ordinary semiconductors with large spin-orbit coupling, such as GaAs, can host stable, robust, and tunable topological states in the presence of quantum confinement and superimposed potentials with hexagonal symmetry. We show that the electronic gaps which support chiral spin edge states can be as large as the electronic bandwidth in the heterostructure miniband. The existing lithographic technology can produce a topological insulator operating at a temperature of 10-100 K. Improvement of lithographic techniques will open the way to a tunable room temperature topological insulator.

Spin Edge Helices in a Perpendicular Magnetic Field

We present an exact solution to the problem of the spin edge states in the presence of equal Bychkov-Rashba and Dresselhaus spin-orbit fields in a two-dimensional electron system, restricted by a hard-wall confining potential and exposed to a perpendicular magnetic field. We find that the spectrum of the spin edge states depends critically on the orientation of the sample edges with respect to the crystallographic axes. Such a strikingly different spectral behavior generates new modes of the persistent spin helix-spin edge helices with novel properties, which can be tuned by the applied electric and magnetic fields.

Spin edge states in two-dimensional electron systems in the presence of Zeeman effect

We study the spin edge states, induced by the combined effect of Bychkov-Rashba spinorbit and Zeeman interactions or of Dresselhaus spin-orbit and Zeeman interactions in a twodimensional electron system, exposed to a perpendicular quantizing magnetic field and restricted by a hard-wall confining potential. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum versus the momentum and the magnetic field. We calculate the average spin components and the average transverse position of electron. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. Depending on the type of spin-orbit coupling and the principal quantum number, the Zeeman term in the combination with spin-orbit interaction increases or decreases essentially the splitting of bulk Landau levels while it has a weak influence on the spin edge states.

Quantum spin Hall effect and spin-charge separation in a kagomé lattice

A two-dimensional kagomé lattice is theoretically investigated within a simple tight-binding model, which includes the nearest-neighbor hopping term and the intrinsic spin–orbit interaction between the next nearest neighbors. By using the topological winding properties of the spin-edge states on the complex-energy Riemann surface, the spin Hall conductance is obtained to be quantized as −e/2π (e/2π) in insulating phases. This result is consistent with the numerical linear-response calculation and the Z2 topological invariance analysis. When the sample boundaries are connected in twist, by which two defects with π flux are introduced, we obtain the spin-charge separated solitons at 1/3 (or 2/3) filling.

Spin edge states in two-dimensional electron systems

We consider the spin edge states, induced by the combined effect of spin-orbit interaction and hard-wall confining potential, in a two-dimensional electron system exposed to a perpendicular quantizing magnetic field. We derive an exact analytical formula for the dispersion relations of spin edge states and analyze their energy spectrum, velocity, and average transverse position. It is shown that by removing the spin degeneracy, spin-orbit interaction splits the spin edge states not only in the energy but also induces their spatial separation. It is revealed that at low magnetic fields, due to the Stark splitting of the spin-resolved edge states, the high-energy bands exhibit anti-crossings. This results in an additional structure in the behavior of the velocity of current-carrying edge states.

Spin edge states: An exact solution and oscillations of the spin current

We study the spin edge states, induced by the combined effect of spin-orbit interaction (SOI) and hard-wall confining potential, in a two-dimensional electron system, exposed to a perpendicular magnetic field. We find an exact solution of the problem and show that the spin resolved edge states are separated in space. The SOI generated rearrangement of the spectrum results in a peaked behavior of the net spin current versus the Fermi energy. The predicted oscillations of the spin current with a period, determined by the SOI renormalized cyclotron energy, can serve as an effective tool for controlling the spin motion in spintronic devices.

Topological winding properties of spin edge states in the Kane-Mele graphene model

We study the spin edge states in the quantum spin-Hall (QSH) effect on a single-atomic layer graphene ribbon system with both intrinsic and Rashba spin-orbit couplings. The Harper equation for solving the energies of the spin edge states is derived. The results show that in the QSH phase, there are always two pairs of gapless spin-filtered edge states in the bulk energy gap, corresponding to two pairs of zero points of the Bloch function on the complex-energy Riemann surface (RS). The topological aspect of the QSH phase can be distinguished by the difference of the winding numbers of the spin edge states with different polarized directions cross the holes of the RS, which is equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys. Rev. Lett. 95, 146802 (2005)].