Inter-edge Coupling Research Articles

Optimizing topological switching in confined 2D-Xene nanoribbons via finite-size effects

In a blueprint for topological electronics, edge state transport in a topological insulator material can be controlled by employing a gate-induced topological quantum phase transition. Here, by studying the width dependence of electronic properties, it is inferred that zigzag-Xene nanoribbons are promising materials for topological electronics with a display of unique physical characteristics associated with the intrinsic band topology and the finite-size effects on gate-induced topological switching. First, due to intertwining with intrinsic band topology-driven energy-zero modes in the pristine case, spin-filtered chiral edge states in zigzag-Xene nanoribbons remain gapless and protected against backward scattering even with finite inter-edge overlapping in ultra-narrow ribbons, i.e., a 2D quantum spin Hall material turns into a 1D topological metal. Second, mainly due to width- and momentum-dependent tunability of the gate-induced inter-edge coupling, the threshold-voltage required for switching between gapless and gapped edge states reduces as the width decreases, without any fundamental lower bound. Third, when the width of zigzag-Xene nanoribbons is smaller than a critical limit, topological switching between edge states can be attained without bulk bandgap closing and reopening. This is primarily due to the quantum confinement effect on the bulk band spectrum, which increases the nontrivial bulk bandgap with decrease in width. The existence of such protected gapless edge states and reduction in threshold-voltage accompanied by enhancement in the bulk bandgap overturns the general wisdom of utilizing narrow-gap and wide channel materials for reducing the threshold-voltage in a standard field effect transistor analysis and paves the way toward low-voltage topological devices.

Mixed magnetic edge states in graphene quantum dots

Graphene quantum dots (GQDs) exhibit abundant magnetic edge states with promising applications in spintronics. Hexagonal zigzag GQDs possess a ground state with an antiferromagnetic (AFM) inter-edge coupling, followed by a metastable state with ferromagnetic (FM) inter-edge coupling. By analyzing the Hubbard model and performing large-scale spin-polarized density functional theory calculations containing thousands of atoms, we predict a series of new mixed magnetic edge states of GQDs arising from the size effect, namely mix-n, where n is the number of spin arrangement parts at each edge, with parallel spin in the same part and anti-parallel spin between adjacent parts. In particular, we demonstrate that the mix-2 state of bare GQDs (C) appears when and the mix-3 state appears when , where N is the number of six-membered-ring at each edge, while the mix-2 and mix-3 magnetic states appear in the hydrogenated GQDs with N = 13 and N = 15, respectively.

Perfect modulation between fully spin-polarized spin-singlet and -triplet Andreev entanglements in a narrow quantum spin Hall system

We consider a quantum spin Hall (QSH) insulator strip touching on one s-wave superconductor sandwiched between two ferromagnetic insulators and study its scattering processes, tunneling conductance, and noise power by using an extended Bogoliubov-de Gennes scattering formalism. It is demonstrated that interedge coupling and noncollinear magnetizations allow for producing the usual and novel crossed Andreev reflections (ARs), respectively, and thus the corresponding spin-singlet and -triplet pairing entanglements. Moreover, by proper tuning of the band structures of the ferromagnetic layers, under the resonance bias voltage, not only perfect but also fully spin-polarized crossed AR at any magnetic orientational angle α is exhibited, which can be experimentally confirmed by the tunneling conductance and noise power. Particularly, the perfect and fully spin-polarized modulation between the spin-singlet and -triplet Andreev entanglements could be performed by α at certain energy values, which suggest that the setup can act as a topological superconducting spintronic device with such a manipulation function.

Excitation and phase transitions of spin density waves in graphene nanoribbons

Anti-ferromagnetic states widely exist on graphene zigzag edges. Our previous work (Xie et al 2018 New J. Phys. 20 013035) shows there are also various spin density wave (SDW) states in the graphene nanoribbons (GNR). In this paper, we propose some excitation mechanism of these SDW by the absorbed magnetic atoms with the mean-field Hubbard model and the first-principles calculations. With the Floquet theory, we also find that by regulating the temperature or the light intensity, there are a lot of phase transitions for these SDW. The temperature or light can dramatically modify the inter-edge coupling or the spin stiffness of GNR. The artificial magnetization technique is employed to explore the establishment process of these SDW states. Some interesting intermedia phase transitions and the corresponding spin orders are discovered. This research may be helpful in the understandings and technique controls of magnetic orders in future nano magnetic devices.

Electric Control of the Edge Magnetization in Zigzag Stanene Nanoribbons from First Principles

There has been tremendous interest in manipulating electron and hole-spin states in low-dimensional structures for electronic and spintronic applications. We study the edge magnetic coupling and anisotropy in zigzag stanene nanoribbons, by first-principles calculations. Taking into account considerable spin-orbit coupling and ferromagnetism at each edge, zigzag stanene nanoribbon is insulating and its band gap depends on the inter-edge magnetic coupling and the magnetization direction. Especially for nanoribbon edges with out-of-plane antiferromagnetic coupling, two non-degenerate valleys of edge states emerge and the spin degeneracy is tunable by a transverse electric field, which give full play to spin and valley degrees of freedom. More importantly, both the magnetic order and anisotropy can be selectively controlled by electron and hole doping, demonstrating a readily accessible gate-induced modulation of magnetism. These intriguing features offer a practical avenue for designing energy-efficient devices based on multiple degrees of freedom of electron and magneto-electric couplings.

Superconductivity switch from spin-singlet to -triplet pairing in a topological superconducting junction

The interedge coupling is the cardinal characteristic of the narrow quantum spin Hall (QSH) insulator, and thus could bring about exotic transport phenomena. Herein, we present a theoretical investigation of the spin-resolved Andreev reflection (AR) in a QSH insulator strip touching on two neighbouring ferromagnetic insulators and one s-wave superconductor. It is demonstrated that, due to the interplay of the interedge coupling and ferromagnetic configuration, there could be not only usual local ARs leading to the spin-singlet pairing with the incident electron and Andreev-reflected hole from different spin subbands, but also novel local ARs giving rise to the spin-triplet pairing from the same spin subband. However, only the latter exists in the absence of the interedge coupling, and therefore the two pairings in turn testify the helical spin texture of the edge states. By proper tuning of the band structures of the ferromagnetic layers, under the resonance bias voltage, the usual and novel local ARs of can be all exhibited, resulting in fully spin-polarized pure spin-singlet superconductivity and pure spin-triplet superconductivity, respectively, which suggests a superconductivity switch from spin-singlet to -triplet pairing by electrical control. The results can be experimentally confirmed by the tunneling conductance and the noise power.

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents are compared also to several recent renormalization group calculations for related long-ranged interacting quantum systems.

Supercurrent switch in \u03c0 topological junctions based upon a narrow quantum spin Hall insulator

The narrow quantum spin Hall (QSH) insulator is characterized by interedge coupling, which could feature exotic transport phenomena, and thus serves as the key element for topological superconducting electronic devices. Herein, we theoretically explore possible Josephson π states in a QSH insulator strip touching on two s-wave superconductors in the presence of the interedge coupling. It is shown that the interedge coupling could give rise to a 0 − π transition modulated by the gate voltage, originating from an additional π phase difference caused by the interedge backscattering. The 0 − π transition in turn can manifest the helical spin texture of the edge states. A considerable residual value of the supercurrent at the 0 − π transition point is always exhibited, suggesting a very efficient performance of the device as a supercurrent switch. Moreover, the region of coexisting 0 and π states is found fairly large, which can be used to improve accuracy in the design of a π superconducting quantum interference device.

Aharonov-Bohm oscillations in phosphorene quantum rings

The Aharonov-Bohm (AB) effect in square phosphorene quantum rings, with armchair and zigzag edges, is investigated using the tight-binding method. The energy spectra and wave functions of such rings, obtained as a function of the magnetic flux $\mathrm{\ensuremath{\Phi}}$ threading the ring, are strongly influenced by the ring width $W$, an in-plane electric field ${E}_{p}$, and a side-gating potential ${V}_{g}$. Compared to a square dot, the ring shows an enhanced confinement due to its inner edges and an interedge coupling along the zigzag direction, both of which strongly affect the energy spectrum and the wave functions. The energy spectrum that is gapped consists of a regular part, of conduction (valence) band states, that shows the usual AB oscillations in the higher- (lower-) energy region, and of edge states, in the gap, that exhibit no AB oscillations. As the width $W$ decreases, the AB oscillations become more distinct and regular and their period is close to ${\mathrm{\ensuremath{\Phi}}}_{0}/2$, where the flux quantum ${\mathrm{\ensuremath{\Phi}}}_{0}=h/e$ is the period of an ideal circular ring ($W\ensuremath{\rightarrow}0$). Both the electric field ${E}_{p}$ and the side-gating potential ${V}_{g}$ reduce the amplitude of the AB oscillations. The amplitude can be effectively tuned by ${E}_{p}$ or ${V}_{g}$ and exhibits an anisotropic behavior for different field directions or side-gating configurations.

Effect of the intrinsic spin-orbit interaction on the tunnel magnetoresistance in graphenelike nanoflakes

This paper is devoted to examining the effect of intrinsic spin-orbit interaction on the possible appearance of edge magnetic moments and spin-dependent transport in graphenelike nanoflakes. In the case of finite-size graphenelike nanostructures it is shown that, on one hand, energetically the most advantageous configuration corresponds to magnetic moments located at zigzag edges with the in-plane antiferromagnetic inter-edge coupling. On the other hand, the tunnel magnetoresistance and the shot noise also have thoroughly been tested both for the in-plane configuration as well as for the out-of-plane one (for comparison reasons). Transport properties are described in terms of the mean-field Kane-Mele-Hubbard model with spin mixing correlations, supplemented by additional terms describing external leads, charging energy, and lead-nanostructure tunneling. The results show that Coulomb blockade stability spectra of graphenelike nanoflakes with ferromagnetic contacts provide information on both the intrinsic spin-orbit interaction and the expected edge magnetism.

First-principles study of stability, electronic structure and magnetic properties of Be2C nanoribbons

First-principles calculations are carried out to investigate the stability, electronic structure and magnetic properties of Be2C nanoribbons (Be2C-NRs) with their ribbon axis along the a and b axes. It is found that except for b-Be2C-NR with the C site terminated edge, a-Be2C-NRs and other b-Be2C-NRs possess good structural stabilities at room temperature. In addition, H passivation enables b-Be2C-NR with C site terminated edge to stabilize at room temperature by saturating the dangling bonds at edges. Furthermore, stable a-Be2C-NRs and b-Be2C-NRs are all nonmagnetic semiconductors and their band gaps are significantly dependent on the edge configuration and the ribbon width. In contrast, H passivated b-Be2C-NR with C site terminated edge is half-metallic with a magnetic ground state, irrespective of the ribbon width. In particular, H passivated b-Be2C-NR with C site terminated edge has a strong intra-edge ferromagnetic coupling interaction in the ground state, and an inter-edge ferromagnetic interaction is found in small-width H passivated nanoribbon. The calculated density of states and the spin density distribution show that the p–p hybridization interaction involving polarized electrons is responsible for intra-edge and inter-edge ferromagnetic coupling.

Unconventional quantized edge transport in the presence of interedge coupling in intercalated graphene

It is generally believed that the inter-edge coupling destroys the quantum spin Hall (QSH) effect along with the gap opening at the Dirac points. Using first-principles calculations, we find that the quantized edge transport persists in the presence of inter-edge coupling in Ta intercalated epitaxial graphene on SiC(0001), being a QSH insulator with the non-trivial gap of 81 meV. In this case, the band is characterized by two perfect Dirac cones with different Fermi velocities, yet only one maintains the edge state feature. We attribute such an anomalous behavior to the orbital-dependent decay of edge states into the bulk, which allows the inter-edge coupling just between one pair of edge states rather than two.

Two-dimensional Kagome phosphorus and its edge magnetism: a density functional theory study

By means of density functional theory calculations, we predict a new two-dimensional phosphorus allotrope with the Kagome-like lattice(Kagome-P). It is an indirect gap semiconductor with a band gap of 1.64 eV. The gap decreases sensitively with the compressive strain. In particular, shrinking the lattice beyond 13% can drive it into metallic state. In addition, both the AA and AB stacked Kagome-P multi-layer structures exhibit a bandgap much smaller than 1.64 eV. Edges in the Kagome-P monolayer probably suffer from the edge reconstruction. An isolated zigzag edge can induce antiferromagnetic (AF) ordering with a magnetic transition temperature of 23 K. More importantly, when applying a stretching strain beyond 4%, such an edge turns to possess a ferromagnetic ground state. A very narrow zigzag-edged Kagome-P ribbon displays the spin moment distribution similar to the zigzag-edged graphene nanoribbon because of the coupling between the opposites edges. But the inter-edge coupling in the Kagome-P ribbon vanishes more rapidly as the ribbon width increases. These properties make it a promising material in spintronics.

Electrical modulation of the edge channel transport in topological insulators coupled to ferromagnetic leads

The counterpropagating edge states of a two-dimensional topological insulator (TI) carry electrons of opposite spins. We investigate the transport properties of edge states in a two-dimensional TI which is contacted to ferromagnetic leads. The application of a side-gate voltage induces a constriction or quantum point contact (QPC) which couples the two edge channels. The transport properties of the system are calculated via the Keldysh nonequilibrium Green's function method. We found that inter-edge spin-flip coupling can significantly enhance (suppress) the charge current when the magnetization of the leads are anti-parallel (parallel) to one another. On the other hand, spin-conserving inter-edge coupling generally reduces the current by backscattering regardless of the magnetization configuration. The charge current and the conductance as a function of the bias voltage, also exhibit similar trends with respect to spin-flip coupling strength, for both parallel and anti-parallel configurations. Hence, gate voltage modulation of edge states via a QPC can provide a means of modulating the spin or charge current flow in TI-based spintronics devices.

Quantum Coherence Engineering in the Integer Quantum Hall Regime

We present an experiment where the quantum coherence in the edge states of the integer quantum Hall regime is tuned with a decoupling gate. The coherence length is determined by measuring the visibility of quantum interferences in a Mach-Zehnder interferometer as a function of temperature, in the quantum Hall regime at a filling factor 2. The temperature dependence of the coherence length can be varied by a factor of 2. The strengthening of the phase coherence at finite temperature is shown to arise from a reduction of the coupling between copropagating edge states. This opens the way for a strong improvement of the phase coherence of quantum Hall systems. The decoupling gate also allows us to investigate how interedge state coupling influences the quantum interferences' dependence on the injection bias. We find that the finite bias visibility can be decomposed into two contributions: a Gaussian envelope which is surprisingly insensitive to the coupling, and a beating component which, on the contrary, is strongly affected by the coupling.

The role of size in spin properties of zigzag graphene nanoribbon

The effects of ribbon size on the spin properties of zigzag graphene nanoribbon (ZGNR) with and without edge pentagon-heptagon reconstruction are investigated using spin-polarized density functional theory. It is found that when ribbon width is less than 26.31 A, the Coulomb and RKKY-like interaction between two ribbon-edges result in the edge state splitting. For a wider ZGNR, the interedge coupling is negligible. In addition to stabilizing the system and weakening the interedge coupling, the edge pentagon-heptagon reconstruction could demagnetize the ZGNR. In perfect and single-edge reconstructed ZGNR, the magnetic moment depends on ribbon width, and the change of magnetic moment becomes inconspicuous with increasing ribbon width. Double-edge reconstructed ZGNR shows nonmagnetic. It may be useful for fabricating graphene-based nanoelectronic and spintronic devices.

Persistent currents in a graphene ring with armchair edges

A graphene nanoribbon with armchair edges is known to have no edge state. However, if the nanoribbon is in the quantum spin Hall state, then there must be helical edge states. By folding a graphene ribbon into a ring and threading it by a magnetic flux, we study the persistent charge and spin currents in the tight-binding limit. It is found that, for a broad ribbon, the edge spin current approaches a finite value independent of the radius of the ring. For a narrow ribbon, inter-edge coupling between the edge states could open the Dirac gap and reduce the overall persistent currents. Furthermore, by enhancing the Rashba coupling, we find that the persistent spin current gradually reduces to zero at a critical value beyond which the graphene is no longer a quantum spin Hall insulator.

Interplay between sublattice and spin symmetry breaking in graphene

We study the effect of sublattice symmetry breaking on the electronic, magnetic and transport properties of two dimensional graphene as well as zigzag terminated one and zero dimensional graphene nanostructures. The systems are described with the Hubbard model within the collinear mean field approximation. We prove that for the non-interacting bipartite lattice with unequal number of atoms in each sublattice midgap states still exist in the presence of a staggered on-site potential $\pm \Delta/2$. We compute the phase diagram of both 2D and 1D graphene with zigzag edges, at half-filling, defined by the normalized interaction strength $U/t$ and $\Delta/t$, where $t$ is the first neighbor hopping. In the case of 2D we find that the system is always insulating and, we find the $U_c(\Delta)$ curve above which the system goes antiferromagnetic. In 1D we find that the system undergoes a phase transition from non-magnetic insulator for $U<U_C(\Delta)$ to a phase with ferromagnetic edge order and antiferromagnetic inter-edge coupling. The conduction properties of the magnetic phase depend on $\Delta$ and can be insulating, conducting and even half-metallic, yet the total magnetic moment in the system is zero. We compute the transport properties of a heterojunction with two non-magnetic graphene ribbon electrodes connected to a finite length armchair ribbon and we find a strong spin filter effect.

Interedge magnetic coupling in transition-metal terminated graphene nanoribbons

The magnetic structures and interedge magnetic couplings of Fe, Co and Ni transition-metal terminated graphene nanoribbons with zigzag (ZGNR) and armchair (AGNR) edges are studied by first-principles calculations. Fe-ZGNR is found to show antiferromagnetic (AF) coupling between two edges, while the interedge coupling of Co-ZGNR is ferromagnetic (FM). For Fe-AGNRs and Co-AGNRs, increasing the interedge distance we follow oscillatory transitions from FM to AF coupling with a period of about 3.7 {\AA}. The damped oscillatory behavior indicates a Ruderman-Kittel-Kasuya-Yosida type interedge magnetic coupling and the oscillation period is determined by the critical spanning vector which connects two inequivalent Dirac points in the graphene Brillouin zone. The two edges in Ni-ZGNR are decoupled independent of the ribbon width and Ni-AGNRs are found to be nonmangetic.

Quasi-particle tunneling at a constriction in a fractional quantum Hall state

Split-gate constrictions can be used to produce controllable scattering in a fractional quantum Hall state and constitute a very versatile model system for the investigation of non-Fermi physics in edge states. Controllable inter-edge tunneling can be achieved by tuning the constriction parameters and its out-of-equilibrium behavior can be explored as well. Here we review our results of tunneling non-linearities at a split-gate constriction in a wide range of temperatures and inter-edge coupling. The results are compared to available theoretical predictions of tunneling characteristics between Luttinger liquids. We show how partial agreement with these theoretical models is obtained in selected ranges of temperatures and inter-edge coupling, while striking deviations are obtained especially in the low-coupling, low-temperature regimes.