CT-invariant quantum spin Hall effect in ferromagnetic graphene

Charge transport through the multiple end zigzag edge states of armchair graphene nanoribbons and heterojunctions

This comprehensive study investigates charge transport through the multiple end zigzag edge states of finite-size armchair graphene nanoribbons/boron nitride nanoribbons (n-AGNR/w-BNNR) junctions under a longitudinal electric field, where n and w denote the widths of the AGNRs and the BNNRs, respectively. In 13-atom wide AGNR segments, the edge states exhibit a blue Stark shift in response to the electric field, with only the long decay length zigzag edge states showing significant interaction with the red Stark shift subband states. Charge tunneling through such edge states assisted by the subband states is elucidated in the spectra of the transmission coefficient. In the 13-AGNR/6-BNNR heterojunction, notable influences on the energy levels of the end zigzag edge states of 13-AGNRs induced by BNNR segments are observed. We demonstrate the modulation of these energy levels in resonant tunneling situations, as depicted by bias-dependent transmission coefficient spectra. Intriguing nonthermal broadening of tunneling current shows a significant peak-to-valley ratio. Our findings highlight the promising potential of n-AGNR/w-BNNR heterojunctions with long decay length edge states in the realm of GNR-based single electron transistors at room temperature.

Band Structure and Quantum Transport of Bent Bilayer Graphene

We investigate the band structures and transport properties of a zigzag-edged bent bilayer graphene nanoribbon under a uniform perpendicular magnetic field. Due to its unique geometry, the edge and interface states can be controlled by an electric field or local potential, and the conductance exhibits interesting quantized behavior. When Zeeman splitting is considered, the edge states are spin-filtered, and a weak quantum spin Hall (WQSH) phase appears. In the presence of an electric field or local potential, a WQSH-QH junction or WQSH-spin-unbalanced QSH junction can be achieved, respectively, while fully spin-polarized currents appear in the interface region. Zeeman splitting lifts the spin degeneracy, leading to a WQSH around zero energy with a quantized two-terminal conductance of 4e2/h, which is robust against weak nonmagnetic disorder. These results provide a way to manipulate the band structures and transport properties of the system using an electric field, local potential, and Zeeman splitting.

Spin-dependent Seebeck effects in a graphene superlattice p-n junction with different shapes

We theoretically calculate the spin-dependent transmission probability and spin Seebeck coefficient for a zigzag-edge graphene nanoribbon p-n junction with periodically attached stubs under a perpendicular magnetic field and a ferromagnetic insulator. By using the nonequilibrium Green's function method combining with the tight-binding Hamiltonian, it is demonstrated that the spin-dependent transmission probability and spin Seebeck coefficient for two types of superlattices can be modulated by the potential drop, the magnetization strength, the number of periods of the superlattice, the strength of the perpendicular magnetic field, and the Anderson disorder strength. Interestingly, a metal to semiconductor transition occurs as the number of the superlattice for a crossed superlattice p-n junction increases, and its spin Seebeck coefficient is much larger than that for the T-shaped one around the zero Fermi energy. Furthermore, the spin Seebeck coefficient for crossed systems can be much pronounced and their maximum absolute value can reach 528 μV [Formula: see text] by choosing optimized parameters. Besides, the spin Seebeck coefficient for crossed p-n junction is strongly enhanced around the zero Fermi energy for a weak magnetic field. Our results provide theoretical references for modulating the thermoelectric properties of a graphene superlattice p-n junction by tuning its geometric structure and physical parameters.

Helical edge states and edge-state transport in strained armchair graphene nanoribbons

A helical type edge state, which is generally supported only on graphene with zigzag boundaries, is found to also appear in armchair graphene nanoribbons in the presence of intrinsic spin-orbit coupling and a suitable strain. At a critical strain, there appears a quantum phase transition from a quantum spin Hall state to a trivial insulator state. Further investigation shows that the armchair graphene nanoribbons with intrinsic spin-orbit coupling, Rashba spin-orbit coupling, effective exchange fields and strains also support helical-like edge states with a unique spin texture. In such armchair graphene nanoribbons, the spin directions of the counterpropogating edge states on the same boundary are always opposite to each other, while is not conserved and the spins are canted away from the -direction due to the Rashba spin-orbit coupling, which is different from the case of the zigzag graphene nanoribbons. Moreover, the edge-state energy gap is smaller than that in zigzag graphene nanoribbons, even absent in certain cases.

Manipulating interface states in monolayer-bilayer graphene planar junctions

We report on transport properties of monolayer-bilayer graphene planar junctions in a magnetic field. Due to its unique geometry, the edge and interface states can be independently manipulated by either interlayer potential or Zeeman field, and the conductance exhibits interesting quantized behaviors. In the hybrid graphene junction, the quantum Hall (QH) conductance is no longer antisymmetric with respect to the charge neutrality point. When the Zeeman field is considered, a quantum spin Hall (QSH) phase is found in the monolayer region while the weak-QSH phase stays in the bilayer region. In the presence of both interlayer potential and Zeeman field, the bilayer region hosts a QSH phase, whereas the monolayer region is still in a QH phase, leading to a spin-polarized current in the interface. In particular, the QSH phase remains robust against the disorder.

Asymmetric bandgaps and Landau levels in a Bernal-stacked hexagonal boron-nitride bilayer

A Bernal-stacked hexagonal boron-nitride (h-BN) bilayer is a two-dimensional polar crystal. Within the tight-binding approximation, we investigate the band structure of a gated h-BN bilayer by analyzing the density of states and the behavior of the charge transfer. We find that the bandgaps of the h-BN bilayer vary asymmetrically under two opposite biases due to asymmetric changes of the interlayer and intralayer polarities. We also find that the bias-driven net charge transfer between layers can be up to 0.2 electron per unit cell. Under the bias along one direction, the system exhibits quantum phase transitions from a semiconductor to a semimetal and then to a semiconductor again, whereas under the reverse bias, the system is always semiconducting. Besides, asymmetric Landau levels under opposite biases arise in the presence of a magnetic field. Moreover, dispersive edge states are found to exist in the bulk bandgap for an h-BN bilayer nanoribbon under the bias along one direction, which does not happen when the bias is reversed. All these properties of h-BN bilayers are measurable in transport experiments.

Measurable spin-polarized current in two-dimensional topological insulators

We propose a simple method for generating a spin-polarized current in a two-dimensional topological insulator. As z-component magnetic impurities exist on one edge of the Kane-Mele model, a subgap is opened in the corresponding pair of edge states, but another pair of gapless edge states is still protected by the time reversal symmetry. Thus the conductance plateau with the value e(2)/h in the subgap corresponds to a single-edge and spin-polarized current. We also find that the spin-polarized current is insensitive to weak non-magnetic disorder. This mechanism for generating spin-polarized currents is independent of the concrete theoretical model and can be generalized to two-dimensional topological insulators, such as HgTe/CdTe quantum wells and silicene nanoribbons.

Spin thermopower and thermoconductance in a ferromagnetic graphene nanoribbon

The spin thermoelectric properties of a zigzag edged ferromagnetic (FM) graphene nanoribbon are studied theoretically by using the non-equilibrium Green's function method combined with the Landauer-Büttiker formula. By applying a temperature gradient along the ribbon, under closed boundary conditions, there is a spin voltage ΔV(s) inside the terminal as the response to the temperature difference ΔT between two terminals. Meanwhile, the heat current ΔQ is accompanied from the 'hot' terminal to the 'cold' terminal. The spin thermopower S = ΔV(s)/ΔT and thermoconductance κ = ΔQ/ΔT are obtained. When there is no magnetic field, S versus E(R) curves show peaks and valleys as a result of band selective transmission and Klein tunneling with E(R) being the on-site energy of the right terminal. The results are in agreement with the semi-classical Mott relation. When |E(R)| < M (M is the FM exchange split energy), κ is infinitesimal because tunneling is prohibited by the band selective rule. While |E(R)| > M, the quantized value of κ = π2k2(B)T/3h appears. In the quantum Hall regime, because Klein tunneling is suppressed, S peaks are eliminated and the quantized value of κ is much clearer. We also investigate how the thermoelectric properties are affected by temperature, FM exchange split energy and Anderson disorder. The results indicate that S and κ are sensitive to disorder. S is suppressed for even small disorder strengths. For small disorder strengths, κ is enhanced and for moderate disorder strengths, κ shows quantized values.

Quantized four-terminal resistances in a ferromagnetic graphene p-n junction

The quantum Hall and longitudinal resistances in four-terminal ferromagnetic graphene p-n junctions under a perpendicular magnetic field are investigated. In the Hall measurement, the transverse contacts are assumed to be located at the p-n interface to avoid the mixing of edge states at the interface and the resulting quantized resistances are then topologically protected. According to the charge carrier type, the resistances in a four-terminal p-n junction can be naturally divided into nine different regimes. The symmetric Hall and longitudinal resistances are observed, with many new robust quantum plateaus revealed due to the competition between spin splitting and local potentials.

Connection of edge states to bulk topological invariance in a quantum spin Hall state

We propose a topological understanding of general characteristics of edge states in a quantum spin Hall phase without considering any symmetries. It follows from the requirement of gauge invariance that either the energy gap or the gap in the spectrum of the projected spin operator needs to close on the sample edges. Based upon the Kane-Mele model with a uniform Zeeman field and a smooth confining potential near the sample boundaries, we demonstrate the existence of gapless edge states in the absence of time-reversal symmetry and their robust properties against impurities. These gapless edge states are protected by the band topology alone, rather than any symmetries.