The topological quantum phase transitions in Lieb lattice driven by the Rashba SOC and exchange field

The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieblattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) anduniform exchange field. The Lieb lattice has a simple cubic symmetry, which ischaracterized by the single Dirac-cone per Brillouin zone and the middle flat band in theband structure. The intrinsic SOC is essentially needed to open the full energy gap in thebulk. The QSH effect could survive even in the presence of the exchange field. In terms ofthe first Chern number and the spin Chern number, we study the topological nature and thetopological phase transition from the time-reversal symmetry broken QSH effect to the QAHeffect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributionsare obtained numerically, where the helical edge states and the chiral edge states revealthe non-trivial topological QSH and QAH properties, respectively.     

Z2 topological order and the quantum spin Hall effect

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.     

Time-reversal-symmetry-broken quantum spin Hall effect

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal (TR) symmetry. We investigate the fate of the QSH effect in the presence of the Rashba spin-orbit coupling and an exchange field, which break both inversion and TR symmetries. It is found that the QSH state characterized by nonzero spin Chern numbers C(±) = ±1 persists when the TR symmetry is broken. A topological phase transition from the TR-symmetry-broken QSH phase to a quantum anomalous Hall phase occurs at a critical exchange field, where the bulk band gap just closes. It is also shown that the transition from the TR-symmetry-broken QSH phase to an ordinary insulator state cannot happen without closing the band gap.     

Multiprobe quantum spin Hall bars

We analyze electron transport in multiprobe quantum spin Hall (QSH) bars using the Büttiker formalism and draw parallels with their quantum Hall (QH) counterparts. We find that in a QSH bar the measured resistance changes upon introducing side voltage probes, in contrast to the QH case. We also study four- and six-terminal geometries and derive the expressions for the resistances. For these our analysis is generalized from the single-channel to the multi-channel case and to the inclusion of backscattering originating from a constriction placed within the bar.     

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

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

Effect of spin–orbit coupling on spin transport at graphene/transition metal interface

In spite of large spin coherence length in graphene due to small spin–orbit coupling, the created potential barrier and antiferromagnetic coupling at graphene/transition metal (TM) contacts strongly reduce the spin transport behavior in graphene. Keeping these critical issues in mind in the present work, ferromagnetic (Co, Ni) nanosheets are grown on graphene surface to elucidate the nature of interaction at the graphene/ferromagnetic interface to improve the spin transistor characteristics. Temperature dependent magnetoconductance shows unusual behavior exhibiting giant enhancement in magnetoconductance with increasing temperature. A model based on spin–orbit coupling operated at the graphene/TM interface is proposed to explain this anomalous result. We believe that the device performance can be improved remarkably tuning the spin–orbit coupling at the interface of graphene based spin transistor. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

缀饰格子中时间反演对称破缺的量子自旋霍尔效应

<正>研究了缀饰格子中的量子自旋霍尔效应,模型中同时考虑了Rashba自旋轨道耦合和交换场的作用.缀饰格子具有简立方对称性,以零能平带和单狄拉克锥结构为主要特点.在缀饰格子中,不论是实现量子自旋霍尔效应还是量子反常霍尔效应,都需要一个不为零的内禀自旋轨道耦合作用来打开一个完全的体能隙,这与石墨烯等六角格子模型有着很大的不同.在交换场破坏了时间反演对称性的情况下,以自旋陈数为标志的量子自旋霍尔效应仍然能够存在,边缘态和极化率的相关结果也证明了这一结论.结果表明自旋陈数比z2拓扑数在表征量子自旋霍尔效应方面有着更广泛的适用范围,相应的结论为利用磁场控制量子自旋霍尔效应提出了一个理论模型和依据.     

基于graphene条带的硅纳米结构

采用分子动力学模拟方法研究了graphene条带上生长硅纳米结构的过程,分析了不同温度下硅原子在graphene条带边沿生成的新型纳米结构.研究表明,随机分布的硅原子吸附到锯齿型graphene条带边沿在不同的温度T下可生成不同类型的硅纳米结构：300K≤T<2000K时形成无规则的团簇,2000K≤T≤2800K时形成单原子链结构,2800K<T<3900K时形成含缺陷的硅链结构,T≥3900K时硅原子逐渐替代条带边沿的碳原子直至graphene条带破坏.而硅原子吸附到扶手椅型graphene条带边沿在300K≤T<3000 K内仅能形成非链状的不定型的硅纳米结构. 关键词： graphene 硅 纳米结构 分子动力学模拟     

Structural stability and electronic properties of Ni-doped armchair graphene nanoribbons

The size dependent electronic properties of armchair graphene nanoribbons (AGNR) with Ni doped atoms have been investigated using spin-unrestricted density functional theory. We predict antiferromagnetic (AFM) ground states for Ni-termination and one edge Ni-doping. The computed formation energy reveals that one edge Ni-terminated AGNR are energetically more favourable as compared to pristine ribbons. One edge substitutional doping is energetically more favourable as compared to centre doping by ∼1 eV whereas both edge doping is unfavourable. The bond length of substitutional Ni atoms is shorter than that of Ni adsorption in GNR, implying a stronger binding for substitutional Ni atoms. It is evident that binding energy is also affected by the coordination number of the foreign atom. The results show that Ni-interaction perturbs the electronic structure of the ribbons significantly, causing enhanced metallicity for all configurations irrespective of doping site. The band structures reveal the separation of spin up and down electronic states indicating towards the existence of spin polarized current in Ni-terminated and one edge doped ribbons. Our calculation predicts that AGNR containing Ni impurities can play an important role for the fabrication of spin filters and spintronic devices.     

Effective spin dephasing mechanism in confined two-dimensional topological insulators

A Kramers pair of helical edge states in quantum spin Hall effect (QSHE) is robust against normal dephasing but not robust to spin dephasing. In our work, we provide an effective spin dephasing mechanism in the puddles of two-dimensional (2D) QSHE, which is simulated as quantum dots modeled by 2D massive Dirac Hamiltonian. We demonstrate that the spin dephasing effect can originate from the combination of the Rashba spin-orbit coupling and electron-phonon interaction, which gives rise to inelastic backscattering in edge states within the topological insulator quantum dots, although the time-reversal symmetry is preserved throughout. Finally, we discuss the tunneling between extended helical edge states and local edge states in the QSH quantum dots, which leads to backscattering in the extended edge states. These results can explain the more robust edge transport in InAs/GaSb QSH systems.     

Current–voltage characteristics of armchair Sn nanoribbons

Two‐dimensional group‐IV lattices silicene and germanene are known to share many of graphene's remarkable mechanical and electronic properties. Due to the out‐of‐plane buckling of the former materials, there are more means of electronic funtionalization, e.g. by applying uniaxial strain or an out‐of‐plane electric field. We consider monolayer hexagonal Sn (stanene) as an ideal candidate to feasibly implement and exploit graphene physics for nanoelectronic applications: with increased out‐of‐plane buckling and sizable spin–orbit coupling it lends itself to improved Dirac cone engineering. We investigate the ballistic charge transport regime of armchair Sn nanoribbons, classified according to the ribbon width W = {3m – 1, 3m, 3m + 1} with integer m. We study transport through (non‐magnetic) armchair ribbons using a combination of density functional theory and non‐equilibrium Green's functions. Sn ribbons have earlier current onsets and carry currents 20% larger than C/Si/Ge‐nanoribbons as the contact resistance of these ribbons is found to be comparable. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Dynamical structure factor and spin-density separation for a weakly interacting two-component Bose gas

We show that spin-density separation in a Bose gas is not restricted to 1D but also occurs in higher dimensions. The ratio (alpha) of the intraspecies atom-atom interaction strength to the interspecies interaction strength strongly influences the dynamics of spin-density separation and the elementary excitations. The density wave is phononlike for all values of alpha. For alpha < 1, the spin wave is also phononlike. The spin waves have a quadratic dispersion in the alpha=1 coupling regime, while in the phase separated regime (alpha > 1) the spin waves are found to be damped. The dynamical structure factor reveals two distinct peaks corresponding to the density and spin waves for alpha < or =1. For alpha > 1 there is only one dynamical structure factor peak corresponding to the density wave.     

Possible polaron formation of zigzag graphene nano-ribbon in the presence of Rashba spin–orbit coupling

In this article we study the role of Rashba spin–orbit coupling and electron–phonon interaction on the electronic structure of zigzag graphene nanoribbon with different width. The total Hamiltonian of nanoribbon is written in the tight binding form and the electron–electron interaction is modeled in the Hubbard term. We used a unitary transformation to reach an effective Hamiltonian for nano ribbon in the presence of electron–phonon interaction. Our results show that small Rashba spin orbit coupling annihilates the anti-ferromagnetic phase in the zigzag edges of ribbon and the electron–phonon interaction yields small polaron formation in graphene nano ribbon. Furthermore, Rashba type spin–orbit coupling increases (decreases) the polaron formation energy for up (down) spin state.     

Ab initio study of gold-doped zigzag graphene nanoribbons

The electronic transport properties of zigzag graphene nanoribbons (ZGNRs) through covalent functionalization of gold (Au) atoms is investigated by using non-equilibrium Green’s function combined with density functional theory. It is revealed that the electronic properties of Au-doped ZGNRs vary significantly due to spin and its non-inclusion. We find that the DOS profiles of Au-adsorbed ZGNR due to spin reveal very less number of states available for conduction, whereas non-inclusion of spin results in higher DOS across the Fermi level. Edge Au-doped ribbons exhibit stable structure and are energetically more favorable than the center Au-doped ZGNRs. Though the chemical interaction at the ZGNR–Au interface modifies the Fermi level, Au-adsorbed ZGNR reveals semimetallic properties. A prominent qualitative change of the I–V curve from linear to nonlinear is observed as the Au atom shifts from center toward the edges of the ribbon. Number of peaks present near the Fermi level ensures conductance channels available for charge transport in case of Au-center-substituted ZGNR. We predict semimetallic nature of the Au-adsorbed ZGNR with a high DOS peak distributed over a narrow energy region at the Fermi level and fewer conductance channels. Our calculations for the magnetic properties predict that Au functionalization leads to semiconducting nature with different band gaps for spin up and spin down. The outcomes are compared with the experimental and theoretical results available for other materials.     

Quantum spin Hall effect in a square-lattice model under a uniform magnetic field

We study a toy square-lattice model under a uniform magnetic field. Using the Landauer-Bttiker formula, we calculate the transport properties of the system on a two-terminal, a four-terminal and a six-terminal device. We find that the quantum spin Hall (QSH) effect appears in energy ranges where the spin-up and spin-down subsystems have different filling factors. We also study the robustness of the resulting QSH effect and find that it is robust when the Fermi levels of both spin subsystems are far away from the energy plateaus but is fragile when the Fermi level of any spin subsystem is near the energy plateaus. These results provide an example of the QSH effect with a physical origin other than time-reversal (TR) preserving spin-orbit coupling (SOC).     

Thermoelectric transport and spin density of graphene nanoribbons with Rashba spin–orbit interaction

In the present paper, we have theoretically investigated thermoelectric transport properties of armchair and zigzag graphene nanoribbons with Rashba spin–orbit interaction, as well as dephasing scattering processes by applying the nonequilibrium Green function method. Behaviors of electronic and thermal currents, as well as thermoelectric coefficients are studied. It is found that both electronic and thermal currents decrease, and thermoelectric properties been suppressed, with increasing strength of Rashba spin–orbit interaction. We have also studied spin split and spin density induced by Rashba spin–orbit interaction in the graphene nanoribbons.     

Classification of Topological Insulators with Time-Reversal and Inversion Symmetry

In this paper, we find that topological insulators with time-reversal symmetryand inversion symmetry featuring two-dimensional quantum spin Hall (QSH) state can be divided into 16 classes, which are characterized by four Z₂topological variables ζ_k=0,1 at four points with high symmetry in the Brillouin zone. We obtain the corresponding edge states for each one of these sixteen classes of QSHs. In addition, it is predicted that massless fermionic excitations appear at the quantum phase transition between different QSH states. In the end, we also briefly discuss the three-dimensional case.     

Magnetic and charge orders in zigzag nanographene ribbons

We theoretically study the electronic states in graphene ribbons which are strongly affected by the edge states, the peculiar non-bonding molecular orbitals localized along the zigzag edges of the ribbons. New kinds of edge localized electronic states with spin and charge polarizations are found in the mean field solutions of the extended Hubbard model with onsite and nearest-neighbor Coulomb repulsions. These novel states appear due to the interplay between the edge states and the Fermi instabilities. We also examine the competition between the charge polarized state and the spin polarized state to draw a phase diagram depending on Coulomb parameters. The results obtained by the mean field calculations with the extended Hubbard model modified to include Coulomb integrals provide useful insights to understand and functionalize the nanoscale materials.     

Controlling the polarization fluctuation of excitons in armchair graphene ribbons by a laser field

We investigate the effect of the laser field on the polarization fluctuation of excitons in graphene ribbons. In order to calculate the fluctuation, we develop a bosonization method to deal with the electron-hole system. Our results show that the polarization fluctuation may be controlled by adjusting the strength and frequency of the laser field. The insulating armchair graphene ribbons may be divided into two types according to the width-dependences of the excitonic polarization fluctuation.     

Modification of the electronic structure of graphene by intercalation of iron and silicon atoms

The ab initio calculations of the electronic structure of low-dimensional graphene–iron–nickel and graphene–silicon–iron systems were carried out using the density functional theory. For the graphene–Fe–Ni(111) system, band structures for different spin projections and total densities of valence electrons are determined. The energy position of the Dirac cone caused by the p _z states of graphene depends weakly on the number of iron layers intercalated into the interlayer gap between nickel and graphene. For the graphene–Si–Fe(111) system, the most advantageous positions of silicon atoms on iron are determined. The intercalation of silicon under graphene leads to a sharp decrease in the interaction of carbon atoms with the substrate and largely restores the electronic properties of free graphene.