Photoinduced anisotropic edge states and signatures of nonequilibrium spin polarization in silicene nanoribbons

Most topological phase transitions are accompanied by the emergence of surface/edge states with spin dependence. Usually, the quantized Hall conductivity cannot characterize the anisotropic transports and spin dependence of topological states. Here, we study the intricate topological phase transition and the anisotropic behavior of edge states in silicene nanoribbon submitted to an electric field or/and a light irradiation. It is interesting to find that a circularly polarized light can induce a type-II quantum anomaly Hall phase, which is manifested as the high Chern number and the strong anisotropic edge states. Besides the measurement of the quantized Hall conductivity, we further propose to probe these topological phase transitions and the anisotropy of edge states by measuring the current-induced nonequilibrium spin polarization. It is found that the spin polarization exhibits more signatures about the behavior of surface/edge states, beyond the quantized Hall conductivity, especially for spin-dependent transports with different velocities.     

The optical conductivity of bilayer zigzag-edge graphene nanoribbons with external transverse electric fields

The optical absorption properties of bilayer zigzag-edge graphene nanoribbons (BL-ZGNRs) with external transverse electric fields are investigated by taking into account the Coulomb interaction effect in the Hartree-Fock approximation. We study the phase transitions of BL-ZGNRs induced by external electric fields and also the optical selection rules for the incident light polarized along the longitudinal and transverse directions. We find that the excitations from the edge states are crucial for the optical properties of BL-ZGNRs in the antiferromagnetic phase. We show that the low energy part of the optical absorption can be modulated by the external transverse electric field, and there is a broad band low frequency absorption enhancement for the transverse-polarized incident light in the charge-polarized state of BL-ZGNRs.     

Assessment of bilayer silicene to probe as quantum spin and valley Hall effect

Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.     

Two-dimensional topological insulator state and topological phase transition in bilayer graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling λ(R), and transitions to a strong TI when λ(R)>√[U(2)+t(⊥)(2)], where U and t(⊥) are, respectively, the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.     

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.     

Floquet spectrum and transport through an irradiated graphene ribbon

Graphene subject to a spatially uniform, circularly polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator. The transport properties of this system, however, are complicated by the nonequilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk dc conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to superdiffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.     

Two-Dimensional Quantum Walk with Non-Hermitian Skin Effects

We construct a two-dimensional, discrete-time quantum walk, exhibiting non-Hermitian skin effects under openboundary conditions. As a confirmation of the non-Hermitian bulk-boundary correspondence, we show that the emergence of topological edge states is consistent with the Floquet winding number, calculated using a non-Bloch band theory, invoking time-dependent generalized Brillouin zones. Further, the non-Bloch topological invariants associated with quasienergy bands are captured by a non-Hermitian local Chern marker in real space, defined via the local biorthogonal eigenwave functions of a non-unitary Floquet operator. Our work aims to stimulate further studies of non-Hermitian Floquet topological phases where skin effects play a key role.     

Edge physics of graphene in the quantum Hall regime

We study the electronic edge states of graphene in the quantum Hall regime. For non-interacting electrons, graphene supports both electron-like and hole-like edge states. We find there are half as many edge states of each type in the lowest Landau level compared to higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to standard two dimensional electron gases. We also consider the effect of quantum Hall ferromagnetism on this edge structure, and find an unusual Luttinger liquid at the edge in undoped graphene. This arises due to a domain wall that forms near the edge between partially spin-polarized and valley-polarized regions. The domain wall has a U(1) degree of freedom which generates both collective and charged gapless excitations, whose consequences for tunneling experiments are discussed.     

Zigzag型边界石墨烯纳米带的电子态

在紧束缚近似下, 提出有限系统的Bloch定理方法, 解析计算了Zigzag型石墨烯纳米带的电子态和能带.研究发现, 其电子态有两类, 分别是驻波态和边缘态; 驻波态的波矢为实数, 波函数是正弦函数形式; 边缘态的波矢主要是虚数, 实数部分为零或者π/2, 波函数是双曲正弦函数形式. Zigzag型石墨烯纳米带的能带由驻波态能量和边缘态能量组成, 我们推导了边缘态的关于无限长方向波矢和能量的精确取值范围. 讨论了边缘态和驻波态的过渡点, 发现两种电子态通过不同的方式在受限波矢趋于零时关于格点位置逼近线性关系. 当受限方向也变成无限长时, 可以得到与无限大石墨烯相同的能带关系. 关键词： 紧束缚模型 Zigzag型石墨烯纳米带 边缘态     

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.     

Aspects of Floquet bands and topological phase transitions in a continuously driven superlattice

The recent creation of novel topological states of matter via periodic driving fields has attracted much attention. To contribute to the growing knowledge on this subject, we study the well-known Harper-Aubry-André model modified by a continuous time-periodic modulation and report on its topological properties along with several other interesting features. The Floquet bands are found to have non-zero Chern numbers which are generally different from those in the original static model. Topological phase transitions (discontinuous change of Chern numbers) take place as we tune the amplitude or period of the driving field. We demonstrate that the non-trivial Floquet band topology manifests via the quantized transport of Wannier states in the lattice space. For certain parameter choices, very flat yet topologically non-trivial Floquet bands emerge, a feature potentially useful for simulating the physics of strongly correlated systems. In some cases with an even number of Floquet bands, the spectrum features linearly dispersing Dirac cones which hold potential for the simulation of high energy physics or Klein tunnelling. Taking open boundary conditions, we observe anomalous counter-propagating chiral edge modes and degenerate zero modes. We end by discussing how these theoretical predictions may be verified experimentally.     

Efficient population transfer by delayed pulses despite coupling ambiguity

In traditional schemes of multilevel multilaser excitation, each laser pulse interacts with only one pair of states, and the rotating wave approximation (RWA) is applicable. Here we study the population transfer process in a three-state system when each of the two lasers interacts with each of the pair of states and when the Rabi frequencies characterizing the interaction strengths of the system are comparable to or larger than the difference of the transition frequencies. We show that complete and robust population transfer is possible under conditions more general than those hitherto considered necessary for stimulated Raman adiabatic passage (STIRAP) or for successive π pulses. Using adiabatic Floquet theory we show that successful population transfer can be interpreted as adiabatic passage by means of a transfer state which connects the initial and final states. The Floquet picture offers a convenient interpretation of the population transfer as accompanied by multiple absorption of photons from or emission into the laser fields.     

Photogalvanic effects in topological insulators

We discuss optical absorption in topological insulators and study possible photoelectric effects theoretically. We found that absorption of circularly polarized electromagnetic waves in two-dimensional topological insulators results in electric current in the conducting 1D edge channels, the direction of the current being determined by the light polarization. We suggest two ways of inducing such a current: due to magnetic dipole electron transitions stimulated by irradiation of frequency below the bulk energy gap, and due to electric dipole transitions in the bulk at frequencies larger than the energy gap with subsequent capture of the photogenerated carriers on conducting edge states.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

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.     

Photoexcitation of graphene with twisted light

We study theoretically the interaction of twisted light with graphene. The light-matter interaction matrix elements between the tight-binding states of electrons in graphene are determined near the Dirac points. We examine the dynamics of the photoexcitation process by posing the equations of motion of the density matrix and working up to second order in the field. The time evolution of the angular momentum of the photoexcited electrons and their associated photocurrents are examined in order to elucidate the mechanisms of angular momentum transfer. We find that the transfer of spin and orbital angular momentum from light to the electrons is more akin here to the case of intraband than of interband transitions in semiconductors, due to the fact that the two relevant energy bands of graphene originate from the same atomic orbitals.     

Screening of Local Magnetic Moment by Electrons of Disordered Graphene

Based on the Anderson impurity model and self-consistent approach, we investigate the condition for the screening of a local magnetic moment by electrons in graphene and the influence of the moment on electronic properties of the system. The results of numerical calculations carried out on a finite sheet of graphene show that when the Fermi energy is above the single occupancy energy and below the double occupancy energy of the local impurity, a magnetic state is possible. A phase diagram in a parameter space spanned by the Coulomb energy U and the Fermi energy is obtained to distinguish the parameter regions for the magnetic and nonmagnetic states of the impurity. We find that the combined effect of the impurity and finite size effect results in a large charge density near the edges of the finite graphene sheet. The density of states exhibits a peak at the Dirac point which is caused by the appearance of the edge states localized at the zigzag edges of the sheet.     

Andreev tunneling and Josephson current in light irradiated graphene

We investigate the Andreev tunneling and Josephson current in graphene irradiated with high-frequency linearly polarized light. The corresponding stroboscopic dynamics can be solved using Floquet mechanism which results in an effective stationary theory to the problem exhibiting an anisotropic Dirac spectrum and modified pseudospin-momentum locking. When applied to an irradiated normal graphene - superconductor (NS) interface, such analysis reveal Andreev reflection (AR) to become an oscillatory function of the optical strength. Specifically we find that, by varying the polarization direction we can both suppress AR considerably or cause the Andreev transport to remain maximum at sub-gap excitation energies even in the presence of Fermi level mismatch. Furthermore, we study the optical effect on the Andreev bound states (ABS) within a short normal-graphene sheet, sandwiched between two s-wave superconductors. It shows redistribution of the low energy regime in the ABS spectrum, which in turn, has major effect in shaping the Josephson super-current. Subjected to efficient tuning, such current can be sufficiently altered even at the charge neutrality point. Our observations provide useful feedback in regulating the quantum transport in Dirac-like systems, achieved via controlled off-resonant optical irradiation on them.     

Interaction of strong laser beam with He-atom using non-perturbative Floquet method

Non-perturbative Floquet method is used to investigate the interaction of strong linearly polarized light with He-atom. In the calculations, six lowest singlet target states and fifteen photon states are taken for absolute convergence. For allowed transitions, accurate oscillator strengths using configuration interaction wave-functions are used. A number of interesting features such as nonlinear effects at high intensities, line broadening, a dynamic Stark effect are obtained and explained.     

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.     

Optical properties of geometrically optimized graphene quantum dots

We derive effective tight-binding model for geometrically optimized graphene quantum dots and based on it we investigate corresponding changes in their optical properties in comparison to ideal structures. We consider hexagonal and triangular dots with zigzag and armchair edges. Using density functional theory methods we show that displacement of lattice sites leads to changes in atomic distances and in consequence modifies their energy spectrum. We derive appropriate model within tight-binding method with edge-modified hopping integrals. Using group theoretical analysis, we determine allowed optical transitions and investigate oscillatory strength between bulk–bulk, bulk–edge and edge–edge transitions. We compare optical joint density of states for ideal and geometry optimized structures. We also investigate an enhanced effect of sites displacement which can be designed in artificial graphene-like nanostructures. A shift of absorption peaks is found for small structures, vanishing with increasing system size.