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Topological edge states exhibit dissipationless transport and electrically-driven topological phase transitions, making them ideal for next-generation transistors that are not constrained by Moore's law. Nevertheless, their dispersion has never been probed and is often assumed to be simply linear, without any rigorous justification. Here we determine the non-linear electrical response of topological edge states in the ballistic regime and demonstrate the way this response ascertains the presence of symmetry breaking terms in the edge dispersion, such as deviations from non-linearity and tilted spin quantization axes. The non-linear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of topological materials and discuss experimental measurement., 8 pages, 4 figures

The current response for the parameter change of a mesoscopic system is a practical issue for future's circuit design. Nowadays most considered cases are various types of bias modulation, while the effect of change of conductor Hamiltonian is seldom addressed. In this paper, we investigate the response of ballistic transport induced by a sudden change of the conductor Hamiltonian. We formulize the terminal current in language of non-equilibrium Green's function. Our method is applied to one-dimensional tight-binding chains and we find that the terminal current has a delay to the Hamiltonian change. The amount of delay is not determined by the velocity of incident electrons in the bias window, but depends on the tight-binding hopping energy γ. The delay of current response at the detecting point away from where the Hamiltonian changes is C γ − 1 , where C is a constant independent of the system.

Recently, the linear and nonlinear planar Hall effect (PHE) on the topological insulators (TIs) surface has been extensively studied in experiments. To explain this phenomenon, various microscopic mechanisms are proposed theoretically, and one has to employ different mechanisms to separately understand the linear and nonlinear PHE even for the same system. Here, we study the planar magnetic resistance effect in TI thin film and find that a peculiar anisotropic scattering and a spin valve structure with respect to the PHE can be caused by the tilt and shift of Dirac cones, respectively, which are induced by the combination of spin-momentum locking of surface states and an in-plane magnetic field. The tilt and shift effects can act as the origin of both the linear and nonlinear PHE by distorting the spin texture of surface states or forming the spin polarization. These two mechanisms interplay and dominate, respectively, in strong coupling (thin TI) and decoupling (thick TI) between bottom and top surfaces. For thick TI film, we show that both the linear and nonlinear PHEs induced by the tilt effect can recover the results observed in recent experiments. Our theory provides a perspective to understand the origin of both linear and nonlinear PHE observed in recent experiments.

Nodal-line semimetals are typically characterized by a nodal ring, a closed line of Dirac points in the Brillouin zone, whose topology is characterized by a quantized Berry phase. The nodal loop is protected by the combined inversion and time-reversal ($\mathcal{PT}$) symmetry in the absence of spin-orbit coupling, exhibiting the parity anomaly. Introduction of the $\mathcal{PT}$-break mass term can lead to the transverse Hall response at each point in the nodal ring, but the net Hall current vanishes due to the existence of inversion-symmetry points that contribute to the transverse current with opposite signs. We show that the combination of an inversion-broken tilt term and finite Fermi energy can cause the nonzero anomalous Hall effect. We explore the DC and AC anomalous Hall conductivity in tilted nodal-line semimetals using Kubo formula and focus on the contribution of the free carriers to the Hall conductivity. We find that the interband transition of free carriers dominates the nonvanishing dynamic Hall conductivity over the filled band contribution. The resulting anomalous Hall conductivity exhibits the parity anomaly for the DC case, and rich characteristic frequencies for the AC case which is closely related to the change of the geometry of the Fermi surface. These features may serve as a diagnostic tool to characterize the topological property, tilting parameter, or the radius of the nodal line.

Nodal-line semimetals (NLSMs) are typically characterized by a nodal ring, a closed line of Dirac points in the Brillouin zone, which features a torus-shaped Fermi surface, as well as a quantized Berry phase $\ensuremath{\pi}$. By investigating the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in NLSMs, a close relationship between the magnetic interaction and the radius ${k}_{0}$ of the nodal ring is revealed. For impurities deposited in the direction normal to the nodal-ring plane, when the long-range interaction at half-band filling follows the decaying law ${R}^{\ensuremath{-}3}$ with impurity distance, which is a result of anisotropic dispersion of semi-Dirac semimetal, the decaying rate for the relatively short-range impurity distance would be prolonged by nodal-ring radius ${k}_{0}$, which is prominent for the intermediate radius. This phenomenon originates from the competition between the contribution from the electron states inside and outside the nodal ring. In contrast, for impurities distributed in the nodal-ring plane, the RKKY interaction $J\ensuremath{\propto}{k}_{0}^{2}\mathrm{cos}(2{k}_{0}R){R}^{\ensuremath{-}4}$ shows an oscillation, from whose period one can easily determine the parameter ${k}_{0}$ of the nodal ring. Furthermore, at finite Fermi energy, we find a distinct signature of the RKKY interaction to characterize the topological trivial and topological nontrivial phases in NLSMs.

Recently, a novel planar Hall effect (PHE), which results from the resistivity anisotropy induced by an in-plane magnetic field, was discovered on the surface of topological insulators (TIs). While the PHE phenomenon in Weyl/Dirac semimetals is understood as a consequence of the chiral anomaly, the origin of the PHE in TIs, however, remains unclear theoretically. Several theories and experiments have ascribed the appearance of the PHE to the anisotropic backscattering induced by magnetic disorders, where the magnetization of the scatterers is indispensable. Instead, we here show that the anisotropic backscattering can arise from the tilt of the Dirac cone by an in-plane magnetic field, which emerges if nonlinear momentum terms are included, irrelevant to the magnetic nature of the scatterers. We further find that a relatively strong scalar potential can further enhance the PHE magnitude significantly, and the resulting impurity resonant state together with the tilted cone can produce the double-peak structure of the PHE and the sign change of the anisotropic magnetoresistivity. Our theory provides another perspective to understand the nontopological origin of the experimentally observed PHE in topological materials.

We propose a mechanism to directly measure the chiral anomaly in disorder Weyl semimetals (WSMs) by the Kondo effect. We find that in a magnetic and electric field driven WSM, the locations of the Kondo peaks can be modulated by the chiral chemical potential, which is proportional to $\mathbf{E}\cdot \mathbf{B}$. The Kondo peaks come from spin fluctuations within the impurities, which apart from the temperature, relate closely to the host's Fermi level. In WSMs, the chiral-anomaly-induced chirality population imbalance will shift the local Fermi levels of the paired Weyl valleys toward opposite directions in energy, and then affects the Kondo effect. Consequently, the Kondo effect can be tunable by an external electric field via the chiral chemical potential. This is unique to the chiral anomaly. Base on this, we argue that the electrically tunable Kondo effect can serve as a direct measurement of the chiral anomaly in WSMs. The Kondo peaks are robust against the disorder effect and therefore, the signal of the chiral anomaly survives for a relatively weak magnetic field., Comment: 7 pages, 4 figures

Silicene offers an ideal platform for exploring the phase transition due to strong spin-orbit interaction and its unique structure with strong tunability. With applied electric field and circularly polarized light, silicone is predicted to exhibit rich phases. We propose that these intricate phase transitions can be detected by measuring the bulk Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. We have in detail analyzed the dependence of RKKY interaction on phase parameters for different impurity configurations along zigzag direction. Importantly, we present an interesting comparison between different terms of RKKY interaction with phase diagram. It is found that the in-plane and out-of-plane terms can exhibit the local extreme value or change of sign at the phase critical point and remarkable difference in magnitude for different phase regions. Consequently, the magnetic measurement provides unambiguous signatures to identify various types of phase transition simultaneously, which can be carried out with present technique.

Three-dimensional Dirac semimetal is an ideal platform in studying topological phase transitions due to its exotic electronic structure. Based on the effective Hamiltonian of material Na3Bi where two degenerated Dirac points are constructed by four Weyl nodes and protected by crystal symmetry, we study its Floquet phase transitions induced by circularly polarized light in off-resonant limit. By breaking the time-reversal symmetry and taking the quadratic momentum into account, abundant phases are realized, including Weyl semimetal, spin-polarized Weyl semimetal (SP-WSM), and normal insulator. The SP-WSM phase is a new phase, in which only pairs of spin-up (or spin-down) opposite-chirality Weyl nodes are remained while the other pairs of spin-down (or spin-up) opposite-chirality Weyl nodes are eliminated. Importantly, all the phase transitions can be manipulated not only by tuning the light intensity but also by changing the incident direction of light. To understand them, we have in detail analyzed the trajectory of Weyl nodes in k space controlled by the circularly polarized light and manifested them with the angle- and spin- dependent Hall conductivity.

Recently discovered Dirac semimetals (DSMs) with two Dirac nodes, such as Na$_{3}$Bi and Cd$_{2}$As$_{3}$, are regarded to carry the $\mathbb{Z}_{2}$ topological charge in addition to the chiral charge. Here, we study the Floquet phase transition of $\mathbb{Z}_{2}$ topological DSMs subjected to a beam of circularly polarized light. Due to the resulting interplay of the chiral and $\mathbb{Z}_{2}$ charges, the Weyl nodes are not only chirality-dependent but also spin-dependent, which constrains the behaviors in creation and annihilation of the Weyl nodes in pair. Interestingly, we find a novel phase: One spinband is in Weyl semimetal phase while the other spinband is in insulator phase, and we dub it Weyl half-metal (WHM) phase. We further study the spin-dependent transport in a Dirac-Weyl semimetal junction and find a spin filter effect as a fingerprint of existence of the WHM phase. The proposed spin filter effect, based on the WHM bulk band, is highly tunable in a broad parameter regime and robust against magnetic disorder, which is expected to overcome the shortcomings of the previously proposed spin filter based on the topological edge/surface states. Our results offer a unique opportunity to explore the potential applications of topological DSMs in spintronics., 6 pages, 4 figures

Spin selectivity in double-stranded DNA (dsDNA) molecules is unambiguously linked to their intrinsic chirality. Nevertheless, how the chiral-induced spin selectivity (CISS) effect in dsDNA influences spin-dependent thermoelectricity needs to be understood well, to comprehend the relationship between spin and heat transport. To this end, the authors explore the spin Seebeck effect of a chiral dsDNA-based magnetic junction, and elucidate the underlying physics relevant to the CISS effect by means of linear-response theory and nonequilibrium Green's functions. Their results provide valuable guidelines for engineering innovative spin-caloritronic devices based on chiral organic molecules.

Recently, a class of Dirac semimetals, such as \textrm{Na}$_{\mathrm{3}}% $\textrm{Bi} and \textrm{Cd}$_{\mathrm{2}}$\textrm{As}$_{\mathrm{3}}$, are discovered to carry $\mathbb{Z}_{2}$ monopole charges. We present an experimental mechanism to realize the $\mathbb{Z}_{2}$ anomaly in regard to the $\mathbb{Z}_{2}$ topological charges, and propose to probe it by magnetotransport measurement. In analogy to the chiral anomaly in a Weyl semimetal, the acceleration of electrons by a spin bias along the magnetic field can create a $\mathbb{Z}_{2}$ charge imbalance between the Dirac points, the relaxation of which contributes a measurable positive longitudinal spin magnetoconductivity (LSMC) to the system. The $\mathbb{Z}_{2}$ anomaly induced LSMC is a spin version of the longitudinal magnetoconductivity (LMC) due to the chiral anomaly, which possesses all characters of the chiral anomaly induced LMC. While the chiral anomaly in the topological Dirac semimetal is very sensitive to local magnetic impurities, the $\mathbb{Z}_{2}$ anomaly is found to be immune to local magnetic disorder. It is further demonstrated that the quadratic or linear field dependence of the positive LMC is not unique to the chiral anomaly. Base on this, we argue that the periodic-in-$1/B$ quantum oscillations superposed on the positive LSMC can serve as a fingerprint of the $\mathbb{Z}_{2}$ anomaly in topological Dirac semimetals., 5 pages, 2 figures

We study the positive longitudinal magnetoconductivity (LMC) and planar Hall effect as emergent effects of the chiral anomaly in Weyl semimetals, following a recent-developed theory by integrating the Landau quantization with Boltzmann equation. It is found that, in the weak magnetic field regime, the LMC and planar Hall conductivity (PHC) obey $\cos^{6}\theta$ and $\cos^{5}\theta\sin \theta$ dependences on the angle $\theta$ between the magnetic and electric fields. For higher magnetic fields, the LMC and PHC cross over to $\cos^{2}\theta$ and $\cos\theta\sin\theta$ dependences, respectively. Interestingly, the PHC could exhibit quantum oscillations with varying $\theta$, due to the periodic-in-$1/B$ oscillations of the chiral chemical potential. When the magnetic and electric fields are noncollinear, the LMC and PHC will deviate from the classical $B$-quadratic dependence, even in the weak magnetic field regime., Comment: 8 pages, 4 figures

Current-induced spin polarization and the resulting spin-orbit torque (SOT) in a ferromagnet/topological insulator (FM/TI) bilayer have been investigated by taking into account the hexagonal warping spectrum of topological surface states. We find that the usually ignored in-plane FM magnetization plays an important role to the spin polarization. The resulting spin polarization and spin torque significantly depend on azimuthal angle of the magnetization, which has not been reported theoretically before in the linear dispersion TI model. These interesting results arise from the combination effect of in-plane magnetization and warping effect by modifying the Berry curvature and impurity scattering. Based on Matsubara-Green function approach, we derive the formula of SOT and analyze the results analytically and numerically, including the contribution from intrabands and interbands, and intrinsic and extrinsic contribution. More importantly, it is found that the hexagonal warping can prominently enhance the antidamping SOT if there exists the in-plane FM magnetization, which provides a new perspective to understand the recent giant SOT effect.

Zigzag phosphorene ribbons can accommodate degenerate edge states that decay from edge to bulk. The electronic structure of phosphorene ribbons, both the bulk bands and the edge bands, can be tuned by normally applying an electric field. The electrical field enlarges the energy gap parabolically, which is a second order perturbation effect. The external field as a first order perturbation lifts the degeneration of the edge bands and changes their decay property. The localization of edge states is increased by the electric field and the decay length as a function of wavevector in the whole Brillouin zone can be obtained by measuring the electric response of the edge band extreme energies.

We studied the electronic structure and optic absorption of phosphorene (monolayer of black phosphorus) under strain. Strain was found to be a powerful tool for the band structure engineering. The in-plane strain in armchair or zigzag direction changes the effective masse components along both directions, while the vertical strain only has significant effect on the effective mass in the armchair direction. The band gap is narrowed by compressive in-plane strain and tensile vertical strain. Under certain strain configurations, the gap is closed and the energy band evolutes to the semi-Dirac type: the dispersion is linear in the armchair direction and is gapless quadratic in the zigzag direction. The band-edge optic absorption is completely polarized along the armchair direction, and the polarization rate is reduced when the photon energy increases. Strain not only changes the absorption edge, but also the absorption polarization., Comment: 5 pages, 5 figures

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.

By generalizing the Kubo-Streda formula for calculating electrical conductivities to the thermoelectric coefficients, we theoretically study the anomalous Nernst effect (ANE) on the surface of a topological insulator induced by a finite concentration of magnetic impurities. The ANE is found to be modulated by the impurity scattering and thermal fluctuations, simultaneously, and so exhibits rich structures in the energy space. While the anomalous Hall conductivity is half-integer quantized with the Fermi level across the magnetic-impurity-induced gap, the anomalous Nernst signal (ANS) is fully suppressed and the thermopower is linear-dependent on the Fermi energy. Around the magnetic-impurity-induced localized levels, the ANS and thermopower are resonant enhanced. The suppression and enhancement of the thermoelectric coefficients will compete with each other as the magnetic impurity potential increases continually. More interestingly, when a finite charge potential is included, the resonant peaks of the ANS and thermopower will be renormalized, making the signs of the ANS and thermopower tunable by the strength of the charge potential., 8 pages, 5 figures

We provide a general transport theory for spin-polarized scanning tunneling microscopy (STM) through a doped topological insulator (TI) surface. It is found that different from the conventional magnetic substrate, the tunneling conductance through the tip-TI surface acquires an extra component determined by the in-plane spin texture, exclusively associated with the spin momentum locking. Importantly, this extra conductance unconventionally depends on the spatial azimuthal angle of the magnetized STM tip. By introducing a magnetic impurity to break the symmetry of rotation and local time reversal of the TI surface, we find that the measurement of the spatial resolved conductance can reconstruct the helical structure of spin texture, from which the spin-momentum locking angle can be extracted if the in-plane magnetization is induced purely by the spin-orbit coupling of surface Dirac electrons. Our theory offers an alternative way, differing from existing in-plane-current polarization probed in a multi-terminal setup or angle resolved photoemission spectroscopy, to electrically identify the helical spin texture on TI surfaces.

We address the long-term controversy on the fundamental question of the role of the surface state on the Kondo effect with Co adatoms on a Ag(111) surface. The width of the Kondo resonance oscillates with the same period of half Fermi wavelength of the surface state. But the amplitude increases for a Co adatom placed next to another Co adatom, at the vicinity of a step edge, and quantum confined within nanocorrals. A greater than three times enhancement of the resonance width can be achieved when quantum confinement is introduced. The experimental results are described quantitatively utilizing an analytical model where the contributions of the bulk and surface states are weighted by their exchange values with the magnetic impurity. These findings clarify the role of the surface state on the Kondo effect and pave a pathway to tailor the Kondo effect via quantum confinement of the surface state.

Phosphorene (a monolayer of black phosphorus) recently spurred much attention due to its potential for application. We notice there are two types of zigzag edge and two types of armchair edge for phosphorene lattice. We study the winding number of various types of edge of phosphorene ribbons and conclude that, besides on the typical zigzag edge, the flat zero-energy edge band can be found in the ribbon of another nontypical armchair edge. The localization of these edge bands is investigated analytically. We find every single edge state of the atypical armchair edge decays to the bulk at two different decay rates.

We present the study of the effect of both magnetic and potential scattering ($M$ and $U$) of magnetic impurities on the local electronic structures on a topological insulator. For single impurity, the local density of states (LDOS) shows distinct patterns of two resonance states with the positions depending on the relative strength of magnetic and potential scattering $M$ and $U$. However, in the usual case where $U$ is much larger than $M$, these two resonance states have very similar energy and become indistinguishable. Thus only one single peak is present, in analog with the experimental observations by scanning tunneling spectroscopy and providing a possible explanation for the recent debate among different experimental results. Interestingly, the effect of $M$ can be significantly magnified when the magnetic impurities are forming nanosized quantum corrals, the apparent different features in the LDOSs allow justifying the existence of $M$ despite its relative smaller strength compared with $U$. Remarkably, we find a one-to-one correspondence between the strength of $U,\phantom{\rule{4pt}{0ex}}M$, and the energy positions of the quantum well states, giving a unique scheme to determine both $U$ and $M$, which are of great importance for future TI based novel device design.

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.

We theoretically study the effect of impurity scattering in a magnetically doped Dirac semimetal. It is found that the magnetic impurity potential can split a Dirac point into a pair of Weyl nodes, due to the broken time-reversal symmetry, and the DSM undergoes a topological phase transition to a Weyl semimetal (WSM). The Chern numbers on a cross section between the Weyl nodes in the Brillouin zone are integer quantized. As a consequence, open Fermi arcs emerge, which connect the projections of the Weyl nodes on the surface Brillouin zone. However, a relatively strong magnetic potential, in addition to separating the Weyl nodes, will introduce some localized states to the system. These localized states smear the Weyl nodes, and the anomalous Hall conductivity deviates from the linear dependence on the momentum distance of the Weyl nodes. Interestingly, though the nonmagnetic charge potential of the impurities is shown to be irrelevant to the topological phase transition, it can modify the Berry curvature and anomalous Hall conductivity of the impurity-induced WSM phase, by redistribution of the energies of the localized states.

We investigate the thermoelectric effect on a topological insulator surface with particular interest in impurity-induced resonant states. To clarify the role of the resonant states, we calculate the dc and ac conductivities and the thermoelectric coefficients along the longitudinal direction within the full Born approximation. It is found that at low temperatures, the impurity resonant state with strong energy de-pendence can lead to a zero-energy peak in the dc conductivity, whose height is sensitively dependent on the strength of scattering potential, and even can reverse the sign of the thermopower, implying the switching from n- to p-type carriers. Also, we exhibit the thermoelectric signatures for the filling process of a magnetic band gap by the resonant state. We further study the impurity effect on the dynamic optical conductivity, and find that the resonant state also generates an optical conductivity peak at the absorption edge for the interband transition. These results provide new perspectives for understanding the doping effect on topological insulator materials.

We consider the Dirac electron scattering off a pointlike impurity absorbed on the surface of a topological insulator, which is irradiated by a beam of circularly polarized light. It is found that the Dirac electron backscattering is allowed even for a nonmagnetic impurity due to the reshuffled spectrum caused by the light, and so exhibits interesting spin texture and Friedel oscillation in the real space. Furthermore, in the charge density of states, the interplay of the light irradiation and impurity scattering can lead to an in-gap bound state around the Dirac point, heavily modulating the Dirac dispersion. We discuss the different scenarios for resonant and off-resonant lights in detail. The impurity scattering feature is sensitive to the parameters of the polarized light, which suggests a possibility to optically manipulate the topological surface states.

We studied the transport properties of the Weyl-node-mismatch junction, beside which the Weyl nodes are mismatch so that their projections on the interface plane cannot overlap. When electrons of one valley are injected onto the junction, the refraction is not coplanar with the injection-reflection plane. The non-coplanar deviation angle is valley dependent, and so if the injection consists of both valley components, the birefraction will take place. When electrons coming from a narrow rod transit across the junction into the bulk region on the other side, the electrons will be diffracted in the unconfined region. The diffraction is dispersed near the rod-bulk interface and is laterally deflected to the direction along the line connecting the Weyl node projections of incident and transmitted sides.

Currently, Weyl semimetals (WSMs) are drawing great interest as a new topological nontrivial phase. When most of the studies concentrated on the clean host WSMs, it is expected that the dirty WSM system would present rich physics due to the interplay between the WSM states and the impurities embedded inside these materials. We investigate theoretically the change of local density of states in three-dimensional Dirac and Weyl bulk states scattered off a quantum impurity. It is found that the quantum impurity scattering can create nodal resonance and Kondo peak/dip in the host bulk states, remarkably modifying the pristine spectrum structure. Moreover, the joint effect of the separation of Weyl nodes and the Friedel interference oscillation causes the unique battering feature. We in detail an- alyze the different contribution from the intra- and inter-node scattering processes and present various scenarios as a consequence of competition between them. Importantly, these behaviors are sensitive significantly to the displacement of Weyl nodes in energy or momentum, from which the distinctive fingerprints can be extracted to identify various semimetal materials experimentally by employing the scanning tunneling microscope.

We reported the collimation and splitting effects of the diffraction of valley electrons in graphene. When the incident energy increases from the neutral point, the diffraction tends to be collimated for one valley and split for the other valley. The difference in the diffraction between valleys results in valley-dependent transport. We investigated the left-right conductance of a four-terminal graphene device. The conductance ratio between the two valleys was derived to be $1\ensuremath{-}(8/3)E$, where $E$ is the incident energy in units of the atom-atom hopping. The ratio is independent of the device dimensions and reflects the intrinsic properties of the electronic structure of graphene.

We proposed a minimal model to describe the Floquet band structure of two-dimensional materials with light-induced resonant inter-band transition. We applied it to graphene to study the band features caused by the light irradiation. Linearly polarized light induces pseudo gaps (gaps are functions of wavevector), and circularly polarized light causes real gaps on the quasi-energy spectrum. If the polarization of light is linear and along the longitudinal direction of zigzag ribbons, flat edge bands appear in the pseudo gaps, and if is in the lateral direction of armchair ribbons, curved edge bands can be found. For the circularly polarized cases, edge bands arise and intersect in the gaps of both types of ribbons. The edge bands induced by the circularly polarized light are helical and those by linearly polarized light are topologically trivial ones. The Chern number of the Floquet band, which reflects the number of pairs of helical edge bands in graphene ribbons, can be reduced into the winding number at resonance., Comment: 7 pages, 4 figures

We investigate the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between two magnetic impurities placed on a phosphorene surface based on the tight-binding model. It is found that the RKKY interaction exhibits strong anisotropy along different lattice directions and is sensitive to the deformed direction. The RKKY interaction is largest for impurities distributed in the armchair direction while the strain effect is strongest for the deformation exerted along the zigzag direction. Applied linear strain can increase the RKKY magnitude nonlinearly, and observably prolong the decay rate from the exponent to the law with the impurity distance. Most interestingly, near the strain-induced closing point of the bandgap, we find that the RKKY interaction is no longer simply ferromagnetic or antiferromagnetic, but presents oscillatory behavior, exhibiting the transition from ferromagnetism to antiferromagnetism. This originates from the combination effect of negative energy in the conduction band due to modification of the Fermi surface and the narrowing bandgap, and importantly both of them are reached simultaneously just by tuning the strain. Therefore, the strain effect proves to be an alternative approach to engineering impurity interactions in phosphorene materials.

By solving the Bogoliubov–de Gennes equation, the influence of the interplay of Rashba spin–orbit coupling, induced superconducting pair potential, and external magnetic field on the spin-polarized coherent charge transport in ferromagnet/semiconductor nanowire/ferromagnet double barrier junctions is investigated based on the Blonder–Tinkham–Klapwijk theory. The coherence effect is characterized by the strong oscillations of the charge conductance as a function of the bias voltage or the thickness of the semiconductor nanowire, resulting from the quantum interference of incoming and outgoing quasiparticles in the nanowire. Such oscillations can be effectively modulated by varying the strength of the Rashba spin–orbit coupling, the thickness of the nanowire, or the strength of the external magnetic field. It is also shown that two different types of zero-bias conductance peaks may occur under some particular conditions, which have some different characteristics and may be due to different mechanisms.

We investigated the valley dependent transport properties of a zigzag graphene ribbon attached with two strained side arms. The conductance of the zigzag ribbon for each valley is increased by the strain of the side arms. On the curves of conductance versus energy, step-like structures appear in some energy intervals, and in such intervals, the conductance does not decay when increasing the length of the intersection region. By applying a strain exceeding a critical amount, the conductance of valley K ( K ′) for the negative (positive) energies can be recovered to that of a graphene ribbon without side arms attached. The critical strain is compressive and is evaluated as about − 10 %. We explained all the features by means of the energy dispersion of the injection ribbon and that of the strained region.

We investigate the influence of in-plane spin-exchange interactions on a topological insulator (TI) surface doped with nanomagnets under the second perturbation theory. We propose a novel self-filling mechanism of the surface-state band gap. It is found that when the out-of-plane exchange coupling favors an energy gap around the Dirac point, the in-plane component tends to suppress the induced gap, and even fill it completely. Our theory is based on the spin-flipping inelastic scattering, which creates a complex structure of self-energy, effectively modifying the band gap by renormalizing the magnetic moment and chemical potential. We explicitly analyze the filling effect in the electronic dispersion relation and density of states for different scenarios set by systemic parameters. This self-filling effect induced by spin-exchange coupling itself opens new perspectives for understanding of various magnetically doping phenomena on the TI materials and is expected to mediate the controversy concerning the magnetically doping induced gap.

The interaction effect between the surface states of a topological insulator (TI) and a STM-coupled Anderson impurity is studied by using equations of motion of the Green's functions. Remarkably, we show that when a coupling between the Anderson impurity and the STM tip is included, the tunneling resonance and the Kondo peak can be tuned to be exactly at the Dirac point, by adjusting the impurity level and Fermi energy, such that the local density of states at the Dirac point is significantly enhanced. This is in contrast to the case of a STM-decoupled Anderson impurity, where both resonances are always fully suppressed at the Dirac point. Our finding suggests a pathway to experimentally control the fundamental properties of the electrons on a TI surface.

We studied the electronic structure and optical absorption properties of phosphorene (a monolayer black phosphorus) under a normally applied electric field. The electric field enlarges the energy gap, weakens the effective mass anisotropy, and increases the effective mass component along the armchair direction (x-direction) for both conduction and valence bands but provides little change to the component along the zigzag direction (y-direction). The band edge optical absorption is completely polarized in the x-direction, and decreases when increasing the electric field. If the exciting frequency is beyond the energy gap, the absorption for the y-polarized light becomes nonzero, but the absorption is still highly polarized.

We have theoretically investigated the spin inelastic scattering of helical electrons off a high-spin nanomagnet absorbed on a topological surface. The nanomagnet is treated as a dynamic quantum spin and driven by the spin transfer torque effect. We proposed a mechanism to electrically manipulate the spin texture of helical Dirac fermions rather than by an external magnetic field. By tuning the bias voltage and the direction of impurity magnetization, we present rich patterns of spin texture, from which important fingerprints exclusively associated with the spin helical feature are obtained. Furthermore, it is found that the nonmagnetic potential can create the resonance state in the spin density with different physics as the previously reported resonance of charge density.

We theoretically study thermally driven transport of the Dirac fermions on the surface of a topological insulator capped with a ferromagnet strip. The generation and manipulation of anomalous Hall and Nernst effects are analyzed, in which the in-plane magnetization of the ferromagnet film is found to take a decisive role. This scenario is distinct from that modulated by Berry phase where the in-plane magnetization is independent. We further discuss the thermal spin-transfer torque as a backaction of the thermoelectric transports on the magnetization and calculate the dynamics of the anomalous Hall and Nernst effects self-consistently. It is found that the magnitude of the long-time steady Hall and Nernst conductance is determined by competition between the magnetic anisotropy and current-induced effective anisotropy. These results open up a possibility of magnetically controlling the transverse thermoelectric transports or thermally manipulating the magnet switching.

We have studied the characteristics of current-induced nonequilibrium spin polarization in semiconductor-nanowire/s-wave superconductor junctions with strong spin–orbit coupling. It was found that within some parameter regions the magnitude of the current-induced nonequilibrium spin polarization density in such structures will increase (or decrease) with the decrease (or increase) of the charge current density, in contrast to that found in normal spin–orbit coupled semiconductor structures. It was also found that the unusual characteristics of the current-induced nonequilibrium spin polarization in such structures can be well explained by the effect of the Andreev reflection.