Valley-based electronics, known as valleytronics, is one of the keys to break through to a new stage of electronics. The valley degree of freedom is ubiquitous in the honeycomb lattice system. The honeycomb lattice structure of silicon called silicene is an fascinating playground of valleytronics. We investigate topological phases of silicene by introducing different exchange fields on the $A$ and $B$ sites. There emerges a rich variety of topologically protected states each of which has a characteristic spin-valley structure. The single Dirac-cone semimetal is such a state that one gap is closed while the other three gaps are open, evading the Nielsen-Ninomiya fermion-doubling problem. We have newly discovered a hybrid topological insulator named the quantum-spin-quantum-anomalous Hall insulator, where the quantum anomalous Hall effect occurs at one valley and the quantum spin Hall effect occurs at the other valley. Along its phase boundary, single-valley semimetals emerge, where only one of the two valleys is gapless with degenerated spins. These semimetals are also topologically protected because they appear in the interface of different topological insulators. Such a spin-valley dependent physics will be observed by optical absorption or edge modes.
In the presence of extrinsic Rashba spin-orbit coupling, we find that silicene can host a new quantum anomalous Hall state with spin- and valley-polarized edge states, which can be effectively controlled by the exchange field and electric field. In this new state, the pair of nontrivial edge states reside in one specific valley and have a strong but opposite spin polarization. A distinctive feature of this new state is that both of the spin and valley index of the edge states can be switched by reversing the electric field. We also present a microscopic mechanism for the origination of the new…
We investigate the electron properties of the monolayer and bilayer silicene which is the honeycomb lattice consist of silicon atoms, including the optical conductivity and charged impurity scattering, due to the quasipatricle Dirac-like behaviors near the K-point of silicene. The spin, valley, sublattice degrees of freedom are taken into consider in the multi-band tight-binding model. In momentum space, the scattering matrix which connects the two bare (without interaction) Green's functions in the quasiparticle momentum transport process, could be momentum-independent for the single impuirit…
Semi-Dirac semimetal is a material exhibiting linear band dispersion in one direction and quadratic band dispersion in the orthogonal direction and, therefore, hosts massless and massive fermions at the same point in the momentum space. While a number of interesting physical properties have been predicted in semi-Dirac semimetals, it has been rare to realize such materials in condensed matters. Based on the fact that some honeycomb materials are easily oxidized or chemically absorb other atoms, here, we theoretically propose an approach of modifying their band structures by covalent addition o…
We investigate the anomalous effects due to the Berry correction and the considerable perturbations in the silicene-like hexagonal lattice system. The Berry curvature in periodic Bloch band system which related to the electromagnetic field is explored, the induced transverse anomalous velocity gives rise to the intrinsic Hall conductivity (without the vertex correction) expecially in the quantum anomalous Hall phase. The quantum anomalous Hall effect which related to the anomalous velocity term is detected, including the band avoided corssing effect and the generated special band gap. %{Enlarg…
Silicene and germanene are key materials for the field of valleytronics. However, interaction with the substrate, which is necessary to support the electronically active medium, becomes a major obstacle. In the present work, we propose a substrate (F-doped WS$_2$) that avoids detrimental effects and at the same time induces the required valley polarization, so that no further steps are needed for this purpose. The behavior is explained by proximity effects on silicene/germanene, as demonstrated by first-principles calculations. Broken inversion symmetry due to the presence of WS$_2$ opens a su…
We report the recent progress on the theoretical aspects of monolayer topological insulators including silicene, germanene and stanene, which are monolayer honeycomb structures of silicon, germanium and tin, respectively. They show quantum spin Hall effects in nature due to the spin orbit interaction. The band gap can be tuned by applying perpendicular electric field, which induces a topological phase transition. We also analyze the topological properties of generic honeycomb systems together with the classification of topological insulators. Phase diagram of topological insulators and superco…
We propose an experimental scheme to realize adiabatic topological spin and valley pumping by using silicene subject to an in-plane $ac$ electric field with amplitude $E_{y}$ and a vertical electric field consisting of an electrostatic component and an $ac$ component with amplitudes $E_{z}^{0}$ and $E_{z}^{1}$. By tuning $E_{z}^{0}$ and $E_{z}^{1}$, topological valley pumping or spin-valley pumping can be achieved. The noisefree valley and spin currents generated could be useful in valleytronic and spintronic applications. This work demonstrates that bulk topological spin or valley pumping is …
Silicene and related buckled materials are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit coupling and the buckled structure. These materials have potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit coupling. We present a theoretical realization of quantum capacitance which has advantages over the scattering problems of traditional transport measurements. We derive and discuss quantum capacitance as a function of the Fermi energy and temperature taking into account ele…
Bilayer silicene has richer physical properties than bilayer graphene due to its buckled structure together with its trigonal symmetric structure. The buckled structure arises from a large ionic radius of silicon, and the trigonal symmetry from a particular way of hopping between two silicenes. It is a topologically trivial insulator since it carries a trivial $\mathbb{Z}_{2}$ topological charge. Nevertheless, its physical properties are more akin to those of a topological insulator than those of a band insulator. Indeed, a bilayer silicene nanoribbon has edge modes which are almost gapless an…
We adopt the tight-binding mode-matching method to study the strain effect on silicene heterojunctions. It is found that valley- and spin-dependent separation of electrons cannot be achieved by the electric field only. When a strain and an electric field are simultaneously applied to the central scattering region, not only are the electrons of valleys K and K' separated into two distinct transmission lobes in opposite transverse directions, but the up-spin and down-spin electrons will also move in the two opposite transverse directions. Therefore, one can realize an effective modulation of val…
We study spin-valley and lattice-pseudo spin currents in a dual ferromagnetic-gated silicene-based junction. Silicene has buckled atomic structure which allows us to take sublattice-dependent ferromagnetism into account in the investigation. One of the study results show that transmission at the junctions exhibits anisotropic property only in anti-parallel cases. Interestingly, the studied junctions can be switched from a pure spin-polarizer to a pure valley-polarizer by reversing directions of exchange fields in the parallel junctions. The perfect control of spin-valley currents can be done o…
We calculate the magneto-optical conductivity and electronic density of states for silicene, the silicon equivalent of graphene, and similar crystals such as germanene. In the presence of a perpendicular magnetic field and electric field gating, we note that four spin- and valley-polarized levels can be seen in the density of states and transitions between these levels lead to similarly polarized absorption lines in the longitudinal, transverse Hall, and circularly polarized dynamic conductivity. While previous spin and valley-polarization predicted for the conductivity is only present in the …
We study massive Dirac fermion tunneling through time periodic potential in a silicene-based N-TP-N junction, where Ns are normal silicene regions and TP is the time periodic potential barrier. The fermions would absorb or emit photons due to the presence of the Floquet sidebands created in the TP. The nearly perfect spin-valley-sideband filtering is predicted. Applying only the exchange field leads to just only the electron absorbing a single photon almost purely allowed to tunnel through the junction for the large electric field. Reversing direction of electric field can select spin of the a…
In Weyl semimetals the location of linear band crossings, the Weyl cones, is not bound to any high symmetry point of the Brillouin zone, unlike the Dirac nodes in graphene. This flexibility is advantageous for valleytronics, where information is encoded in the valleys of the band structure when intervalley scattering is weak. However, if numerous Weyl cones coexist the encoded information can decohere rapidly because of band mixing. Here, we investigate how the helical iso-spin texture of Weyl cones affects valleytronics in heterojunctions of Weyl materials, and show how the chirality of this …
We carry out both the tight-binding model and the $ab\ initio$ to study the layered silicene, the spin, valley, sublattice degrees of freedom are taken into consider and the effects of electric field, magnetic field, and even the light in finite frequency together with its interesting optical propertice, which are all closely related to the spin-orbit coupling and Rashba coupling and lead to the tunable phase transitions (between the nontrivial topological phase which has nonzero Chern number or nonzero spin Chern number and the trivial phase). An exotic quantum anomalous Hall insulator phase …
Silicene is a competitive and promising 2D material, possessing interesting topological, electronic and optical properties. The presence of strong spin orbit interaction in silicene and its analogues, germanene and tinene, leads to the opening of a gap in the energy spectrum and spin-splitting of the bands in each valley. We develop a general method to determine the magneto-optic response of silicene, when a Gaussian beam is incident on silicene grown on a dielectric substrate in the presence of a static magnetic field. We use a semiclassical treatment of silicene monolayer to describe the Far…
We investigate real- and lattice-spin currents controlled by strain in a silicene-based junction, where chemical potential, perpendicular electric field and circularly polarized light are applied into the strained barrier. We find that the junction yields strain filtering effect with perfect strain control of real- (or lattice-) spin currents. (i) By applying electric field without circularly polarized light we show that total current is carried by pure lattice-spin up (or down) electrons tunable by strain. (ii) When circularly polarized light is irradiated onto silicene sheet without applying…
The Goos-Hänchen (GH) shift and the Imbert-Fedorov (IF) shift are optical phenomena which describe the longitudinal and transverse lateral shifts at the reflection interface, respectively. Here, we report the GH and IF shifts in Weyl semimetals (WSMs) - a promising material harboring low energy Weyl fermions, a massless fermionic cousin of photons. Our results show that GH shift in WSMs is valley-independent which is analogous to that discovered in a 2D relativistic material - graphene. However, the IF shift has never been explored in non-optical systems, and here we show that it is valley-dep…
We study the hybrid excitations due to the coupling between surface optical phonons of a polar insulator substrate and plasmons in the valley-spin-polarized metal phase of silicene under an exchange field. We perform the calculations within the generalized random-phase approximation where the plasmon-phonon coupling is taken into account by the long-range Fr$\ddot{\mathrm{o}}$hlich interaction. Our investigation on two hybridized plasmon branches in different spin and valley subbands shows distinct behavior compared to the uncoupled case. Interestingly, in one valley, it is found that while th…
We study the band structure and transport properties of ferromagnetic tetragonal silicene nanoribbons by using the non-equilibrium Green's function method. The band structure and spin-dependent conductance are discussed under the combined effect of the external electric field, potential energy, exchange field and the spin-orbit coupling. One can easily realize a phase transition from a semimetallic to a semiconducting state by changing the transverse width of the nanoribbon. Separation of spin-dependent conductances arises from the effect of exchange field and the spin-orbit coupling, while ze…
Silicene consists of a monolayer of silicon atoms in a buckled honeycomb structure. It was recently discovered that the symmetry of such a system allows for interesting Rashba spin-orbit effects. A perpendicular electric field is able to couple to the sublattice pseudospin, making it possible to electrically tune and close the band gap. Therefore, external electric fields may generate a topological phase transition from a topological insulator to a normal insulator (or semimetal) and vice versa. The contribution of the present article to the study of silicene is twofold: First, we perform a gr…
Multi-Weyl semimetals are a kind of topological phase of matter with discrete Weyl nodes characterized by multiple monopole charges, in which the chiral anomaly, the anomalous nonconservation of an axial current, occurs in the presence of electric and magnetic fields. Electronic transport properties related to the chiral anomaly in the presence of both electromagnetic fields and axial electromagnetic fields in multi-Weyl semimetals are systematically studied. It has been found that the anomalous Hall conductivity has a modification linear in the axial vector potential from inhomogeneous strain…
Spin-valley locking in the band structure of monolayers of MoS$_2$ and other group-VI dichalcogenides has attracted enormous interest, since it offers potential for valleytronic and optoelectronic applications. Such an exotic electronic state has sparsely been seen in bulk materials. Here, we report spin-valley locking in a bulk Dirac semimetal BaMnSb$_2$. We find valley and spin are inherently coupled for both valence and conduction bands in this material. This is revealed by comprehensive studies using first principle calculations, tight-binding and effective model analyses, angle-resolved p…
Alloyed transition metal dichalcogenides provide an opportunity for coupling band engineering with valleytronic phenomena in an atomically-thin platform. However, valley properties in alloys remain largely unexplored. We investigate the valley degree of freedom in monolayer alloys of the phase change candidate material WSe$_{2(1-x)}$Te$_{2x}$. Low temperature Raman measurements track the alloy-induced transition from the semiconducting 1H phase of WSe$_2$ to the semimetallic 1T$_d$ phase of WTe$_2$. We correlate these observations with density functional theory calculations and identify new Ra…
In the presence of spin-orbit coupling (SOC), achieving both spin and valley polarized Dirac state is significant to promote the fantastic integration of Dirac physics, spintronics and valleytronics. Based on ab initio calculations, here we demonstrate that a class of spin-valley-coupled Dirac semimetals (svc-DSMs) in the functionalized SbAs monolayers (MLs) can host such desired state. Distinguished from the graphene-like 2D Dirac materials, the Dirac cones in svc-DSMs hold giant spin-splitting induced by strong SOC under inversion symmetry breaking. In the 2.3% strained SbAsH2 ML, the Dirac …
We study a Josephson junction involving an inversion-asymmetric Weyl semimetal in presence of time-reversal symmetric (TRS) or time-reversal symmetry broken tilt in the Weyl spectra. We reveal that both types of tilts in the Weyl nodes lead to a Josephson $0$-$π$ transition and a zero bias valley/chiral supercurrent. Strikingly, the TRS tilt gives rise to a pure valley Josephson current (VJC) and TRS broken tilt induces a pure chirality Josephson current (CJC) in this system. The VJC and CJC are the manifestation of valley symmetry broken and $\mathbb{Z}_2$ symmetry broken by the respective ti…
Weyl semimetals are three-dimensional crystalline systems where pairs of bands touch at points in momentum space, termed Weyl nodes, that are characterized by a definite topological charge: the chirality. Consequently, they exhibit the Adler-Bell-Jackiw anomaly, which in this condensed matter realization implies that application of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields pumps electrons between nodes of opposite chirality at a rate proportional to $\mathbf{E}\cdot\mathbf{B}$. We argue that this pumping is measurable via nonlocal transport experiments, in the limit o…
Topological magnetotransport in modified-Haldane systems
National Centre for physics（国家物理中心）；Department of Physics, Quaid-I-Azam University（真纳大学物理系）；Department of Physics, Zhejiang Normal University（浙江师范大学物理系）；Zhejiang Institute of Photoelectronics（浙江光电子研究所）
Quantum anomalous Hall conductivity in altermagnets under applied magnetic field
International Research Centre Magtop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Department of Physics, University of Guilan（吉尔兰大学物理系）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）
We investigate the photoinduced effect to the silicene, which is a topological insulator, by the circularly polarized light in off-resonance regime with a frequency much larger than the critical value (also much larger than the frequency about the particle-hole pair creation), and with a perpendicular electric field. The anomalous Rabi frequency which is a non-linear optical, arised by the off-resonance circularly polarized light. The temporal behavior of the pseudospin, valley, and spin degrees of freedom, which are momentum- and quasienergy-dependent, are explored. The anomalous Rabi oscilla…
We investigate topological phases of monolayer jacutingaite (Pt$_2$HgSe$_3$) that arise when considering the competing effects of spin-orbit coupling (SOC), magnetic exchange interactions, and staggered sublattice potential V. The interplay between the staggered potential and exchange field offers the possibility of attaining different topological phases. By analyzing the Berry curvatures and computing the Chern numbers and Hall conductivities, we demonstrate that the system is time-reversal-symmetry-broken quantum spin Hall insulator when $m_b<λ_{so}$, where $m_b$ is the exchange field operat…
