Using first-principles Density Functional Theory calculations, we showed that electronic and magnetic properties of bare and Ti adatom adsorbed single-layer silicene and germanene, which are charged or exerted by a perpendicular electric field are modified to attain new functionalities. In particular, when exerted by a perpendicular electric field, the symmetry between the planes of buckled atoms is broken to open a gap at the Dirac points. The occupation of 3d-orbitals of adsorbed Ti atom changes with charging or applied electric field to induce significant changes of magnetic moment. We predict that neutral silicene uniformly covered by Ti atoms becomes a half-metal at a specific value of coverage and hence allows the transport of electrons in one spin direction, but blocks the opposite direction. These calculated properties, however exhibit a dependence on the size of the vacuum spacing between periodically repeating silicene and germanene layers, if they are treated using plane wave basis set within periodic boundary condition. We clarified the cause of this spurious dependence and show that it can be eliminated by the use of local orbital basis set.
We study the lattice thermal conductivity of two-dimensional (2D) pentagonal systems, such as penta-silicene and penta-germanene. Penta-silicene has been recently reported, while the stable penta-germanene, belonging to the same group IV element, is revealed firstly by our ab initio calculations. We find that both penta-silicene and penta-germanene at room temperature have ultralow lattice thermal conductivities $κ$ of 1.29 W/mK and 0.30 W/mK respectively. To the best of our knowledge, penta-germanene may have the lowest $κ$ in 2D crystal materials. We attribute ultralow $κ$ to the weak phonon…
By using first-principles calculations, we predict that an in-plane homogenous electrical field can induce half-metallicity in hydrogen-terminated zigzag silicene and germanene nanoribbons (ZSiNRs and ZGeNRs). A dual-gated finite ZSiNR device reveals a nearly perfect spin-filter efficiency of up to 99% while a quadruple-gated finite ZSiNR device serves as an effective spin field effect transistor (FET) with an on/off current ratio of over 100 from ab initio quantum transport simulation. This discovery opens up novel prospect of silicene and germanene in spintronics.
We present first-principles calculations of silicene/graphene and germanene/graphene bilayers. Various supercell models are constructed in the calculations in order to reduce the strain of the lattice-mismatched bilayer systems. Our energetics analysis and electronic structure results suggest that graphene can be used as a substrate to synthesize monolayer silicene and germanene. Multiple phases of single crystalline silicene and germanene with different orientations relative to the substrate could coexist at room temperature. The weak interaction between the overlayer and the substrate preser…
The O2 dissociation and O atoms adsorption on free-standing germanene are studied by using first-principles calculations in this letter. Compared with the spontaneous dissociation of oxygen molecule on free-standing silicene in air, germanene is more stable than silicene from kinetic point of view, with overcoming energy barrier of about 0.55 eV. Especially, in contrast with the unique chemical adsorption of O2-dissociation-induced O atoms on silicene, oxygen molecule can behave a correspondingly stable adsorption on germanene surface. Moreover, single O atom adsorption on germanene is also di…
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…
Silicene and germanene derivatives constructed from periodic dumbbell units play a crucial role in multilayers of these honeycomb structures. Using first-principles calculations based on density functional theory, here we investigate the dumbbell formation mechanisms and energetics of Group IV atoms adsorbed on graphene, silicene, germanene and stanene monolayer honeycomb structures. The stabilities of the binding structures are further confirmed by performing ab-initio molecular dynamics calculations at elevated temperatures, except for stanene which is subject to structural instability upon …
Due to nonzero intrinsic spin-orbit interaction in buckled honeycomb crystal structures, silicene and germanene exhibit interesting topological properties, and are therefore candidates for the realization of the quantum spin Hall effect. We employ the Kane-Mele model to investigate the electron states in hexagonal silicene and germanene nanorings having either zigzag or armchair edges in the presence of a perpendicular magnetic field. We present results for the energy spectra as function of magnetic field, the electron density of the spin-up and spin-down states in the ring plane, and the calc…
Following the work in graphene, we report a first-principles study of electron-phonon coupling (EPC) in low-buckled (LB) monolayer silicene and germanene. Despite of the similar honeycomb atomic arrangement and linear band dispersion, the EPC matrix-element squares of the $Γ$-$E_g$ and K-$A_1$ modes in silicene are only about 50% of those in graphene. However, the smaller Fermi velocity in silicene compensates this reduction by providing a larger joint electronic density of states near the Dirac point. We predict that Kohn anomalies associated with these two optical modes are significant in si…
We theoretically investigated two kinds of density oscillations: the Friedel oscillation and collective excitation in the silicene and germanene within random phase approximation, and found that the tunable spin-valley coupled band structure could lead to some exotic properties in such two phenomena. Based on the exact analytical and numerical analysis, we demonstrated that the beating of screened potential as well as the undamped plasmon mode can be taken as fingerprints of topological phase transition in doped silicene and doped germanene. Thus our proposal here establishes the connection be…
The thermoelectric properties in one- and two-dimensional silicon and germanium structures have been investigated using first-principle density functional techniques and linear response for the thermal and electrical transport. We have considered here the two-dimensional silicene and germanene, together with nano-ribbons of different widths. For the nano-ribbons, we have also investigated the possibility of nano-structuring these systems by mixing silicon and germanium. We found that the figure of merit at room temperature of these systems is remarkably high, up to 2.5.
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 theoretically study electrically tunable magnetoplasmons in a monolayer of silicene or germanene. We derive the dynamical response function and take into account the effects of strong spin-orbit coupling (SOC) and of an external electric filed $E_z$ perpendicular to the plane of the buckled silicene/germanene. Employing the random-phase approximation we analyze the magnetoplasmon spectrum. The dispersion relation has the same form as in a two-dimensional electron gas with the cyclotron and plasma frequencies modified due to the SOC and the field $E_z$. In the absence of SOC and $E_z$, our r…
Based on first principles calculations and self-consistent solution of linearized Boltzmann-Peierls equation for phonon transport approach within a three-phonon scattering framework, we characterize lattice thermal conductivities k of freestanding silicene, germanene and stanene under different isotropic tensile strains and temperatures. We find a strong size dependence of k for silicene with tensile strain, i.e., divergent k with increasing system size, in contrast, the intrinsic room temperature k for unstrained silicene converges with system size to 19.34 W/m-K by 178 nm. The room temperatu…
Silicene, germanene and stanene are two-dimensional topological insulators exhibiting helical edge states. We investigate global and local manipulations at the edges by exposing them to (i) a charge-density-wave order, (ii) a superconductor, (iii) an out-of-plane antiferromagnetic, and (iv) an in-plane antiferromagnetic field. We show that these perturbations affect the helical edge states in a different fashion. As a consequence one can realize quantum spin-Hall effect without edge states. In addition, these edge manipulations lead to very promising applications: a giant magnetoresistance and…
We investigate van der Waals (vdW) heterostructures made of germanene, stanene or silicene with hexagonal Boron Nitride (h-BN). The intriguing topological properties of these buckled honeycomb materials can be maintained and further engineered in the heterostructures, where the competition between the substrate effect and external electric fields can be used to control the tunable topological phase transitions. Using such heterostructures as building blocks, various vdW topological domain walls (DW) are designed, along which there exist valley polarized quantum spin Hall edge states or valley-…
Using a multi-orbital tight-binding model, we have studied the edge states of zigzag silicene, germanene, and stanene nanoribbons (ZSiNRs, ZGeNRs and ZSnNRs, respectively) in the presence of the Coulomb interaction and a vertical electric field. The resulting edge states have non-linear energy dispersions due to multi-orbital effects, and the nanoribbons show induced magnetization at the edges. Owing to this non-linear dispersion, ZSiNRs, ZGeNRs and ZSnNRs may not provide superior performance in field effect transistors, as has been proposed from single-orbital tight-binding model calculations…
The intrinsic spin and valley Hall conductivities of silicene, germanene and other similar two dimensional crystals are explored theoretically. Particular attention is given to the effects of the intrinsic spin-orbit coupling, electron doping and the type of insulating phase of the system (i.e., a topological insulator or a band insulator) which can be tuned by a perpendicular electric field. At finite frequency, the transverse edge to which carriers of particular spin and valley label flow can be controlled such that an accumulation of a particular combination of spin and valley index can be …
We have calculated numerically electron exchange, correlation energies and dynamical polarization function for newly discovered silicene, germanene and black phosphorus (BP), consisting of puckered layers of elemental phosphorus atoms, broadening the range of two-dimensional (2D) materials at various temperatures. As a matter of fact, monolayer BP, produced by mechanical and liquid exfoliation techniques, has been predicted to be an insulator with a large energy splitting 1.6 eV for the quasiparticle band structure. We compare the dependence of these energies on the chemical potential, field-i…
We investigate the energy dispersion of the edge states in zigzag silicene, germanene and stanene nanoribbons with and without hydrogen termination based on a multi-orbital tight-binding model. Since the low buckled structures are crucial for these materials, both the $π$ and $σ$ orbitals have a strong influence on the edge states, different from the case for graphene nanoribbons. The obtained dispersion of helical edge states is nonlinear, similar to that obtained by first-principles calculations. On the other hand, the dispersion derived from the single-orbital tight-binding model is always …
We start with the silicene or germanene single-particle Hamiltonian in buckled 2D hexagonal lattices expressed in terms of Dirac matrices in the Weyl basis. The Hamiltonian of these systems comprises of the Dirac kinetic energy, a mass gap term, and the spin-orbit coupling. The second term breaks the sub-lattice symmetry of the honey-comb lattice structure and generates a gap. The buckled structure generates a staggered sub-lattice potential between silicon atoms at A sites and B sites for an applied electric field perpendicular to its plane. Tuning of the electric field, allows for rich behav…
The discovery of intriguing properties related to the Dirac states in graphene has spurred huge interest in exploring its two-dimensional group-IV counterparts, such as silicene, germanene, and stanene. However, these materials have to be obtained via synthesizing on substrates with strong interfacial interactions, which usually destroy their intrinsic $π$($p_z$)-orbital Dirac states. Here we report a theoretical study on the existence of Dirac states arising from the $p_{x,y}$ orbitals instead of $p_z$ orbitals in silicene on 4H-SiC(0001), which survive in spite of the strong interfacial inte…
Unlike silicene, for which the demonstration of its existence has been done through numerous independent studies, the possibility of growing epitaxial germanene remains highly controversial. It has been recently shown by scanning tunneling microscopy that the (3 x 3) surface reconstruction formed upon Ge deposition on Al(111) presents a honeycomb structure, and it was assigned to a pure germanene monolayer. Using quantitative measurements by surface X-ray diffraction compared to density functional theory calculations, we demonstrate that this Ge/Al(111) (3 x 3) reconstruction corresponds, in f…
It has been argued that stanene has lowest lattice thermal conductivity among 2D group-IV materials because of largest atomic mass, weakest interatomic bonding, and enhanced ZA phonon scattering due to the breaking of an out-of-plane symmetry selection rule. However, we show that although the lattice thermal conductivity $κ$ for graphene, silicene and germanene decreases monotonically with decreasing Debye temperature, unexpected higher $κ$ is observed in stanene. By enforcing all the invariance conditions in 2D materials and including Ge $3d$ and Sn $4d$ electrons as valence electrons for ger…
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying the electric field to a silicene sheet. In particular, the gap closes at a certain critical electric field. Examining the band structure of a silicene nanoribbon, we demonstrate that a topological phase transition occurs from a topol…
Electronic Coulomb excitations in monolayer silicene are investigated by using the Lindhard dielectric function and a newly developed generalized tight-binding model (G-TBM). G-TBM simultaneously contains the atomic interactions, the spin-orbit coupling, the Coulomb interactions, and the various external fields at an arbitrary chemical potential. We exhibit the calculation results of the electrically tunable magnetoplasmons and the strong magnetic field modulation of plasmon behaviors. The two intriguing phenomena are well explained by determining the dominant transition channels in the dielec…
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 investigate the optical response of the silicene and similar materials, such as germanene, in the presence of an electrically tunable band gap for variable doping. The interplay of spin orbit coupling, due to the buckled structure of these materials, and a perpendicular electric field gives rise to a rich variety of phases: a topological or quantum spin Hall insulator, a valley-spin-polarized metal and a band insulator. We show that the dynamical conductivity should reveal signatures of these different phases which would allow for their identification along with the determination of paramet…
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…
The recently synthesized silicene as well as theoretically discussed germanene are examples of buckled honeycomb structures. The buckled structures allow one to manipulate asymmetry between two underlying sublattices of honeycomb structures. Here by taking germanene as a prototype of buckled honeycomb lattices, we explore magnetism induced by breaking sublattice symmetry through saturating chemical bonds on one-side of the buckled honeycomb lattice. It is shown that when fractions of chemical bonds on one-side are saturated, two narrow bands always exist at half filling. Furthermore, the narro…
Intervalley Magnetotrions Tunable by Electric and Magnetic Fields in Buckled Two-Dimensional Materials
New York City College of Technology, The City University of New York（纽约市立学院，纽约市立大学）；The Graduate School and University Center, The City University of New York（研究生院与大学中心，纽约市立大学）；Borough of Manhattan Community College, The City University of New York（曼哈顿社区学院，纽约市立大学）
The independent predictions of edge ferromagnetism and the Quantum Spin Hall phase in graphene have inspired the quest of other two dimensional honeycomb systems, such as silicene, germanene, stanene, iridiates, and organometallic lattices, as well as artificial superlattices, all of them with electronic properties analogous to those of graphene, but much larger spin orbit coupling. Here we study the interplay of ferromagnetic order and spin orbit interactions at the zigzag edges of these graphene-like systems. We find an in-plane magnetic anisotropy that opens a gap in the otherwise conductin…
Edge states in narrow quasi two-dimensional nanostructures determine, to a large extent, their electric, thermoelectric and magnetic properties. Non-magnetic edge states may quite often lead to topological insulator type behavior. However another scenario develops when the zigzag edges are magnetic and the time reversal symmetry is broken. In this work we report on the electronic band structure modifications, electrical conductance and thermoelectric properties of narrow zigzag nanoribbons with spontaneously magnetized edges. Theoretical studies based on the Kane-Mele- Hubbard tight-binding mo…
A generalized tight-binding model, which is based on the subenvelope functions of the different sublattices, is developed to explore the novel magnetic quantization in monolayer gray tin. The effects due to the $sp^{3}$ bonding, the spin-orbital coupling, the magnetic field and the electric field are simultaneously taken into consideration. The unique magneto-electronic properties lie in two groups of low-lying Landau levels, with different orbital components, localization centers, state degeneracy, spin configurations, and magnetic- and electric-field dependences. The first and second groups …
We study the binding energies and optical properties of direct and indirect excitons in monolayers and double layer heterostructures of Xenes: silicene, germanene, and stanene. It is demonstrated that an external electric field can be used to tune the eigenenergies and optical properties of excitons by changing the effective mass of charge carriers. The Schrödinger equation with field-dependent exciton reduced mass is solved by using the Rytova-Keldysh (RK) potential for direct excitons, while both the RK and Coulomb potentials are used for indirect excitons. It is shown that for indirect exci…
We report on the fractional quantum Hall states of germanene and silicene where one expects a strong spin-orbit interaction. This interaction causes an enhancement of the electron-electron interaction strength in one of the Landau levels corresponding to the valence band of the system. This enhancement manifests itself as an increase of the fractional quantum Hall effect gaps compared to that in graphene and is due to the spin-orbit induced coupling of the Landau levels of the conduction and valence bands, which modifies the corresponding wave functions and the interaction within a single leve…
A new family of the low-buckled Dirac materials which includes silicene, germanene, etc. is expected to possess a more complicated sequence of Landau levels than in pristine graphene. Their energies depend, among other factors, on the strength of the intrinsic spin-orbit (SO) and Rashba SO couplings and can be tuned by an applied electric field $E_z$. We studied the influence of the intrinsic Rashba SO term on the energies of Landau levels using both analytical and numerical methods. The quantum magnetic oscillations of the density of states are also investigated. A specific feature of the osc…
The layered graphene systems exhibit the rich and unique excitation spectra arising from the electron-electron Coulomb interactions. The generalized tight-binding model is developed to cover the planar/buckled/cylindrical structures, specific lattice symmetries, different layer numbers, distinct configurations, one-three dimensions, complicated intralayer and interlayer hopping integrals, electric field, magnetic quantization; any temperatures and dopings simultaneously. Furthermore, we modify the random-phase approximation to agree with the layer-dependent Coulomb potentials with the Dyson eq…
We study theoretically the properties of buckled graphene-like materials, such as silicene and germanene, in a strong perpendicular magnetic field and a periodic potential. We analyze how the spin-orbit interaction and the perpendicular electric field influences the energy spectra of these systems. When the magnetic flux through a unit cell of the periodic potential measured in magnetic flux quantum is a rational number, ? = p/q, then in each Landau level the energy spectra have a band structure, which is characterized by the corresponding gaps. We study the dependence of those gaps on the par…
Monolayer tinene presents rich absorption spectra in electric fields. There are three kinds of special structures, namely shoulders, logarithmically symmetric peaks and asymmetric peaks in the square-root form, corresponding to the optical excitations of the extreme points, saddle points and constant-energy loops. With the increasing field strength, two splitting shoulder structures, which are dominated by the parabolic bands of ${5p_z}$ orbitals, come to exist because of the spin-split energy bands. The frequency of threshold shoulder declines to zero and then linearly grows. The third should…
We study tunable polaritons in monolayers of silicene, germanene, and stanene (Xenes) via an external electric field in an open optical microcavity whose length can be adjusted. An external electric field applied perpendicular to the plane of the Xene monolayer simultaneously changes the band gap and the exciton binding energy, while the variable length of the open microcavity allows one to keep the exciton and cavity photon modes in resonance. First, the Schrödinger equation for an electron and hole in an Xene monolayer is solved, yielding the eigenergies and eigenfunctions of the exciton as …
Induced polarization by Dirac electrons in double-layer graphene can affect hybridization of radiative and evanescent fields. Electron back action appears as a localized optical field to modify an incident surface-plasmon-polariton (SPP) evanescent field. This leads to high sensitivity (beyond the diffraction limit) to local environments and provides a scrutiny tool for molecules or protein selectively bounded with carbon. A scattering matrix with frequencies around the surface-plasmon (SP) resonance supports this scrutiny tool and exhibits sensibly the increase, decrease and even a full suppr…
We study direct and indirect magnetoexcitons in Rydberg states in monolayers and double-layer heterostructures of Xenes (silicene, germanene, and stanene) in external parallel electric and magnetic fields, applied perpendicular to the monolayer and heterostructure. We calculate binding energies of magnetoexcitons for the Rydberg states 1$s$, 2$s$, 3$s$, and 4$s$, by numerical integration of the Schrödinger equation using the Rytova-Keldysh potential for direct magnetoexciton and both the Rytova-Keldysh and Coulomb potentials for indirect excitons. Latter allows understanding a role of screenin…
