We propose a new concept of two-dimensional (2D) Dirac semiconductor which is characterized by the emergence of fourfold degenerate band crossings near the band edge and provide a generic approach to realize this novel semiconductor in the community of material science. Based on the first-principle calculations and symmetry analysis, we discover recently synthesised triple-layer (TL)-BiOS2 is such Dirac semiconductor that features Dirac cone at X/Y point, protected by nonsymmorphic symmetry. Due to sandwich-like structure, each Dirac fermion in TL-BiOS2 can be regarded as a combination of two Weyl fermions with opposite chiralities, degenerate in momentum-energy space but separated in real space. Such Dirac semiconductor carries layer-dependent helical spin textures that never been reported before. Moreover, novel topological phase transitions are flexibly achieved in TL-BiOS2: (i) an vertical electric field can drive it into Weyl semiconductor with switchable spin polarization direction, (ii) an extensive strain is able to generate ferroelectric polarization and actuate it into Weyl nodal ring around X point and into another type of four-fold degenerate point at Y point. Our work extends the Dirac fermion into semiconductor systems and provides a promising avenue to integrate spintronics and optoelectronics in topological materials.
By means of the first-principles calculations combined with the tight-binding approximation, the strain-induced semiconductor-semimetal transition in graphdiyne is discovered. It is shown that the band gap of graphdiyne increases from 0.47 eV to 1.39 eV with increasing the biaxial tensile strain, while the band gap decreases from 0.47 eV to nearly zero with increasing the uniaxial tensile strain, and Dirac cone-like electronic structures are observed. The uniaxial strain-induced changes of the electronic structures of graphdiyne come from the breaking of geometrical symmetry that lifts the deg…
Three-dimensional (3D) Dirac semimetals are new quantum materials and can be viewed as 3D analogues of graphene. Many fascinating electronic properties have been proposed and realized in 3D Dirac semimetals, which demonstrates their potential applications in next generation quantum devices. Bismuth-antimony Bi1-xSbx can be tuned from a topological insulator to a band insulator through a quantum critical point at x ~ 4%, where 3D Dirac fermions appear. Here, we report on a magnetotransport study of Bi1-xSbx at such a quantum critical point. An unusual magnetic-field induced semimetal-semiconduc…
Recent studies have reported an interesting class of semiconductor materials that bridge the gap between semiconductors and halfmetallic ferromagnets. These materials, called spin gapless semiconductors, exhibit a bandgap in one of the spin channels and a zero bandgap in the other and thus allow for tunable spin transport. Here, a theoretical and experimental study of the spin gapless Heusler compound Mn2CoAl is presented. It turns out that Mn2CoAl is a very peculiar ferrimagnetic semiconductor with a magnetic moment of 2 μB and a high Curie temperature of 720 K. Below 300 K, the compound exhi…
A Dirac fermion in a topological Dirac semimetal is a quadruple-degenerate quasi-particle state with a relativistic linear dispersion. Breaking either time-reversal or inversion symmetry turns this system into a Weyl semimetal that hosts double-degenerate Weyl fermion states with opposite chiralities. These two kinds of quasi-particles, although described by a relativistic Dirac equation, do not necessarily obey Lorentz invariance, allowing the existence of so-called type-II fermions. Recent theoretical discovery of type-II Weyl fermions evokes the prediction of type-II Dirac fermions in PtSe$…
We report measurements of Shubnikov-de Haas oscillations in the giant Rashba semiconductor BiTeI under applied pressures up to $\sim 2\,\mathrm{GPa}$. We observe one high frequency oscillation at all pressures and one low frequency oscillation that emerges between $\sim 0.3-0.7\,\mathrm{GPa}$ indicating the appearance of a second small Fermi surface. BiTeI has a conduction band bottom that is split into two sub-bands due to the strong Rashba coupling, resulting in a `Dirac point'. Our results suggest that the chemical potential starts below the Dirac point in the conduction band at ambient pre…
Despite the growing interest in topological materials, the difficulty of experimentally synthesizing and integrating them with other materials has been one of the main barriers restricting access to their unique properties. Recent advances in synthesizing metastable phases of crystalline materials can help to overcome this barrier and offer new platforms to experimentally study and manipulate band topology. Because III-V semiconductors have a wide range of functional material applications (including optoelectronic devices, light-emitting diodes, and highly efficient solar cells), and because B…
Spin-1 condensed matter systems characterized by the combination of a Dirac-like dispersion and flat bands are ideal for realizing high-temperature electronics and spintronic technologies in the absence of external magnetic field. In this study, we propose a three-band tight binding model, with spin-polarized Haldane-like next-nearest-neighbour tunnelling, on dice lattice and show that spin-1 Dirac half-metal, spin-1 Dirac spin-gapless semiconductor, and spin-polarized spin-1 massive Dirac dispersion with nontrivial topology can exist in two-dimensional ferromagnetic condensed matter systems w…
The great obstacle for practical applications of the quantum anomalous Hall (QAH) effect is the lack of suitable QAH materials (Chern insulators) with large non-trivial band gap, room-temperature magnetic order and high carrier mobility. The Nickle chloride (NiCl3) monolayer characteristics are investigated herein using first-principles calculations. It is reported that NiCl3 monolayers constitute a new class of Dirac materials with Dirac spin-gapless semiconducting and high-temperature ferromagnetism (~400K). Taking into account the spin-orbit coupling, the NiCl3 monolayer becomes an intrinsi…
Spin gapless semiconductors (SGSs) are a new class of zero gap materials which have a fully spin polarised electrons and holes. They bridge zero gap materials and half-metals. The band structures of the SGSs can have two types of energy dispersions: Dirac linear dispersion and parabolic dispersion. The Dirac type SGSs exhibit fully spin polarized Dirac cones, and offer a platform for massless and fully spin polarized spintronics as well as dissipationless edge state via quantum anomalous Hall effect. Due to its fascinating spin and charge states, they hold great potential application in spintr…
We demonstrate theoretically the coexistence of Dirac semimetal and topological insulator phases in InSb/$α$-Sn conventional semiconductor superlattices, based on advanced first-principles calculations combined with low-energy $k\cdot p$ theory. By proper interfaces designing, a large interface polarization emerges when the growth direction is chosen along {[}111{]}. Such an intrinsic polarized electrostatic field reduces band gap largely and invert the band structure finally, leading to emerge of the topological Dirac semimetal phase with a pair of Dirac nodes appearing along the (111) crysta…
Optical excitations of BiTeI with large Rashba spin splitting have been studied in an external magnetic field ($B$) applied parallel to the polar axis. A sequence of transitions between the Landau levels (LLs), whose energies are in proportion to $\sqrt{B}$ were observed, being characteristic of massless Dirac electrons. The large separation energy between the LLs makes it possible to detect the strongest cyclotron resonance even at room temperature in moderate fields. Unlike in 2D Dirac systems, the magnetic field induced rearrangement of the conductivity spectrum is directly observed.
We report on the clear evidence of massless Dirac fermions in two-dimensional system based on III-V semiconductors. Using a gated Hall bar made on a three-layer InAs/GaSb/InAs quantum well, we restore the Landau levels fan chart by magnetotransport and unequivocally demonstrate a gapless state in our sample. Measurements of cyclotron resonance at different electron concentrations directly indicate a linear band crossing at the $Γ$ point of Brillouin zone. Analysis of experimental data within analytical Dirac-like Hamiltonian allows us not only determing velocity $v_F=1.8\cdot10^5$ m/s of massl…
Electronic structures of Ge$_{1-x}$Sn$_{x}$ alloys (0 $\leq$ $x$ $\leq$ 1) are theoretically studied by nonlocal empirical pseudopotential method. For relaxed Ge$_{1-x}$Sn$_{x}$, a topological semimetal is found for $\textit x$ $>$ 41$\%$ with gapless and band inversion at $Γ$ point, while there is an indirect-direct bandgap transition at $x$ = 8.5$\%$. For strained Ge$_{1-x}$Sn$_{x}$ on a Ge substrate, semimetals with a negative indirect bandgap appear for $x$ $>$ 43$\%$, and the strained Ge$_{1-x}$Sn$_{x}$ on Ge is always an indirect bandgap semiconductor for $x$ $<$ 43$\%$. With appropriate…
Quantum geometry in low-energy linear and nonlinear optical responses of magnetic Rashba semiconductor (Ge,Mn)Te
University of Tokyo（东京大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 涌现物质科学中心）；Department of Advanced Materials Science, University of Tokyo（东京大学 先进材料科学系）；Institute for Materials Research, Tohoku University（东北大学 材料科学研究所）；Tokyo College, University of Tokyo（东京大学 东京学院）；RIKEN Baton Zone Program (BZP)（理化学研究所 Baton Zone 项目）
It is proposed that the new generation of spintronics should be ideally massless and dissipationless for the realization of ultra-fast and ultra-low-power spintronic devices. We demonstrate that the spin-gapless materials with linear energy dispersion are unique materials that can realize these massless and dissipationless states. Furthermore, we propose four new types of spin Hall effects which consist of spin accumulation of equal numbers of electrons and holes having the same or opposite spin polarization at the sample edge in Hall effect measurements, but with vanishing Hall voltage. These…
A way to represent the band structure that distinguishes between energy-momentum and energy-crystal momentum relationships is proposed upon the band-unfolding concept. This momentum-resolved band structure offers better understanding of the physical processes requiring the information of wave functions in momentum space and provides a good description of angle-resolved photoelectron spectroscopy (ARPES) spectra together with a still informative band structure. Following this approach, we demonstrate that Dirac cones in graphene are intrinsically broken in momentum space and can be described by…
Band crossings observed in a wide range of condensed matter systems are recognized as a key to understand low-energy fermionic excitations that behave as massless Dirac particles. Despite rapid progress in this field, the exploration of non-equilibrium topological states remains scarce and it has potential ability of providing a new platform to create unexpected massless Dirac states. Here we show that in a semiconductor quantum-well driven by a cw-laser with linear polarization, the optical Stark effect conducts bulk-band crossing, and the resulting Floquet-Dirac semimetallic phase supports a…
"What is the difference between space and time?" is an ancient question that remains a matter of intense debate. In Newtonian mechanics time is absolute, while in Einstein's theory of relativity time and space combine into Minkowski spacetime. Here, we firstly propose Minkowski fermions in 2+1 dimensional Minkowski spacetime which have two space-like and one time-like momentum axes. These quasiparticles can be further classified as Klein-Gordon fermions and Dirac-Minkowski fermions according to the linearly and quadratically dispersing excitations. Realization of Dirac-Minkowski quasiparticles…
Superconducting and topological states are two distinct quantum states of matter. Superconductors with topologically nontrivial electronic states provide a platform to study the interplay between them. Recent study revealed that a bulk superconductor PdTe2 is a topological Dirac semimetal with type-II Dirac fermions. However, the Dirac fermions in PdTe2 have no contribution to the superconducting pair because the Dirac points reside far below the Fermi level (EF). Here, we show that in the isostructural compounds (Ir1-xPtx)Te2, the type-II Dirac points can be adjusted to EF by element substitu…
We have investigated several classes of strong spin-orbit chalcogenides related to the (Pb,Sn)Te series studied in connection with the Dirac fermion physics in the 1980s. Our first-principle theoretical calculations suggest that ternary chalcogenides TlBiX$_2$ and TlSbX$_2$ (X=Te, Se, S) series harbor small bandgap topological insulators with single Dirac cone on some selective surfaces whereas the isostructural and isoelectronic silver-based AgBiX$_2$ and AgSbX$_2$ (X=Te, Se, S) series do not. We find that several Tl-compounds are in the vicinity of a topological critical point. We identify t…
We show that the previously predicted Fermion particle that has no analogue in the standard model of particle theory - the cubically dispersed Dirac semimetal (CDSM) - is realized in a specific, stable solid state system that has been made years ago, but was not appreciated to host such a unique Fermion, composed of six Weyl Fermions, 3 with left-handed and 3 with right-handed chirality. We identified the crystal symmetry constraints and found the space group P63/m as one of the two that can support a CDSM, of which the characteristic band crossing has linear dispersion along the principle axi…
The nodal line semimetals have attracted much attention due to their unique topological electronic structure and exotic physical properties. A genuine nodal line semimetal is qualified by the presence of Dirac nodes along a line in the momentum space that are protected against the spin-orbit coupling. In addition, it requires that the Dirac points lie close to the Fermi level allowing to dictate the macroscopic physical properties. Although the material realization of nodal line semimetals have been theoretically predicted in numerous compounds, only a few of them have been experimentally veri…
The quantum spin Hall insulator (QSHI) state has been demonstrated in two semiconductor systems - HgTe/CdTe quantum wells (QWs) and InAs/GaSb QW bilayers. Unlike the HgTe/CdTe QWs, the inverted band gap in InAs/GaSb QW bilayers does not open at the $Γ$ point of the Brillouin zone, preventing the realization of massless Dirac fermions. Here, we propose a new class of semiconductor systems based on InAs/Ga(In)Sb multilayers, hosting a QSHI state, a graphene-like phase and a bilayer graphene analogue, depending on their layer thicknesses and geometry. The QSHI gap in the novel structures can reac…
The disadvantage of BaBiO$_3$ of not being a topological insulator despite having symmetry protected Dirac state is overcome by shifting the Fermi level (E$_F$) via fluorination. The DFT calculations reveal that the fluorination neither affects the spin-orbit coupling nor the parity of the states, but it acts as a perfect electron donor to shift the E$_F$. We find that 33 % fluorination is sufficient to shift the E$_F$ by $\sim$ 2 eV so that the invariant Dirac state lies on it to make BaBiO$_2$F a topological insulator. The fluorinated cubic compound can be experimentally synthesized as the p…
We propose a hierarchy set of minimal optical Raman lattice schemes toward the experimental realization of spin-orbit (SO) couplings of various types for ultracold atoms, including two-dimensional (2D) Dirac type of $C_4$ symmetry, 2D Rashba and 3D Weyl types. These schemes are well accessible with current cold-atom technology, and in particular, a long-lived Bose-Einstein condensation of the 2D Dirac SO coupling has been experimentally proved. The generation of 2D Rashba and 3D Weyl types has an exquisite request that two sources of laser beams have distinct frequencies of factor-two differen…
Room-temperature ferromagnetic semiconductor is vital in nonvolatile digital circuits and it can provide an idea system where we can make use of both charge and spin of electrons. However, seeking room-temperature ferromagnetic semiconductors is still just an appealing idea that has never been realized in practice up to now. Here we demonstrate that graphene monolayer, hybridized with underlying Ni(111) substrate, is the room-temperature ferromagnetic semiconductor that has been continuously searched for decades. Our spin-polarized scanning tunnelling microscopy (STM) experiments, complemented…
Thickness-Dependent Spintronic Terahertz Emission in MBE-Grown PtTe$_2$: From Semiconductor to Type-II Dirac Semimetal
Univ. Grenoble Alpes, CEA, CNRS, IRIG-SPINTEC（格勒诺布尔阿尔卑斯大学、法国原子能和替代能源委员会、法国国家科学研究中心、IRIG自旋技术中心）；Centre for Nanodiagnostics of Materials, Faculty of Materials Science and Technology, Slovak University of Technology（材料纳米诊断中心、材料与科技学院、斯洛伐克科技大学）
Observation of sequential quantum oscillations induced by mini-Landau bands in a three-dimensional Dirac semiconductor
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院高磁场科学中心）；Hefei National Laboratory（合肥国家实验室）
The phase transition between type-I and type-II Dirac semimetals will reveal a series of significant physical properties because of their completely distinct electronic, optical and magnetic properties. However, no mechanism and materials have been proposed to realize the transition to date. Here, we propose that the transition can be realized in two-dimensional (2D) materials consisting of zigzag chains, by tuning external strains. The origination of the transition is that some orbital interactions in zigzag chains vary drastically with structural deformation, which changes dispersions of the…
The Dirac electrons of graphene, an intrinsic zero gap semiconductor, uniquely carry spin and pseudospin that give rise to many fascinating electronic and transport properties. While isolated zigzag graphene nanoribbons are antiferromagnetic semiconductors, we show by means of first-principles and tight-binding calculations that zigzag graphene nanoribbons supported on graphene are half-metallic as a result of spin- and pseudospin-symmetry breaking. In particular, half-metallic Dirac cones are formed at K (K') near the Fermi level. The present results demonstrate that the unique combination of…
We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. The applied voltage reduces the band gap, and eventually a semiconductor to semimetal transition takes place. This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. As a consequence, the Landau levels are not e…
The three dimensional (3D) Dirac semimetal, which has been predicted theoretically, is a new electronic state of matter. It can be viewed as 3D generalization of graphene, with a unique electronic structure in which conduction and valence band energies touch each other only at isolated points in momentum space (i.e. the 3D Dirac points), and thus it cannot be classified either as a metal or a semiconductor. In contrast to graphene, the Dirac points of such a semimetal are not gapped by the spin-orbit interaction and the crossing of the linear dispersions is protected by crystal symmetry. In co…
Non-symmorphic symmetries protect Dirac line nodes in square net materials. This phenomenon has been most prominently observed in ZrSiS. Here, we systematically study the symmetry-protected nodal fermions that result from different ways of embedding the square net into a larger unit cell. Surprisingly, we find that a nonsymmorphic space group is not a necessary condition for a filling enforced semimetal: symmorphic space groups can also host nodal fermions that are enforced by band folding and electron count, that is, a combination of a particular structural motif combined with electron fillin…
Topological semimetals (TSMs) in which conduction and valence bands cross at zero-dimensional (0D) Dirac nodal points (DNPs) or 1D Dirac nodal lines (DNLs), in 3D momentum space, have recently drawn much attention due to their exotic electronic properties. Here we generalize the TSM state further to a higher-symmetry and higher-dimensional pseudo Dirac nodal sphere (PDNS) state, with the band crossings forming a 2D closed sphere at the Fermi level. The PDNS state is characterized with a spherical backbone consisting of multiple crossing DNLs while band degeneracy in between the DNLs is approxi…
In the effective-mass approximation, the step-like crystal potential of a wurtzite semiconductor heterostucture should be supplemented by Dirac delta-function heterointerface terms. They stem from the difference in the Bloch functions of the semiconductors and remain finite even for structures with graded chemical composition, where the terms are presented by a smeared Dirac delta function. We find these heterointerface potentials by employing the k*p method, and evaluate their strength from band-structure parameters of bulk materials. These potentials are weak for semiconductors compliant wit…
The development of spin-based applications of topological insulators requires the knowledge and understanding of spin texture configuration maps as they change via gating in the vicinity of an isolated Dirac node. An isolated (graphene-like) Dirac node, however, does not exist in Bi2Te3. While the isolation of surface states via transport channels has been promisingly achieved in Bi2Te3, it is not known how spin textures modulate while gating the surface. Another drawback of Bi2Te3 is that it features multiple band crossings while chemical potential is placed near the Dirac node (at least 3 no…
Lieb lattice, a two-dimensional edge-depleted square lattice, has been predicted to host various exotic electronic properties due to its unusual band structure, i.e., Dirac cone intersected by a flat band (Dirac-flat bands). Until now, although a few artificial Lieb lattices have been discovered in experiments, the realization of a Lieb lattice in a real material is still unachievable. In this article, based on tight-binding modeling and first-principles calculations, we predict that the two covalent organic frameworks (COFs), i.e., sp2C-COF and sp2N-COF, which have been synthesized in the rec…
Black phosphorus consists of stacked layers of phosphorene, a two-dimensional semiconductor with promising device characteristics. We report the realization of a widely tunable bandgap in few-layer black phosphorus doped with potassium using an in-situ surface doping technique. Through band-structure measurements and calculations, we demonstrate that a vertical electric field from dopants modulates the bandgap owing to the giant Stark effect and tunes the material from a moderate-gap semiconductor to a band-inverted semimetal. At the critical field of this band inversion, the material becomes …
Graphene and phosphorene are monolayer of graphite and phosphorous, respectively. Graphene is completely relativistic (Dirac) fermionic system, but phosphorene is pseudorelativistic fermionic system. In phosphorene, electronic spectrum of phosphorene has a Dirac like (linear) band in one direction and Schrodinger like (parabolic) band in other direction. Conventional Rabi oscillations are studied by using rotating wave approximation in resonance case. The Floquet theory is an alternative way of study Rabi oscillations in off-resonance case and dominating in case of low energy physics. In this …
Dirac and Weyl nodal materials can host low-energy relativistic quasiparticles. Under strong magnetic fields, the topological properties of Dirac/Weyl materials can directly manifest through quantum Hall states. However, most Dirac/Weyl nodes generically exist in semimetals without exploitable bandgaps due to their accidental band-crossing origin. Here we report the first experimental observation of Weyl fermions in a semiconductor. Tellurene, the 2D form of tellurium, possesses chiral crystal structure which induces unconventional Weyl nodes with a hedgehog-like radial spin texture near the c…
Motivated by recent experimental observation of an hydrostatic pressure induced transition from semiconductor to semimetal in black phosphorus [Chen et al. in arXiv:1504.00125], we present the first principles calculation on the pressure effect of the electronic structures of black phosphorus. It is found that the band crossover and reversal at the Z point occur around the critical pressure Pc1=1.23 Gpa, and the band inversion evolves into 4 twofold-degenerate Dirac cones around the Z point, suggesting a 3D Dirac semimetal. With further increasing pressure the Dirac cones in the Gamma-Z line m…
Large-gap quantum spin Hall insulators are promising materials for room-temperature applications based on Dirac fermions. Key to engineer the topologically non-trivial band ordering and sizable band gaps is strong spin-orbit interaction. Following Kane and Mele's original suggestion, one approach is to synthesize monolayers of heavy atoms with honeycomb coordination accommodated on templates with hexagonal symmetry. Yet, in the majority of cases, this recipe leads to triangular lattices, typically hosting metals or trivial insulators. Here, we conceive and realize "indenene", a triangular mono…
Recent experimental success in the realization of two-dimensional (2D) magnetism has stimulated the search for new magnetic 2D materials with strong magnetic anisotropy and high Curie temperature. One promising subgroup of 2D magnetic systems are Dirac half-metals (DHM) which have gained a lot of interest recently, as they host a high-temperature quantum anomalous Hall effect (QAHE). This article discusses predictions for intrinsic DHMs and identifies them as realizations of the Kane-Mele Hubbard model at quarter filling. This proposed unification contributes to a firmer understanding of these…
Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type dispersion. We present symmetry conditions for realizing such hourglass Weyl loops, which involve nonsymmorphic lattice symmetries. Depending on the symmetry, the loops may exhibit different patterns in the Brillouin zone. Based on first-principles calculations, we identify the monolayer GaTeI-family materials as a realistic material platform to realize such loops.…
A theory of relativistic space-charge-limited current (SCLC) is formulated to determine the SCLC scaling, $J\propto V^α/L^β$, for a finite bandgap Dirac material of length $L$ biased under a voltage $V$. In a one-dimensional (1D) bulk geometry, our model allows ($α$, $β$) to vary from (2,3) for the non-relativistic model in traditional solids to (3/2,2) for the ultra-relativistic model of massless Dirac fermions. For a two-dimensional (2D) thin-film geometry, we obtain $α= β$ that varies between 2 and 3/2, respectively, at the non-relativistic and ultra-relativistic limits. We further provide …
We demonstrate how a Dirac-like magnon spectrum is generated for localized magnetic moments forming a two-dimensional honeycomb lattice. The Dirac crossing point is proven to be robust against magnon-magnon interactions, as these only shift the spectrum. Local defects induce impurity resonances near the Dirac point, as well as magnon Friedel oscillations. The energy of the Dirac point is controlled by the exchange coupling, and thus a two-dimensional array of magnetic dots is an experimentally feasible realization of Dirac magnons with tunable dispersion.
Ultrathin films of topological Dirac semimetal, Na$_3$Bi, has recently been revealed as an unusual electronic materials with field-tunable topological phases. Here we investigate the electronic and transport properties of ultrathin Na$_3$Bi as an electrical contact to two-dimensional (2D) metal, i.e. graphene, and 2D semiconductor, i.e. MoS$_2$ and WS$_2$ monolayers. Using combined first-principle density functional theory and nonequilibrium Green's function simulation, we show that the electrical coupling between Na$_3$Bi bilayer thin film and graphene results in a notable interlayer charge t…
