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In this letter, we investigate the stable and commensurate van der Waals heterostructures of metallic and semiconducting $1H$ transition-metal dichalcogenides, NbS$_2$ and MoSe$_2$ (WSe$_2$), which possess almost the same lattice constant of the pristine honeycomb structure. In the most stable structure, the metallic and semiconducting layers are stacked in a similar manner to $3R$ stacking but the period is a pair of a metallic layer and a semiconducting layer. The heterostructure aligns the spin-polarization in each valley among all layers and induces spin-selective charge transfer between the metallic and semiconducting layers. Especially in hetero-trilayers, the electronic spin is conserved due to mirror symmetry along the out-of-plane axis in contrast to the $3R$ stacking structure. A drastic enhancement of spin Hall effect is numerically shown as an example of electronic spin transport phenomena in the hetero-trilayers., Comment: 5 pages, 6 figures

A multifold Hopf semimetal is a topological point node semimetal possessing an anisotropy in the internal electronic structure, e.g., the dipole structure of the Berry curvature. In this paper, the unique features of threefold Hopf semimetals in terms of the optical conductivity are theoretically investigated with a minimal theoretical model by using linear response theory for a linearly polarized photon. The frequency spectrum of the optical conductivity shows an anisotropic dependence on the polarization angle of the incident photon even if the electronic band structure is completely isotropic. The longitudinal optical conductivity linearly depends on the photon frequency and possesses step-like changes in the frequency spectrum. The anisotropic electronic structure has a varying the number of steps with the orientation of the photon polarization axis. We reveal that the anisotropy is attributed to symmetries preserving the point node in threefold Hopf semimetals. The linearly polarized photon also induces a Hall current but it vanishes with the photon polarization axis parallel to the Berry dipole axis. The numerical calculations show that these characteristic features can be observed even with a non-zero temperature and disorder., Comment: 7 pages, 3 figures

A proximity effect at a van der Waals (vdW) interface enables creation of an emergent quantum electronic ground state. Here we demonstrate that an originally-superconducting two-dimensional (2D) NbSe2 forms a ferromagnetic ground state with spontaneous spin polarization at a vdW interface with a 2D ferromagnet V5Se8. We investigated the anomalous Hall effect (AHE) of the NbSe2/V5Se8 magnetic vdW heterostructures, and found that the sign of the AHE was reversed as the number of the V5Se8 layer was thinned down to the monolayer limit. Interestingly, the AHE signal of those samples was enhanced with the in-plane magnetic fields, suggesting an additional contribution to the AHE signal other than magnetization. This unusual behavior is well reproduced by band structure calculations, where the emergence of the Berry curvature along the spin-degenerate nodal lines in 2D NbSe2 by the in-plane magnetization plays a key role, unveiling a unique interplay between magnetism and Zeeman-type spin-orbit interaction in a non-centrosymmetric 2D quantum material., Comment: accepted to Nature Communications

Lateral-hetero structures of atomic layered materials alter the electronic properties of pristine crystals and provide a possibility to produce useful monolayer materials. We reveal that metal-semiconductor-metal lateral-hetero junctions of $1H$-transition-metal dichalcogenides intrinsically possess conducting channels of electrons with spin-valley locking, e.g., gate electrode. We theoretically investigate the electronic structure and transport properties of the lateral-hetero junctions and show that the hetero-structure produces conducting channels through the $K$ and $K'$ valleys in the semiconducting transition-metal dichalcogenide and restricts the spin of the conducting electrons in each valley due to the valley dependent charge transfer effect. Moreover, the theoretical investigation shows that the hetero-junction of WSe$_2$ realizes a high transmission probability for valley-spin locked electrons even in a long semiconducting region. The hetero-junction also provides a useful electronic transport property, a step-like I-V characteristic., Comment: 10 pages, 11 figures

We investigate the optical property of monolayer and layered BiI$_3$ and reveal the presence of exciton only in the monolayer crystal. We evaluate the energy spectrum of a dielectric function by using time-dependent density functional theory. Bulk crystal of BiI$_3$ is an atomic layered semiconductor with the band gap corresponding to the frequency of visible light. The numerical result for the bulk crystal is confirmed to be consistent with the previous experimental results and it does not depend on the number of layers except the monolayer. We reveal the excitons appearing below the resonant peak associated with the inter-band excitation in the monolayer crystal. The unique optical property can be directly observed in the optical absorption or differential reflectance spectrum and distinguish the monolayer crystal from the stacked BiI$_3$., Comment: 6 pages, 6 figures

We theoretically investigate the electronic states in monolayer NbSe$_2$ and develop continuous models to describe these states in Fermi pockets. In $1H$-type metallic transition-metal dichalcogenides(TMDCs), the Femi surface consists of three pockets enclosing the $\Gamma$, $K$, and $K'$ points. We reveal that the conventional effective model used for semiconducting TMDCs is not sufficient to describe the electronic states in metallic TMDCs and thus introduce a scheme to construct the effective model from the first-principles results. All models can be represented by $3\times3$ Hamiltonian and well reproduce electronic states around the Fermi energy in terms of the orbital composition and the phase factor. We also show that the $p$ orbitals in chalcogen atoms, which are ignored in the conventional $2\times2$ model, play a crucial role in metallic TMDCs. Although the aim of these models is to reproduce electronic states, they can well describe states near the high-symmetry points and the profile of Berry curvature in the wave vector space. The continuous model can be a handleable tool to describe the electronic states and to analyze the transport phenomena in metallic TMDCs., Comment: 13 pages, 10 figures

We investigate the Andreev-bound-state (ABS) spectra of three-terminal Josephson junctions which consist of 1D topological superconductors (TSCs) harboring multiple zero-energy edge Majorana bound states (MBSs) protected by chiral symmetry. Our theoretical analysis relies on the exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian describing the three interfaced TSCs, complemented by an effective low-energy description solely based on the coupling of the interfacial MBSs arising before the leads get contacted. Considering the 2D synthetic space spanned by the two independent superconducting phase differences, we demonstrate that the ABS spectra may contain either point or line nodes, and identify $\mathbb{Z}_2$ topological invariants to classify them. We show that the resulting type of nodes depends on the number of preexisting interfacial MBSs, with nodal lines necessarily appearing when two TSCs harbor an unequal number of MBSs. Specifically, the precise number of interfacial MBSs determines the periodicity of the spectrum under $2\pi$-slidings of the phase differences and, as a result, also controls the shape of the nodal lines in synthetic space. When chiral symmetry is preserved, the lines are open and coincide with high-symmetry lines of synthetic space, while when it is violated the lines can also transform into loops and chains. The nodal spectra are robust by virtue of the inherent particle-hole symmetry of the BdG Hamiltonian, and give rise to distinctive experimental signatures that we identify., Comment: 21 pages, 9 figures

We study theoretically the Josephson effect between two time-reversal two-band superconductors, where we assume the equal-time spin-singlet $s$-wave pair potential in each conduction band. %as well as the band asymmetry and the band hybridization in the normal state. The superconducting phase at the first band $\varphi_1$ and that at the second band $\varphi_2$ characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green's function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band $\delta\varphi_1$, the phase difference at the second band $\delta\varphi_2$, and the difference at the center-of-mass phase $\delta(\varphi_1+\varphi_2)/2$. A Cooper pairs generated by the band hybridization carries the last current component. In some cases, the current-phase relationship deviates from the sinusoidal function as a result of time-reversal symmetry breaking down., Comment: 6 page, 2 figures

We study the refraction effect of electronic wave in hole-doped lateral heterojunctions of metallic and semiconducting transition-metal dichalcogenide monolayers. This effect is theoretically investigated in 2$H$-type MoSe$_2$-NbS$_2$ and WSe$_2$-NbS$_2$ junctions by combining the first-principles calculation and the lattice Green's function method. We show that the electronic waves change the direction of motion at the interface and collimate the velocity along two different directions depending on the spin. We find that the transmission probability increases with the charge density and that the direction of refracted electron beams is close to $\pm30^\circ$ with respect to the perpendicular axis to the interface. The metallic transition-metal dichalcogenide is essential for the refraction effect because of the strong trigonal-warping effect, the large Fermi surface, and the Zeeman-type spin-orbit coupling. The refraction effect enables to generate the spin-polarized electronic current by using a simple fabrication of transition-metal dichalcogenide monolayers., Comment: 6 pages, 5 figures

We study the pseudo-spin of electron pair in superconducting transition-metal dichalcogenide monolayers and show that the pseudo-spin affects the electric transport property of lateral heterojunction of the superconducting and metallic monolayers. The pseudo-spins of two electrons forming a Cooper pair are parallel to each other unlike the real spins being anti-parallel. In the lateral heterojunction, the electronic transport with forming a Cooper pair, the Andreev reflection, is suppressed with the Fermi level crossing the valence band near the edge in the metallic monolayer. We numerically investigate the electric transport property of the lateral heterojunctions of semiconducting and superconducting transition-metal dichalcogenides, MoSe$_2$ monolayer and NbSe$_2$ monolayer with the charge doping, respectively. We find the sign change of conductance difference between the normal and superconducting phases by varying the charge density and show that the sign change is resulted from the pseudo-spin triplet superconductivity., Comment: 10 pages, 6 figures

We investigate the electronic transport property of lateral heterojunctions of semiconducting and metallic transition-metal dichalcogenide monolayers, MoSe$_2$ and NbSe$_2$, respectively. We calculate the electronic transmission probability by using a multi-orbital tight-binding model based on the first-principles band structure. The transmission probability depends on the spin and valley degrees of freedom. This dependence qualitatively changes by the interface structure. The heterostructure with a zig-zag interface preserves the spin and the valley of electron in the transmission process. On the other hand, the armchair interface enables conduction electrons to transmit with changing the valley and increases the conductance in hole-doped junctions due to the valley-flip transmission. We also discuss the spin and valley polarizations of electronic current in the heterojunctions., Comment: 8 pages, 10 figures

We investigate the dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi. In the semimetal, the band structure holds point nodes at the $\Gamma$ and R points in the Brillouin zone and more than three bands touch at the nodes. Around the nodes, electronic states are predicted to be described as the multifold chiral fermion, a new class of fermion. We show that the dynamical conductivity exhibits a characteristic spectrum corresponding to the band structure and the chiral fermionic states. The dynamical conductivity of CoSi is calculated as a function of photon energy by using the first-principles band calculation and linear response theory. We show that a dip structure in the low photon-energy region is attributed to not only the band structure but also the chirality of electronic states. The chirality leads to the prohibition of transition between the lower and upper bands of threefold chiral fermion and thus the transition between the middle and lower bands is relevant to the dynamical conductivity. This transition property is different from the Dirac and Weyl semimetals, the other point-nodal semimetals, where the excitation between the upper and lower bands is relevant to the dynamical conductivity. We discuss the relation between the prohibition and the dip structure by using an effective Hamiltonian describing threefold chiral fermion., Comment: 8 pages, 5 figures

We study theoretically the proximity effect in a ferromagnetic semiconductor with Rashba spin-orbit interaction. The exchange potential generates opposite-spin-triplet Cooper pairs which are transformed into equal-spin-triplet pairs by the spin-orbit interaction. In the limit of strong spin-orbit interaction, symmetry of the dominant Cooper pair depends on the degree of disorder in a ferromagnet. In the clean limit, spin-singlet $s$-wave Cooper pairs are the most dominant because the spin-momentum locking stabilizes a Cooper pair consisting of a time-reversal partner. In the dirty limit, on the other hand, equal-spin-triplet $s$-wave pairs are dominant because random impurity potentials release the locking. We also discuss the effects of the spin-orbit interaction on the Josephson current., Comment: 9 pages, 12 figures

ZrSiS is one of the strong candidates for realistic nodal-line semimetal. We theoretically investigate the dynamical conductivity in ZrSiS by using a multi-orbital theoretical model based on the first-principles band calculation. We find that the dynamical conductivity in the clean limit is actually not frequency independent unlike the ideal Dirac model, while nearly flat dependence is achieved by introducing the energy broadening possibly induced by the disorder. The results can be applied to other compounds with the similar crystal structure, such as ZrSiSe, ZrSiTe, and HfSiS., Comment: 6 pages, 7 figures

We study the electronic band structure of three-dimensional ABC-stacked (rhombohedral) graphdiyne, which is a new planar carbon allotrope recently fabricated. Using the first-principles calculation, we show that the system is a nodal-line semimetal, in which the conduction band and valence band cross at a closed ring in the momentum space. We derive the minimum tight-binding model and the low-energy effective Hamiltonian in a $4\times 4$ matrix form. The nodal line is protected by a non-trivial winding number, and it ensures the existence of the topological surface state in a finite-thickness slab. The Fermi surface of the doped system exhibits a peculiar, self-intersecting hourglass structure, which is quite different from the torus or pipe shape in the previously proposed nodal semimetals. Despite its simple configuration, three-dimensional graphdiyne offers unique electronic properties distinct from any other carbon allotropes., Comment: 6 pages, 5 figures

We theoretically study the spin and charge currents induced by a spin-motive force in a two-dimensional Dirac semimetal protected by nonsymmorphic symmetries. Glide mirror plane symmetry, a nonsymmorphic symmetry, leads to a constraint to the induced current; the spin-motive force acting on out-of-plane spin (in-plane spin) induces the pure spin (charge) current. We calculate the response function to the spin-motive force in linear response theory and find that the conductivity for the pure spin current remains non-zero even if the Fermi energy is crossing the node of linear dispersion. We also find that the dissipationless spin current is induced at the charge neutral point., Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. B

We investigate the topological phase derived by time-reversal breaking fields in a nonsymmorphic symmetry-protected two-dimensional Dirac semimetal. When the nonsymmorphic symmetry is preserved even in the presence of the field, the two-dimensional electronic states change into two distinct topological phases with the insulating gap. One phase is well-known as quantum Hall states with chiral edge modes accompanying the Hall current, but the other one is an unconventional topological phase with helical edge modes in the absence of time-reversal symmetry., Comment: 4 pages, 2 figures

We study the anomalous Hall effect in monolayers of transition-metal dichalcogenides 2H-$MX_2$ ($M$=Mo, W, and $X$=S, Se, Te) under a proximity effect of ferromagnetic substrate. If a proximity-induced exchange field is introduced, the spin-polarized energy bands in $K$ and $K'$ valleys are shifted in the opposite directions, and it causes the Hall effect by breaking time-reversal symmetry. The induced Hall effect is the most prominent in the valence band which has a large intrinsic spin splitting. Moreover, we find that tilting the magnetization from the perpendicular direction gives rise to a sensitive change in the Hall conductivity only in the electron side, and it is attributed to the mixing of the Berry phase by the in-plane field in the nearly degenerate conduction bands., Comment: 8 pages, 8 figures

We theoretically study a tunneling effect in a two-dimensional Dirac semimetal with two Dirac points protected by non-symmorphic symmetries. The tunnel barrier can be arranged by a magnetic exchange potential which opens a gap at the Dirac points which can be induced by a magnetic proximity effect of a ferromagnetic insulator. We found that the tunnel decay length increases with a decrease in the strength of the spin-orbit coupling, and moreover the dependence is attributed to the correlation of sublattice and spin degree of freedoms which lead to symmetry-protected Dirac points. The tunnel probability is quite different in two Dirac points, and thus the tunnel effect can be applied to the highly-selective valley filter., Comment: 5 pages

We study the electronic spin relaxation effect in the hole-doped monolayer and bilayer transition-metal dichalcogenides in the presence of the crystal defects. We consider realistic models of the lattice vacancy and actually estimate the spin relaxation rate using the multi-orbital tight-binding model. In the monolayer, the spin-relaxation time is found to be extremely long compared to the momentum relaxation time, and this is attributed to the fact that the spin hybridization in the band structure is suppressed by the mirror reflection symmetry. The bilayer TMD has a much shorter spin relaxation time in contrast, and this is attributed to stronger spin hybridization due to the absence of the mirror symmetry., Comment: 5 pages, 5 figures

We theoretically propose a novel spin-dependent electronic transport mechanism in which the spin-unpolarized electron beam is split into different directions depending on spins at an atomic domain boundary in non-magnetic material. Specifically, we calculate the electronic transmission across a boundary between monolayer and bilayer of the transition metal dichalcogenide, and demonstrate that up-spin and down-spin electrons entering the boundary are refracted and collimated to opposite directions. The phenomenon is attributed to the strong spin-orbit interaction, the trigonally-warped Fermi surface, and the different crystal symmetries between the monolayer and bilayer systems. The spin-dependent refraction suggests a potential application for a spin splitter, which spatially separates up-spin and down-spin electrons simply by passing the electric current through the boundary., Comment: 6 pages, 6 figures

We theoretically study low energy electric transport in a junction consisting of a Weyl semimetal and a metallic superconductor. The characteristic features of the differential conductance depend on the relative directions between the current and the vector connecting the two Weyl points. When the electric current is perpendicular to the vector, the conductance spectra are sensitive to the direction and the amplitude of magnetic moment at the junction interface. This is a direct consequence of the chiral spin configuration on the fermi surface near the Weyl points., Comment: 6 pages, 6 figures embedded

We theoretically study the electric current induced by the temporally oscillating magnetic field onto a three-dimensional topological insulator based on the linear response theory. The electric current flows on its surface because of the unique characters of the surface states: the linear dispersion in two-dimension and the chiral spin texture on the Fermi surface. In the bulk region, on the other hand, the current is absent because of the degeneracy for the bulk bands. The response function has a peak structure when the frequency of the magnetic field is equal to twice of the Fermi energy of the surface states measured from the Dirac node. This feature is unique to the surface states on the three-dimensional topological insulator., Comment: 8pages, 4figures

We study theoretically the two-dimensional topological electric state in a single band semiconductor with strong spin-orbit interactions under harmonic scalar electrostatic potentials. The electronic states described by the spin Landau levels are insulating in the bulk and host gapless edge states in the presence of time-reversal symmetry. Such topological states show the properties of the quantized electric conductivity and the quantized spin Hall conductivity characterized by the spin Chern number $\mathbb{Z}$. The quantization of the two conductivities are robust under various perturbations such as the potential disorder, the Zeeman field, and the spin-orbit scatterings. Existing semiconductor technologies would realize the topological states discussed in the present paper., Comment: 4 pages, 2 figures

We discuss topological electronic states described by the Dirac Hamiltonian plus an additional one in three-dimension. When the additional Hamiltonian is an element of an Abelian group, electronic states become topologically nontrivial even in the absence of fundamental symmetries such as the time-reversal and the particle-hole symmety. The symmetry-breaking topological states are charercterized by the Chern number defined in the two-dimensional partial Brillouin zone. The topological insulators under Zeeman field are an example of the symmetry-breaking topological matters. We show the transision from the topological insulating phase to the topological semimetal one under the strong Zeeman field., Comment: 5 pages, 4 figures

We theoretically study the phonon mediated intersurface electron-electron interactions on the pseudo two-dimensional metallic states at the two surfaces of a three-dimensional topological insulator. From a model of a three-dimensional topological insulator including the phonon excitation in it, we derive the effective Lagrangian which describes the two surface metallic states and the interaction between them. The intersurface electron-electron interactions can be either repulsive or attractive depending on parameters such as temperature, the speed of the phonon, and the Fermi velocity of the surface states. The attractive interaction removes the Dirac nodes from the two surface states as a result of the spontaneous symmetry breaking. On the basis of the calculated results, we also discuss how to tune the inter-surface interaction., Comment: 8 pages, 6 figures

We theoretically study subgap states appearing at the interface between two three-dimensional topological insulators which have different configurations in the spin-orbit interactions from each other. The coupling of spin $\boldsymbol{\sigma}$ with momenta $\boldsymbol{p}$ is configured by a material dependent $3\times 3$ matrix $\boldsymbol{\Lambda}$ as ${\sigma}^\mu {\Lambda}_\mu^\nu p_\nu$. We show that the spectra of the interface suggap states depend strongly on the relative choices of $\boldsymbol{\Lambda}$ in the two topological insulators. In particular, we focus on properties of gapless states which appear when $\boldsymbol{\Lambda}$ in two topological insulators are connected by the inversion in momentum space. We also discuss the robustness of the gapless states under perturbations breaking the time-reversal symmetry or the band-inversion symmetry by the numerical simulation., Comment: 13 pages, 9 figures

We discuss the excitation spectra around the Dirac node on a surface of a three-dimensional topological insulator. By using the diagrammatic expansion, we show that the coupling of an electron with the gauge field in the presence of impurity scatterings opens a gap around the Dirac node. The results are consistent with a recent experimental finding by T. Sato,et. al.[ Nature Phys. \textbf{7}, 840 (2011)]. We also discuss the consistency between the present results and the bulk-boundary correspondence of the topological insulator in the presence of time reversal symmetry. The conclusion can be applied any two dimensional massless fermions., Comment: 6 pages, 2 figures

We discuss bound states appearing at the interface between two different superconductors characterized by different nontrivial topological numbers such as one-dimensional winding numbers and Chern numbers. The one-dimensional winding number characterizes d_{xy} and p_x wave superconductors. The Chern number characterizes chiral-p, chiral-d, and chiral-f wave superconductors. The interfacial bound state appears at the zero-energy when the topological numbers of the two superconductors are different from each other. When the two superconductors are characterized by the Chern numbers n and m, for example, the number of the zero-energy bound is |n-m| independent of junction parameters such as the phase difference across the junction and the transmission probability of interface. We generalize a concept of bulk-boundary correspondence to the Josephson junctions consisting of two topological superconductors., Comment: 9 pages, 7 figures

We study electronic structures at an interface between a topological insulator and a ferromagnetic insulator by using three-dimensional two-band model. In usual ferromagnetic insulators, the exchange potential is much larger than the bulk gap size in the topological insulators and electronic structures are asymmetric with respect to the fermi level. In such situation, we show that unusual metallic states appear under the magnetic moment pointing the perpendicular direction to the junction plane, which cannot be described by the two-dimensional effective model around the Dirac point. When the magnetic moment is in the parallel direction to the plane, the number of Dirac cones becomes even integers. The conclusions obtained in analytical calculations are confirmed by numerical simulations on tight-binding lattice., Comment: 9 pages, 5 figures

We discuss the surface impedance (Z=R-iX) of a normal-metal/superconductor proximity structure taking into account the spin-dependent potential at the junction interface. Because of the spin mixing transport at the interface, odd-frequency spin-triplet s-wave Cooper pairs penetrate into the normal metal and cause the anomalous response to electromagnetic fields. At low temperature, the local impedance at a surface of the normal metal shows the nonmonotonic temperature dependence and the anomalous relation R>X. We also discuss a possibility of observing such anomalous impedance in experiments., Comment: 7pages, 7 figures