Nonlinear Optical Properties of Transition Metal Dichalcogenide MX2_2 (M = Mo, W; X = S, Se) Monolayers and Trilayers from First-principles Calculations

Due to the absence of interlayer coupling and inversion symmetry, transition metal dichalcogenide (MX$_2$) semiconductor monolayers exhibit novel properties that are distinctly different from their bulk crystals such as direct optical band gaps, large band spin splittings, spin-valley coupling, piezoelectric and nonlinear optical responses, and thus have promising applications in, e.g., opto-electronic and spintronic devices. Here we have performed a systematic first-principles study of the second-order nonlinear optical properties of MX$_2$ (M = Mo, W; X = S, Se) monolayers and trilayers within the density functional theory with the generalized gradient approximation plus scissors correction. We find that all the four MX$_2$ monolayers possess large second-order optical susceptibility $\chi^{(2)}$ in the optical frequency range and significant linear electro-optical coefficients in low frequency limit, thus indicating their potential applications in non-linear optical devices and electric optical switches. The $\chi^{(2)}$ spectra of the MX$_2$ trilayers are overall similar to the corresponding MX$_2$ monolayers, {\it albeit} with the magnitude reduced by roughly a factor of 3. The prominent features in the $\chi^{(2)}$ spectra of the MX$_2$ multilayers are analyzed in terms of the underlying band structures and optical dielectric function, and also compared with available experiments.Comment: references updated, new Figure 2, revised Figure 8 and text improve

High spin polarization of the anomalous Hall current in Co-based Heusler compounds

Based on first principles density functional calculations of the intrinsic anomalous and spin Hall conductivities, we predict that the charge Hall current in Co-based full Heusler compounds Co$_2$XZ (X = Cr and Mn; Z = Al, Si, Ga, Ge, In and Sn) except Co$_2$CrGa would be almost fully spin-polarized even although Co$_2$MnAl, Co$_2$MnGa, Co$_2$MnIn and Co$_2$MnSn do not have a half-metallic band structure. Furthermore, the ratio of the associated spin current to the charge Hall current is slightly larger than 1.0. This suggests that these Co-based Heusler compounds, especially Co$_2$MnAl, Co$_2$MnGa and Co$_2$MnIn which are found to have large anomalous and spin Hall conductivities, might be called anomalous Hall half-metals and could have valuable applications in spintronics such as spin valves as well as magnetoresistive and spin-torque driven nanodevices. These interesting findings are discussed in terms of the calculated electronic band structures, magnetic moments and also anomalous and spin Hall conductivities as a function of the Fermi level.Comment: Accepted for publication in New Journal of Physic

Topological insulator associated with quantum anomalous Hall phase in ferromagnetic perovskite superlattices

We do a search for topological insulators which are associated with ferromagnetic ordering and show anomalous quantum Hall effect, among transition metal oxide superlattices taking the parent compounds as LaAlO3 and SrTiO3. Among the various superlattices which are studied here, (LaAlO3)10/(LaOsO3)2 exhibits a ferromagnetic ground state with a topologically non-trivial energy gap when a spin-orbit interaction is turned on. The study of transverse conductivity shows that the system has quantized Hall conductivity inside the topological energy gap without applying any external magnetic field. The ferromagnetic order parameters and the ordering temperature (Tc) have been estimated by taking a simple Heisenberg model of ferromagnetism.Comment: 6 pages, 6 figure

Large anomalous Nernst and spin Nernst effects in noncollinear antiferromagnets Mn3X_3X (XX = Sn, Ge, Ga)

Noncollinear antiferromagnets have recently been attracting considerable interest partly due to recent surprising discoveries of the anomalous Hall effect (AHE) in them and partly because they have promising applications in antiferromagnetic spintronics. Here we study the anomalous Nernst effect (ANE), a phenomenon having the same origin as the AHE, and also the spin Nernst effect (SNE) as well as AHE and the spin Hall effect (SHE) in noncollinear antiferromagnetic Mn$_3X$ ($X$ = Sn, Ge, Ga) within the Berry phase formalism based on {\it ab initio} relativistic band structure calculations. For comparison, we also calculate the anomalous Nernst conductivity (ANC) and anomalous Hall conductivity (AHC) of ferromagnetic iron as well as the spin Nernst conductivity (SNC) of platinum metal. Remarkably, the calculated ANC at room temperature (300 K) for all three alloys is huge, being up to 5 times larger than that of iron. Moreover, the calculated SNC for Mn$_3$Sn and Mn$_3$Ga is also large, being as large as that of platinum. This suggests that these anitferromagnets would be useful materials for thermoelectronic devices and spin caloritronic devices. The calculated ANC of Mn$_3$Sn and iron are in reasonably good agreement with the very recent experiments. The calculated SNC of platinum also agrees with the very recent experiments in both sign and magnitude. The calculated thermoelectric and thermomagnetic properties are analyzed in terms of the band structures as well as the energy-dependent AHC, ANC, SNC and spin Hall conductivity via the Mott relations.Comment: Revised version with new Table II, new Figures 3-6, and the corrected ANC and SNC value

Magnetism and Magneto-optical Effects in Bulk and Few-layer CrI3_3: A Theoretical GGA + U Study

The latest discovery of ferromagnetism in atomically thin films of semiconductors Cr$_2$Ge$_2$Te$_6$ and CrI$_3$ has unleashed numerous opportunities for fundamental physics of magnetism in two-dimensional (2D) limit and also for technological applications based on 2D magnetic materials. In this paper, we present a comprehensive theoretical study of the magnetic, electronic, optical and magneto-optical(MO) properties of multilayers [monolayer(ML), bilayer and trilayer] and bulk CrI$_3$, based on the density functional theory with the generalized gradient approximation plus on-site Coulomb repulsion scheme. Interestingly, all the structures are found to be single-spin ferromagnetic(FM) semiconductors. They all have a large out-of-plane magnetic anisotropy energy(MAE) of $\sim$0.5 meV/Cr. These large MAEs suppress transverse spin fluctuations and thus stabilize long-range magnetic orders at finite temperatures down to the ML limit. They also exhibit strong MO effects with their Kerr and Faraday rotation angles being comparable to that of best-known bulk MO materials. The shape and position of the main features in the optical and MO spectra are found to be nearly thickness-independent although the magnitude of Kerr rotation angles increases monotonically with the film thickness. Magnetic transition temperatures estimated based on calculated exchange coupling parameters, calculated optical conductivity, MO Kerr and Faraday rotation angles agree quite well with available experimental data. The calculated MAE as well as optical and MO properties are analyzed in terms of the calculated orbital-decomposed densities of states, band state symmetries and dipole selection rules. Our findings of large out-of-plane MAEs and strong MO effects in these single-spin FM semiconducting CrI$_3$ ultrathin films suggest that they will find valuable applications in semiconductor MO and spintronic nanodevices

Tuning Topological Phase Transitions in Hexagonal Photonic Lattices Made of Triangular Rods

In this paper, we study topological phases in a 2D photonic crystal with broken time ($\mathcal{T}$) and parity ($\mathcal{P}$) symmetries by performing calculations of band structures, Berry curvatures, Chern numbers, edge states and also numerical simulations of light propagation in the edge modes. Specifically, we consider a hexagonal lattice consisting of triangular gyromagnetic rods. Here the gyromagnetic material breaks $\mathcal{T}$ symmetry while the triangular rods breaks $\mathcal{P}$ symmetry. Interestingly, we find that the crystal could host quantum anomalous Hall (QAH) phases with different gap Chern numbers ($C_g$) including $|C_g| > 1$ as well as quantum valley Hall (QVH) phases with contrasting valley Chern numbers ($C_v$), depending on the orientation of the triangular rods. Furthermore, phase transitions among these topological phases, such as from QAH to QVH and vice versa, can be engineered by a simple rotation of the rods. Our band theoretical analyses reveal that the Dirac nodes at the $K$ and $K'$ valleys in the momentum space are produced and protected by the mirror symmetry ($m_y$) instead of the $\mathcal{P}$ symmetry, and they become gapped when either $\mathcal{T}$ or $m_y$ symmetry is broken, resulting in a QAH or QVH phase, respectively. Moreover, a high Chern number ($C_g = -2$) QAH phase is generated by gapping triply degenerate nodal points rather than pairs of Dirac points by breaking $\mathcal{T}$ symmetry. Our proposed photonic crystal thus provides a platform for investigating intriguing topological phenomena which may be challenging to realize in electronic systems, and also has promising potentials for device applications in photonics such as reflection-free one-way waveguides and topological photonic circuits

Optical left-handed metamaterials made of arrays of upright split-ring pairs

Electromagnetic metamaterials are man-made structures that have novel properties such as a negative refraction index, not attainable in naturally occurring materials. Although negative index materials (NIMs) in microwave frequencies were demonstrated in 2001, it has remained challenging to design NIMs for optical frequencies especially those with both negative permittivity and negative permeability [known as left-handed metamaterials (LHMs)]. Here, by going beyond the traditional concept of the combination of artificial electronic and magnetic meta-atoms to design NIMs, we propose a novel LHM composed of an array of simple upright split-ring pairs working in the near infrared region. Our electromagnetic simulations reveal the underlying mechanism that the coupling of the two rings can stimulate simultaneously both the electric and magnetic resonances. The proposed structure has a highest refractive index of -2, a highest figure of merit of 21, good air-matched impedance and 180 nm double negative bandwidth, which excel the performances of many previous proposals. We also numerically demonstrate the negative refraction of this metamaterial in both the single-layer form and wedge-shaped lens

A lower bound of the least signless Laplacian eigenvalue of a graph

Let $G$ be a simple connected graph on $n$ vertices and $m$ edges. In [Linear Algebra Appl. 435 (2011) 2570-2584], Lima et al. posed the following conjecture on the least eigenvalue $q_n(G)$ of the signless Laplacian of $G$: $\displaystyle q_n(G)\ge {2m}/{(n-1)}-n+2$. In this paper we prove a stronger result: For any graph with $n$ vertices and $m$ edges, we have $\displaystyle q_n(G)\ge {2m}/{(n-2)}-n+1 (n\ge 6)$

Cooling of a levitated nanoparticle with digital parametric feedback

The motion control of a levitated nanoparticle plays a central role in optical levitation for fundamental studies and practical applications. Here, we presented a digital parametric feedback cooling based on switching between two trapping laser intensity levels with square wave modulations. The effects of modulation depth and modulation signal phase on the cooling result were investigated in detail. With such a digital parametric feedback method, the centre-of-mass temperature of all three motional degrees of freedom can be cooled to dozens of milli-Kelvin, which paved the way to fully control the motion of the levitated nanoparticle with a programmable digital process for wild applications.Comment: 5 pages, 6 figure

Advances in quantum dense coding

Quantum dense coding is one of the most important protocols in quantum communication. It derives from the idea of using quantum resources to boost the communication capacity and now serves as a key primitive across a variety of quantum information protocols. Here, we focus on the basic theoretical ideas behind quantum dense coding, discussing its development history from discrete and continuous variables to quantum networks, then to its variant protocols and applications in quantum secure communication. With this basic background in hand, we then review the main experimental achievements, from photonic qubits and qudits to optical modes, nuclear magnetic resonance, and atomic systems. Besides the state of the art, we finally discuss potential future steps.Comment: Accepted by Advanced Quantum Technologies (Invited review