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The original formula of Bell inequality (BI) in terms of two-spin singlet has to be modified for the entangled-state with parallel spin polarization. Based on classical statistics of the particle-number correlation, we prove in this paper an extended BI, which is valid for two-spin entangled states with both parallel and antiparallel polarizations. The BI and its violation can be formulated in a unified formalism based on the spin coherent-state quantum probability statistics with the state-density operator, which is separated to the local and non-local parts. The local part gives rise to the BI, while the violation is a direct result of the non-local quantum interference between two components of entangled state. The Bell measuring outcome correlation denoted by $P_{B}$ is always less than or at most equal to one for the local realistic model ($P_{B}^{lc}\leq1$) regardless of the specific superposition coefficients of entangled state. Including the non-local quantum interference the maximum violation of BI is found as $P_{B}^{\max}$ $=2$, which, however depends on state parameters and three measuring directions as well. Our result is suitable for entangled photon pairs., Comment: 7 pages, 2 figures

Multiferroic materials are potential to be applied in novel magnetoelectric devices, for example, high-density non-volatile storage. Last decades, research on multiferroic materials was focused on three-dimensional (3D) materials. However, 3D materials suffer from the dangling bonds and quantum tunneling in the nano-scale thin films. Two-dimensional (2D) materials might provide an elegant solution to these problems, and thus are highly on demand. Using first-principles calculations, we predict ferromagnetism and driven ferroelectricity in the monolayer and even a few-layers of CuCrP2S6. Although the total energy of the ferroelectric phase of monolayer is higher than that of the antiferroelectric phase, the ferroelectric phases can be realized by applying a large electric field. Besides the degrees of freedoms in the common multiferroic materials, the valley degree of freedom is also polarized according to our calculations. The spins, electric dipoles and valleys are coupled with each other as shown in the computational results. In experiment, we observe the out-of-plane ferroelectricity in a few-layer CuCrP2S6 (approximately 13 nm thick) at room temperature. 2D ferromagnetism of few-layers is inferred from magnetic hysteresis loops of the massively stacked nanosheets at 10 K. The experimental observations support our calculation very well. Our findings may provide a series of 2D materials for further device applications.

The experimental test of Bell's inequality is mainly focused on Clauser-Horne-Shimony-Holt (CHSH) form, which provides a quantitative bound, while little attention has been pained on the violation of Wigner inequality (WI). Based on the spin coherent state quantum probability statistics we in the present paper extend the WI and its violation to arbitrary two-spin entangled states with antiparallel and parallel spin-polarizations. The local part of density operator gives rise to the WI while the violation is a direct result of non-local interference between two components of the entangled states. The Wigner measuring outcome correlation denoted by $W$ is always less than or at most equal to zero for the local realist model ($% W_{lc_{{}}}\leq 0$) regardless of the specific initial state. On the other hand the violation of\ WI is characterized by any positive value of $W$, which possesses a maximum violation bound $W_{\max }$ $=1/2$. We conclude that the WI is equally convenient for the experimental test of violation by the quantum entanglement., Comment: 6 pages, 0 figures

Valleytronics is a rising topic to explore the emergent degree of freedom for charge carriers in energy band edges and has attracted a great interest due to many intriguing quantum phenomena and potential application in information processing industry. Creation of permanent valley polarization, i.e. unbalanced occupation at different valleys, is a chief challenge and also urgent question to be solved in valleytronics. Here we predict that the spin-orbit coupling and magnetic ordering allow spontaneous valley Zeeman-type splitting in pristine monolayer of VAgP2Se6 by using first-principles calculations. The Zeeman-type valley splitting can lead to permanent valley polarization after suitable doping. The Zeeman-type valley splitting is similar to the role of spin polarization in spintronics and is a vital requirement for practical devices in valleytronics. The nonequivalent valleys of VAgP2Se6 monolayer can emit or absorb circularly polarized photons with opposite chirality, and thus this material shows a great potential to work as a photonic spin filter and circularly-polarized-light resource. A valley pseudospin field effect transistor (VPFET) is designed based on the monolayer VAgP2Se6 akin to the spin field effect transistors. Beyond common transistors, VPFETs carry information of not only the electrons but also the valley pseudospins.

Topological materials are of great interest for applications in quantum computing, providing intrinsic robustness against environmental noises. A popular direction is to look for Majorana modes in integrated systems interfaced with superconducting materials. However, is superconductivity necessary for materials to exhibits non-abelian statistics? Here we predict with strong theoretical and numerical evidences that there exist topologically phases in a class of one-dimensional single crystals, which contain large bandgaps and are within experimental reach. Specifically, the nontrivial Zak phases are associated with gapless boundary states, which provides the non-Abelian statistics required for constructing topologically-protected quantum gates, even without superconductivity and magnetic field. Another anomalous feature of these materials is that the electric polarization is quantized and a transverse field induces a longitudinal polarization. This novel material property provides an experimentally-accessible mechanism for braiding the non-Abelian anyons.

Colloidal Cadmium Selenide (CdSe) nanoplatelets (NPLs) are a recently developed class of efficient luminescent nanomaterial suitable for optoelectronic device applications. A change in temperature greatly affects their electronic bandstructure and luminescence properties. It is important to understand how-and-why the characteristics of NPLs are influenced, particularly at elevated temperature, where both reversible and irreversible quenching processes come into picture. Here we present a study on the effect of elevated temperature on the characteristics of colloidal CdSe NPLs. We used an effective-mass envelope function theory based 8-band k$\cdot$p model and density-matrix theory considering exciton-phonon interaction. We observed the photoluminescence (PL) spectra at various temperatures for their photon emission energy, PL linewidth and intensity by considering the exciton-phonon interaction with both acoustic and optical phonons using Bose-Einstein statistical factors. With rise in temperature we observed a fall in the transition energy (emission redshift), matrix element, Fermi factor and quasi Fermi separation, with reduction in intraband state gaps and increased interband coupling. Also, there was a fall in the PL intensity, along with spectral broadening due to an intraband scattering effect. The predicted transition energy values and simulated PL spectra at varying temperatures exhibit appreciable consistency with experimental results. Our findings have important implications for application of NPLs in optoelectronic devices, such as NPL lasers and LEDs, operating much above room temperature., Comment: Published in Royal Society of Chemistry, Nanoscale (12 pages, 9 figures)

Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins. The spin parity effect originally demonstrated with the antiparallel spin-polarizations (Mod. Phys. Lett. B28, 145004) still exists for the parallel case. The quantum non-locality does not lead to the violation for integer spins due to the cancellation of non-local interference effects by the quantum statistical-average. Again the violation of BIs seems a result of the measurement induced nontrivial Berry-phase for half-integer spins.

Formation of low-resistance metal contacts is the biggest challenge that masks the intrinsic exceptional electronic properties of 2D WSe2 devices. We present the first comparative study of the interfacial properties between ML/BL WSe2 and Sc, Al, Ag, Au, Pd, and Pt contacts by using ab initio energy band calculations with inclusion of the spin-orbital coupling (SOC) effects and quantum transport simulations. The interlayer coupling tends to reduce both the electron and hole Schottky barrier heights (SBHs) and alters the polarity for WSe2-Au contact, while the SOC chiefly reduces the hole SBH. In the absence of the SOC, Pd contact has the smallest hole SBH with a value no less than 0.22 eV. Dramatically, Pt contact surpasses Pd contact and becomes p-type Ohmic or quasi-Ohmic contact with inclusion of the SOC. Our study provides a theoretical foundation for the selection of favorable metal electrodes in ML/BL WSe2 devices.

Recently, phosphorene electronic and optoelectronic prototype devices have been fabricated with various metal electrodes. We systematically explore for the first time the contact properties of monolayer (ML) phosphorene with a series of commonly used metals (Al, Ag. Cu, Au, Cr, Ni, Ti, and Pd) via both ab initio electronic structure calculations and more reliable quantum transport simulations. Strong interactions are found between all the checked metals, with the energy band structure of ML phosphorene destroyed. In terms of the quantum transport simulations, ML phosphorene forms a n-type Schottky contact with Au, Cu, Cr, Al, and Ag electrodes, with electron Schottky barrier heights (SBHs) of 0.30, 0.34, 0.37, 0.51, and 0.52 eV, respectively, and p-type Schottky contact with Ti, Ni, and Pd electrodes, with hole SBHs of 0.30, 0.26, and 0.16 eV, respectively. These results are in good agreement with available experimental data. Our findings not only provide an insight into the ML phosphorene-metal interfaces but also help in ML phosphorene based device design.

Although many prototype devices based on two-dimensional (2D) MoS2 have been fabricated and wafer scale growth of 2D MoS2 has been realized, the fundamental nature of 2D MoS2-metal contacts has not been well understood yet. We provide a comprehensive ab initio study of the interfacial properties of a series of monolayer (ML) and bilayer (BL) MoS2-metal contacts (metal = Sc, Ti, Ag, Pt, Ni, and Au). A comparison between the calculated and observed Schottky barrier heights (SBHs) suggests that many-electron effects are strongly suppressed in channel 2D MoS2 due to a charge transfer. The extensively adopted energy band calculation scheme fails to reproduce the observed SBHs in 2D MoS2-Sc interface. By contrast, an ab initio quantum transport device simulation better reproduces the observed SBH in the two types of contacts and highlights the importance of a higher level theoretical approach beyond the energy band calculation in the interface study. BL MoS2-metal contacts have a reduced SBH than ML MoS2-metal contacts due to the interlayer coupling and thus have a higher electron injection efficiency., Comment: 36 pages, 13 figures, 3 tables

In this Letter, a tunable valley polarization is investigated for honeycomb systems with broken inversion symmetry such as transition-metal dichalcogenide MX2 (M = Mo, W; X = S, Se) monolayers through elliptical pumping. As compared to circular pumping, elliptical pumping is more universal and effective method to create coherent valley polarization. When two valleys of MX2 monolayers are doped or polarized, a novel anomalous valley orbital magnetic moment Hall effect driven by opposite Berry curvatures at different valleys is predicted and can generate orbital magnetic moment current without the accompaniment of a charge current, opening a new avenue for exploration of valleytronics and orbitronics. Valley orbital magnetic moment Hall effect is expected to obscure spin Hall effect and is tunable under elliptical pumping.

Using the tight-binding method in combination with first-principles calculations, we systematically derive a low-energy effective Hilbert subspace and Hamiltonian with spin-orbit coupling for two-dimensional hydrogenated and halogenated group-V monolayers. These materials are proposed to be giant-gap quantum spin Hall insulators with record huge bulk band gaps opened by the spin-orbit coupling at the Dirac points, e.g., from 0.74 to 1.08 eV in Bi\textit{X} (\textit{X} = H, F, Cl, and Br) monolayers. We find that the low-energy Hilbert subspace mainly consists of $p_{x}$ and $p_{y}$ orbitals from the group-V elements, and the giant first-order effective intrinsic spin-orbit coupling is from the on-site spin-orbit interaction. These features are quite distinct from those of group-IV monolayers such as graphene and silicene. There, the relevant orbital is $p_z$ and the effective intrinsic spin-orbit coupling is from the next-nearest-neighbor spin-orbit interaction processes. These systems represent the first real 2D honeycomb lattice materials in which the low-energy physics is associated with $p_{x}$ and $p_{y}$ orbitals. A spinful lattice Hamiltonian with an on-site spin-orbit coupling term is also derived, which could facilitate further investigations of these intriguing topological materials., Comment: 4 figures

Large bulk band gap is critical for application of the quantum spin Hall (QSH) insulator or two dimensional (2D) topological insulator (TI) in spintronic device operating at room temperature (RT). Based on the first-principles calculations, here we predict a group of 2D topological insulators BiX/SbX (X = H, F, Cl, and Br) monolayers with extraordinarily large bulk gaps from 0.32 to a record value of 1.08 eV. These giant-gaps are entirely due to the result of strong spin-orbit interaction related to px and py orbitals of Bi/Sb atoms around the two valley K and K' of honeycomb lattice, which is different significantly from the one consisted of pz orbital just like in graphene/silicene. The topological characteristic of BiX/SbX monolayers is confirmed by the calculated nontrivial Z2 index and an explicit construction of the low energy effective Hamiltonian in these systems. We show that the honeycomb structures of BiX monolayers remain stable even at a temperature of 600 K. These features make the giant-gap TIs BiX/SbX monolayers an ideal platform to realize many exotic phenomena and fabricate new quantum devices operating at RT. Furthermore, biased BiX/SbX monolayers become a quantum valley Hall insulator, showing valley-selective circular dichroism., Comment: 7 pages, 5 figures

We in this Letter derive analytic formulas of Bell correlations in terms of quantum probability statistics under the assumption of measuring outcome-independence. For a spin-1/2 singlet state we find analytically that the violations of Bell-type inequalities are really related to the quantum non-local correlations. However, the Bell and Clauser-Horne-Shimony-Holt (CHSH) inequalities are always satisfied for the spin-1 singlet states. More generally the quantum non-locality does not lead to the violation of Bell and CHSH inequalities for the integer-spin singlet since the non-local interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spin singlets due to the nontrivial Berry phase, and thus the relevant Bell-type inequalities can be violated. Specifically, our generic observations can be experimentally tested with the entangled photon-pairs. Our arguments are based on the spin-singlet states, but could be generalized to other bipartite quantum states.