The current study aims to investigate the particular case of two zeros in a Majorana neutrino mass matrix based on A_(4) symmetry,where charged lepton mass matrix is diagonal.The texture is M_(ν)^(S7) with(μ,μ)and(...The current study aims to investigate the particular case of two zeros in a Majorana neutrino mass matrix based on A_(4) symmetry,where charged lepton mass matrix is diagonal.The texture is M_(ν)^(S7) with(μ,μ)and(τ,τ)vanishing element of the neutrino mass matrix.The texture M_(ν)^(S7) has magic and μ−τsymmetry,with a tribimaximal form of the mixing matrix,which leads to θ_(13)=0 that it is not consistent with experimental data and at first,does not seem to be allowed.Since θ_(13) a small mixing angle compared to others neutrino mixing angles justifies the use of perturbation theory.We propose that,θ_(13),and the Dirac phase δ,and two Majorana phases ρ and σ could be generated by using a complex symmetric perturbation mass matrix in the mass basis and find that δm^(2)≡m_(2)^(2)-m_(1)^(2)≠0affect to the atmospheric mixing angle.We show that only the predictions of the case I,with Δ<0 and Re(α)<0,are consistent with the experimental data.Furthermore,the allowed range of our parameter space and complex elements of perturbation mass matrix are found,which led to finding the allowed region of the neutrino masses,the Majorana phases,the effective neutrino mass for the neutrinoless double beta decay,the allowed deviation of θ_(23) from 45°,and to predict the normal neutrino mass hierarchy.The predicted region of<m_(νββ)> and θ_(23) are in line with the current experimental data which indicate the accuracy of our model and its results.The results of the case II,with Δ>0 and Re(α)>0,are ruled out.展开更多
Based on irreducible representations(or symmetry eigenvalues) and compatibility relations(CR), a material can be predicted to be a topological/trivial insulator(satisfying CR) or a topological semimetal(violating CR)....Based on irreducible representations(or symmetry eigenvalues) and compatibility relations(CR), a material can be predicted to be a topological/trivial insulator(satisfying CR) or a topological semimetal(violating CR). However, Weyl semimetals(WSMs) usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy CR, or if the symmetry indicators are zero. In this work, we propose a new topological invariant v for the systems with S4 symmetry(i.e., the improper rotation S_(4)(≡IC_(4z)) is a proper fourfold rotation(C_(4z)) followed by inversion(I)), which can be used to diagnose the WSM phase. Moreover, v can be easily computed through the onedimensional Wilson-loop technique. By applying this method to the high-throughput screening in our first-principles calculations, we predict a lot of WSMs in both nonmagnetic and magnetic compounds.Various interesting properties(e.g., magnetic frustration effects, superconductivity and spin-glass order,etc.) are found in predicted WSMs, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states.展开更多
文摘The current study aims to investigate the particular case of two zeros in a Majorana neutrino mass matrix based on A_(4) symmetry,where charged lepton mass matrix is diagonal.The texture is M_(ν)^(S7) with(μ,μ)and(τ,τ)vanishing element of the neutrino mass matrix.The texture M_(ν)^(S7) has magic and μ−τsymmetry,with a tribimaximal form of the mixing matrix,which leads to θ_(13)=0 that it is not consistent with experimental data and at first,does not seem to be allowed.Since θ_(13) a small mixing angle compared to others neutrino mixing angles justifies the use of perturbation theory.We propose that,θ_(13),and the Dirac phase δ,and two Majorana phases ρ and σ could be generated by using a complex symmetric perturbation mass matrix in the mass basis and find that δm^(2)≡m_(2)^(2)-m_(1)^(2)≠0affect to the atmospheric mixing angle.We show that only the predictions of the case I,with Δ<0 and Re(α)<0,are consistent with the experimental data.Furthermore,the allowed range of our parameter space and complex elements of perturbation mass matrix are found,which led to finding the allowed region of the neutrino masses,the Majorana phases,the effective neutrino mass for the neutrinoless double beta decay,the allowed deviation of θ_(23) from 45°,and to predict the normal neutrino mass hierarchy.The predicted region of<m_(νββ)> and θ_(23) are in line with the current experimental data which indicate the accuracy of our model and its results.The results of the case II,with Δ>0 and Re(α)>0,are ruled out.
基金supported by the National Natural Science Foundation of China (11974395,11674369, and 11925408)the Strategic Priority Research Program of Chinese Academy of Sciences (CAS XDB33000000)+2 种基金the Center for Materials Genomesupport from the National Key Research and Development Program of China (2016YFA0300600, 2016YFA0302400, and 2018YFA0305700)the K. C. Wong Education Foundation (GJTD-2018-01)。
文摘Based on irreducible representations(or symmetry eigenvalues) and compatibility relations(CR), a material can be predicted to be a topological/trivial insulator(satisfying CR) or a topological semimetal(violating CR). However, Weyl semimetals(WSMs) usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy CR, or if the symmetry indicators are zero. In this work, we propose a new topological invariant v for the systems with S4 symmetry(i.e., the improper rotation S_(4)(≡IC_(4z)) is a proper fourfold rotation(C_(4z)) followed by inversion(I)), which can be used to diagnose the WSM phase. Moreover, v can be easily computed through the onedimensional Wilson-loop technique. By applying this method to the high-throughput screening in our first-principles calculations, we predict a lot of WSMs in both nonmagnetic and magnetic compounds.Various interesting properties(e.g., magnetic frustration effects, superconductivity and spin-glass order,etc.) are found in predicted WSMs, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states.
