Two noncentrosymmetric ternary pnictides, CaAgP and CaAgAs, are reported as topological line-node semimetals protected solely by mirror-reflection symmetry. The band gap vanishes on a circle in momentum space, and surface states emerge within the circle. Extending this study to spin-orbit coupled systems reveals that, compared with CaAgP, a substantial band gap is induced in CaAgAs by large spin-orbit interaction. The resulting states are a topological insulator, in which the Z 2 topological invariant is given by 1; 000. To clarify the Z 2 topological invariants for time-reversal-invariant systems without spatial-inversion symmetry, we introduce an alternative way to calculate the invariants characterizing a line node and topological insulator for mirror-reflection-invariant systems.

We investigate the electronic reconstruction across the tetragonal-orthorhombic structural transition in FeSe by employing polarization-dependent angle-resolved photoemission spectroscopy (ARPES) on detwinned single crystals. Across the structural transition, the electronic structures around the  and M points are modified from four-fold to two-fold symmetry due to the lifting of degeneracy in d xz /d yz orbitals.The d xz band shifts upward at the  point while it moves downward at the M point, suggesting that the electronic structure of orthorhombic FeSe is characterized by a momentum-dependent sign-changing orbital polarization. The elongated directions of the elliptical Fermi surfaces (FSs) at the  and M points are rotated by 90 degrees with respect to each other, which may be related to the absence of the antiferromagnetic order in FeSe. Keywords: PACS:Most of the parent compounds of the iron-based superconductors show the tetragonal-orthorhombic structural transition at T s and the stripe-type antiferromagnetic (AFM) order below T N ( T s ) [1,2]. Near the structural transition, an orbital order defined by the inequivalent electron occupation of 3d xz (xz) and 3d yz (yz) orbitals [3][4][5], has been reported by ARPES [6,7] and X-ray linear dichroism measurements [8] in several parent compounds. Experimental and theoretical studies suggested that the structural transition is caused by the electronic nematicity of the spin [9,10] or orbital [11][12][13] degrees of freedoms. Since superconductivity develops when such complex ordered states are suppressed, it is crucial to understand how the phase transitions couple to each other.In Ba(Fe,Co) 2 As 2 , the spin-driven nematicity has been suggested from the phase diagram in which T s and T N closely follow each other as the carrier is doped [14]. The scaling behavior between the nematic fluctuation and spin fluctuation was also reported by the nuclear magnetic resonance (NMR) and shear modulus measurements [10]. On the other hand, in NaFeAs, the orbital-driven nematicity has been proposed by ARPES [11]. In this compound, the structural transition at T s = 54 K is well separated from the AFM transition at T N = 43 K. Inequivalent shift in the xz/yz orbital bands appearing above T s changes the FSs from four-fold to two-fold symmetric shape [11,15], which may be a possible trigger of the stripe type AFM order and the orthorhombicity [11,16]. The variety of iron-based

Nematicity and magnetism are two key features in Fe-based superconductors, and their interplay is one of the most important unsolved problems. In FeSe, the magnetic order is absent below the structural transition temperature Tstr = 90K, in stark contrast that the magnetism emerges slightly below Tstr in other families. To understand such amazing material dependence, we investigate the spin-fluctuation-mediated orbital order (nxz = nyz) by focusing on the orbital-spin interplay driven by the strong-coupling effect, called the vertex correction. This orbital-spin interplay is very strong in FeSe because of the small ratio between the Hund's and Coulomb interactions (J/Ū ) and large dxz, dyz-orbitals weight at the Fermi level. For this reason, in the FeSe model, the orbital order is established irrespective that the spin fluctuations are very weak, so the magnetism is absent below Tstr. In contrast, in the LaFeAsO model, the magnetic order appears just below Tstr both experimentally and theoretically. Thus, the orbital-spin interplay due to the vertex correction is the key ingredient in understanding the rich phase diagram with nematicity and magnetism in Fe-based superconductors in a unified way.

To understand the nematicity in Fe-based superconductors, nontrivial k-dependence of the orbital polarization (∆Exz(k), ∆Eyz(k)) in the nematic phase, such as the sign reversal of the orbital splitting between Γ-and X,Y-points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole-and electron-pockets are elongated along the ky-and kx-axes respectively, consistently with experiments. In addition, an electron-pocket splits into two Dirac cone Fermi pockets with increasing the orbital polarization. The orbital-order in Fe-based superconductors originates from the strong positive feedback between the nematic orbital order and spin susceptibility. The spontaneous symmetry breaking from C 4 -to C 2 -symmetry, so called the electronic nematic transition, is one of the fundamental unsolved electronic properties in Fe-based superconductors. To explain this nematicity, both the spin-nematic scenario [1][2][3][4][5][6] and the orbital order scenario [7][8][9][10][11][12][13] have been studied intensively. Above the structural transition temperatures T str , large enhancement of the electronic nematic susceptibility predicted by both scenarios [1,10] is actually observed by the measurements of the softening of the shear modulus C 66 [1,10,14,15], Raman spectroscopy, [16][17][18], and in-plane resistivity anisotropy ∆ρ [19].To investigate the origin of the nematicity, FeSe (T c = 9 K) is a favorable system since the electronic nematic state without magnetization is realized below T str = 90 K down to 0 K. Above T str , the antiferromagnetic fluctuations is weak and T -independent according to the NMR [20,21] and neutron scattering [22][23][24] The nontrivial electronic state below T str gives a crucial test for the theories proposed so far. In the orthorhombic phase with (a − b)/(a + b) ∼ 0.3%, large orbital-splitting |E xz − E yz | of order 50 meV is observed at X,Y-points by ARPES studies in BaFe 2 As 2 [30], NaFeAs [31], and FeSe [32][33][34][35][36][37][38][39][40]. Especially, noticeable deformation of the Fermi surfaces (FSs) with C 2 -symmetry is realized in FeSe, because of the smallness of the Fermi momenta. In FeSe, Ref. [38] reports that the orbital splitting E xz − E yz is positive at Γ-point, whereas it is negative at X,Y-points. This sign-reversing orbital splitting is not realized in the non-magnetic orthorhombic phase in NaFeAs [31]. In addition, the e-FS1 at X-point is deformed to two Dirac cone Fermi pockets in thin-film FeSe [37,40]. The aim of this study is to explain these nontrivial electronic states in the orbital-ordered states based on the realistic multiorbital Hubbard model. Microscopically, the orbital order is expressed by the symmetry breaking in the self-energy. In the mean-field level approximations, however, the self-energy is constant in k-space unless large inter-site Coulomb interactions are in...