The charge density wave (CDW) state of $2H\text{−}{\mathrm{NbSe}}_2$ features commensurate domains separated by domain boundaries accompanied by phase slips known as discommensurations. We have unambiguously visualized the structure of CDW domains using a displacement-field measurement algorithm on a scanning tunneling microscopy image. Each CDW domain is delimited by three vertices and three edges of discommensurations and is designated by a triplet of integers whose sum identifies the types of commensurate structure. The observed structure is consistent with the alternating triangular tiling pattern predicted by a phenomenological Landau theory. The domain shape is affected by crystal defects and also by topological defects in the CDW phase factor. Our results provide a foundation for a complete understanding of the CDW state and its relation to the superconducting state.

In this study, we investigate the bulk electronic structure of Pb-substituted ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ single crystals, using two types of hard x-ray spectroscopy. High-energy-resolution fluorescence-detected x-ray absorption spectroscopy revealed a spectral change at low temperatures. Using density functional theory (DFT) simulations, we find that the temperature-induced change originates from a structural phase transition, similar to the pressure-induced transition in ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$. This finding suggests that the mechanism of bulk superconductivity induced by Pb substitution is the same as that under high pressure. Furthermore, a low-valence state with a mixture of divalent and trivalent Bi ions is discovered using hard x-ray photoemission spectroscopy with the aid of DFT calculations.

First-principles calculations for underdoped La_2−xSr_xCuO₄ (LSCO) have revealed a Fermi surface consisting of spin-triplet (KS) particles at the antinodal Fermi-pockets and spin-singlet (SS) particles at the nodal Fermi-arcs in the presence of AF local order. By performing a unique method of calculating the electronic-spin state of overdoped LSCO and by measurement of the spin-correlation length by neutron inelastic scattering, the origin of the phase-diagram, including the pseudogap phase in the high temperature superconductor, Sr-doped copper-oxide LSCO, has been elucidated. We have theoretically solved the long-term problem as to why the angle-resolved photoemission spectroscopy (ARPES) has not been able to observe Fermi pockets in the Fermi surface of LSCO. As a result, we show that the pseudogap region is bounded below the characteristic temperature T*(x) and above the superconducting transition temperature T_c(x) in the T vs. x phase diagram, where both the AF order and the KS particles in the Fermi pockets vanish at T*(x), whilst KS particles contribute to d-wave superconductivity below T_c. We also show that the relationship T*(x_c) = T_c(x_c) holds at x_c = 0.30, which is consistent with ARPES experiments. At T*(x), a phase transition occurs from the pseudogap phase to an unusual metallic phase in which only the SS particles exist.