We show how an accurate first-principles treatment of the antiferromagnetic ground state of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ can be obtained without invoking any free parameters such as the Hubbard $U$. The magnitude and orientation of our theoretically predicted magnetic moment of $0.495{\mu }_B$ on Cu sites along the (100) direction are in excellent accord with experimental results. The computed values of the band gap (1.00 eV) and the exchange coupling ($-138$ meV) match the corresponding experimental values. We identify interesting band splittings below the Fermi energy, including an appreciable Hund's splitting of 1.25 eV. The magnetic form factor obtained from neutron scattering experiments is also well described by our calculations. Our study thus opens up a pathway for first-principles investigations of electronic and atomic structures and phase diagrams of cuprates and other complex materials.

Significance: High-temperature superconductivity, first discovered in materials with copper-oxide planes, is still not well understood. Cuprates exhibit complex phase diagrams under temperature and doping and have not been amenable to first-principles description using previous density functionals, but the recent SCAN functional correctly predicts many properties of the undoped and doped YBCO compounds. In the oxygen-doped YBa ₂ Cu ₃ O ₇ , SCAN finds many competing states with charge and spin stripes. Thermal energies will mix these states, creating fluctuations of the spin moments on the copper atoms in the pseudogap phase from which superconductivity emerges. Our study suggests a paradigm in which the physics of the mysterious pseudogap phase in the cuprates is encoded through a landscape of underlying competing phases in the material.

Optical measurements and band structure calculations are reported on three-dimensional Dirac materials. The electronic properties associated with the Dirac cone are identified in the reflectivity spectra of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ and ${\mathrm{Na}}_3\mathrm{Bi}$ single crystals. In ${\mathrm{Na}}_3\mathrm{Bi}$, the plasma edge is found to be strongly temperature dependent due to thermally excited free carriers in the Dirac cone. The thermal behavior provides an estimate of the Fermi level $E_F=25$ meV and the $z$-axis Fermi velocity $v_z=0.3$ eV Å associated with the heavy bismuth Dirac band. At high energies above the $\mathrm{\Gamma }$-point Lifshitz gap energy, a frequency- and temperature-independent ${\epsilon }_2$ indicative of Dirac cone interband transitions translates into an ab-plane Fermi velocity of 3 eV Å. The observed number of IR phonons rules out the $P{6}_3/mmc$ space-group symmetry but is consistent with the $P\overline{3}c1$ candidate symmetry. A plasmaron excitation is discovered near the plasmon energy that persists over a broad range of temperature. The optical signature of the large joint density of states arising from saddle points at $\mathrm{\Gamma }$ is strongly suppressed in ${\mathrm{Na}}_3\mathrm{Bi}$, consistent with band structure calculations that show the dipole transition-matrix elements to be weak due to the very small $s$-orbital character of the Dirac bands. In ${\mathrm{Cd}}_3{\mathrm{As}}_2$, a distinctive peak in reflectivity due to the logarithmic divergence in ${\epsilon }_1$ expected at the onset of Dirac cone interband transitions is identified. The center frequency of the peak shifts with temperature quantitatively consistent with a linear dispersion and a carrier density of $n=1.3\times {10}^{17}{\text{cm}}^{-3}$. The peak width gives a measure of the Fermi-velocity anisotropy of $10\%$, indicating a nearly spherical Fermi surface. The line shape gives an upper bound estimate of 7 meV for the potential fluctuation energy scale.

We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functional for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally.

The layered crystal structures of cuprates enable collective charge excitations fundamentally different from those of three-dimensional metals. Acoustic plasmons have been observed in electron-doped cuprates by resonant inelastic x-ray scattering (RIXS); in contrast, the characteristics of acoustic plasmons in hole-doped cuprates are under debate, despite extensive measurements. This contrast led us to investigate the charge excitations of hole-doped cuprate ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$. Here we present incident-energy-dependent RIXS measurements and calculations of collective charge response via the loss function to reconcile the issues above. Our results provide evidence for the acoustic plasmons of Zhang-Rice singlet (ZRS), which has a character of the Cu $3d_{x^2-y^2}$ strongly hybridized with the O $2p$ orbitals; the metallic behavior is implied to result from the movement of ZRS rather than the simple hopping of O $2p$ holes.

Recent progress in the synthesis of monolayer MoS₂, a two-dimensional direct band-gap semiconductor, is paving new pathways toward atomically thin electronics. Despite the large amount of literature, fundamental gaps remain in understanding electronic properties at the nanoscale. Here, we report a study of highly crystalline islands of MoS₂ grown via a refined chemical vapor deposition synthesis technique. Using high resolution scanning tunneling microscopy and spectroscopy (STM/STS), photoemission electron microscopy/spectroscopy (PEEM) and μ-ARPES we investigate the electronic properties of MoS₂ as a function of the number of layers at the nanoscale and show in-depth how the band gap is affected by a shift of the valence band edge as a function of the layer number. Green’s function based electronic structure calculations were carried out in order to shed light on the mechanism underlying the observed bandgap reduction with increasing thickness, and the role of the interfacial Sulphur atoms is clarified. Our study, which gives new insight into the variation of electronic properties of MoS₂ films with thickness bears directly on junction properties of MoS₂, and thus impacts electronics application of MoS₂.