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Bulk and surface sensitive x-ray spectroscopic techniques are applied in tandem to show that the valence band edge for In₂O₃ is found significantly closer to the bottom of the conduction band than expected on the basis of the widely quoted bulk band gap of 3.75 eV. First-principles theory shows that the upper valence bands of In₂O₃ exhibit a small dispersion and the conduction band minimum is positioned at Γ. However, direct optical transitions give a minimal dipole intensity until 0.8 eV below the valence band maximum. The results set an upper limit on the fundamental band gap of 2.9 eV.

The valence and core levels of In₂O₃ and Sn-doped In₂O₃ have been studied by hard x-ray photoemission spectroscopy (hν=6000 eV) and by conventional Al Kα (hν=1486.6 eV) x-ray photoemission spectroscopy. The experimental spectra are compared with density-functional theory calculations. It is shown that structure deriving from electronic levels with significant In or Sn 5s character is selectively enhanced under 6000 eV excitation. This allows us to infer that conduction band states in Sn-doped samples and states at the bottom of the valence band both contain a pronounced In 5s contribution. The In 3d core line measured at hν=1486.6 eV for both undoped and Sn-doped In₂O₃ display an asymmetric lineshape, and may be fitted with two components associated with screened and unscreened final states. The In 3d core line spectra excited at hν=6000 eV for the Sn-doped samples display pronounced shoulders and demand a fit with two components. The In 3d core line spectrum for the undoped sample can also be fitted with two components, although the relative intensity of the component associated with the screened final state is low, compared to excitation at 1486.6 eV. These results are consistent with a high concentration of carriers confined close to the surface of nominally undoped In₂O₃. This conclusion is in accord with the fact that a conduction band feature observed for undoped In₂O₃ in Al Kα x-ray photoemission is much weaker than expected in hard x-ray photoemission.

We report on the first application of the stochastic Laplacian Heaviside method for computing multiparticle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a set of positive-definite two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the SU(3)-flavor-symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of a≈0.086 fm, lattice volume of L=48a≈4.1 fm and pion mass mπ≈714 MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.

We report the results of a lattice quantum chromodynamics calculation of FK/Fπ using Möbius domain-wall fermions computed on gradient-flowed Nf=2+1+1 highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from 130 400 MeV, four lattice spacings of a∼0.15, 0.12, 0.09 and 0.06 fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the a∼0.06 fm ensemble is helpful, but not necessary to achieve a subpercent determination of FK/Fπ. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of FK+/Fπ+=1.1942(45) with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of |Vus|/|Vud|=0.2311(10).

Bulk and surface sensitive x-ray spectroscopic techniques are applied in tandem to show that the valence band edge for In2O3 is found significantly closer to the bottom of the conduction band than expected on the basis of the widely quoted bulk band gap of 3.75 eV. First-principles theory shows that the upper valence bands of In2O3 exhibit a small dispersion and the conduction band minimum is positioned at Gamma. However, direct optical transitions give a minimal dipole intensity until 0.8 eV below the valence band maximum. The results set an upper limit on the fundamental band gap of 2.9 eV.

Bulk and surface sensitive x-ray spectroscopic techniques are applied in tandem to show that the valence band edge for In2O3 is found significantly closer to the bottom of the conduction band than expected on the basis of the widely quoted bulk band gap of 3.75 eV. First-principles theory shows that the upper valence bands of In2O3 exhibit a small dispersion and the conduction band minimum is positioned at Gamma. However, direct optical transitions give a minimal dipole intensity until 0.8 eV below the valence band maximum. The results set an upper limit on the fundamental band gap of 2.9 eV.

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