Using density-functional methods, we study the electronic structure of ${\mathrm{Ba}}_{3}\mathrm{Cu}{\mathrm{Sb}}_{2}{\mathrm{O}}_{9}$, a candidate material for the quantum spin liquid behavior. We study both the triangular lattice as well as the recently proposed hexagonal lattice structures with flipped Cu-Sb dumbbells. The band structure near the Fermi energy is described very well by a tight-binding Hamiltonian involving the Cu (${e}_{g}$) orbitals, confirming their central role in the physics of the problem. A minimal tight-binding Hamiltonian for the triangular structure is presented. The Cu (${d}^{9}$) ions (a single ${e}_{g}$ hole in the band structure) present in the compound are expected to be Jahn-Teller centers, while the nature of the Jahn-Teller distortions in this material is still under debate. Solving a simple model by exact diagonalization, we show that electronic correlation effects in general enhance the tendency towards a Jahn-Teller distortion by reducing the kinetic energy due to correlation effects. Our density-functional calculations do indeed show a significant Jahn-Teller distortion of the $\mathrm{Cu}{\mathrm{O}}_{6}$ octahedra when we include the correlation effects within the Coulomb-corrected GGA+U method, so that the Jahn-Teller effect is correlation driven. We argue for the presence of a random static Jahn-Teller distortion in the hexagonal structure rather than a dynamical one because of the broken octahedral symmetry around the $\mathrm{Cu}{\mathrm{O}}_{6}$ octahedra and the potential fluctuations inherently present in the system caused by a significant disorder, which is believed to be present, in particular, due to the flipped Cu-Sb dumbbells.
The paper contained the following misprints:(1) After Eq. ( 14), k2= -a2E is the correct definition of k2.(2) (a/2) should be replaced by (2a) in Eqs. ( 23) and ( 24).(3) (2a/k) should be replaced by (a/k) in the definition of a in the line following Eq. ( 16).All calculations reported in the original paper were performed with the correct equations and all numerical results and con- clusions remain unchanged.
We show that the exciton photoluminescence line shape in the GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells under pressure is broadened by hybridization of the \ensuremath{\Gamma} exciton with the X and the L continua via electron-phonon coupling. Furthermore, we demonstrate the pressure tuning of the resonance-broadening effect which can be used to extract the electron-phonon coupling parameters directly. For GaAs we estimate the intervalley electron-phonon deformation potential ${\mathit{D}}_{\mathrm{\ensuremath{\Gamma}}\mathit{X}}$ to be 10.7\ifmmode\pm\else\textpm\fi{}0.7 eV/\AA{}. The resonance effect should be observable in other semiconductors as well.
We formulate the photonic band-structure problem for a one-dimensional photonic crystal in terms of the reflection and transmission coefficients, obtaining a transcendental photonic band equation. The reflection and the transmission coefficients may be evaluated by using the standard transfer-matrix method. The structure of the equation reveals the existence of gaps, analogous to the Kronig-Penney model in the electronic band-structure problem. As an example, the photonic band equation is solved for the simple case of the ``Kronig-Penney'' dielectric structure, consisting of alternating slabs of refractive indices ${n}_{1}$ and ${n}_{2}.$