Electronic structure ofBa3CuSb2O9: A candidate quantum spin liquid compound

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.