Simplicity out of complexity: band structure for W$_{20}$O$_{58}$ superconductor

The band structure, density of states, and the Fermi surface of a recently discovered superconductor, oxygen-deficient tungsten oxide WO$_{2.9}$ that is equivalent to W$_{20}$O$_{58}$, studied within the density functional theory (DFT) in the generalized gradient approximation (GGA). Here we show that despite the extremely complicated structure containing 78 atoms in the unit cell, the low-energy band structure is quite feasible. Fermi level is crossed by no more than 10 bands per one spin projection (and even 9 bands per pseudospin projection when the spin-orbit coupling is considered) originating from the $d$-orbitals of tungsten atoms forming zigzag chains.