Electronic structures of spin-orbit-coupled metal candidate PbRe$_2$O$_6$: one dimensionality and molecular orbital formation

We present a first-principles investigation of the electronic structure of the inversion-symmetry-broken spin-orbit-coupled metal candidate PbRe$_2$O$_6$. Our calculations reveal that the Fermi surfaces derived from the $d_{yz}$ and $d_{zx}$ orbitals exhibit pronounced one-dimensional characteristics, which naturally account for the highly anisotropic charge transport observed experimentally. In addition, the $d_{x^2-y^2}$ orbitals on each Re haxagon form molecular orbitals, where the resulting $E_g$ molecular states generate nearly dispersionless bands in close proximity to the Fermi level. The coexistence of these quasi-1D Fermi surfaces and molecular-orbital-induced flat bands provides a possible microscopic origin for the successive phase transitions observed in PbRe$_2$O$_6$.