A neck-collapsing-type lifshitz transition induced by orbital symmetry breaking in lightly hole doped t _2g bands

We report on a new type of orbital symmetry breaking in the CoO ₂ triangular lattice with hole doped t _2g bands. Unrestricted Hartree-Fock calculations on a multi-orbital d-p Hamiltonian show that, in the lightly hole doped t _2g bands, the é _g orbitals are fully occupied with a circular charge distribution, and the doped holes in the a _1g band form a hole pocket sandwiched by two concentric Fermi surfaces with sixfold (and almost continuous) rotational symmetry. This symmetric state has an instability to an anisotropic state with twofold rotational symmetry, where the hole pocket is split into two pieces. This transition is governed by the anisotropic interaction between the a _1g and é _g orbitals.