Molecular orbital polarization in Na$_2$Ti$_2$Sb$_2$O: a scenario to metal-to-metal phase transition without spontaneous symmetry breaking

We suggest a scenario of partial Fermi surface (FS) gapping related to metal-to-metal phase transition without a spontaneous symmetry breaking. This theory is applied to Na$_2$Ti$_2$Sb$_2$O, where the density polarization of spin-orbital entangled molecular orbitals occurs due to spin-orbit coupling. This is further enhanced by electronic correlations of Ti d-orbitals. Sharp increase of the polarization happens above a critical electronic interaction strength which then gaps out a part of FS made of d-orbitals, while the rest of FS associated with Sb p-orbitals remain almost intact. Experimental implications to test our proposal are also discussed.