Singlet-bipolaron formation among degenerate electronic orbitals: Softening bipolarons

Bipolaron formation among degenerate electronic orbitals is considered. Symmetry-breaking deformations that lift the electronic degeneracy are shown to be required to stabilize a singlet with respect to a triplet. These symmetry-breaking deformations mix singlet states of the undeformed system. Mixing singlets of different energies causes the electronic energy of the lowest-energy singlet to fall nonlinearly with symmetry-breaking deformations. Through this nonlinearity, a singlet pair of the lowest energy not only fosters symmetry-breaking deformations but also reduces the stiffness constants of these symmetry-breaking distortions. The concomitant singlet-induced lowering of the vibrational frequencies reduces the vibrational free energy. Thus, singlet-induced atomic displacements and vibrational softening both contribute to lowering the free energy of a singlet bipolaron below that of a triplet and of two separated polarons. At strong enough electron-lattice coupling, stabilization of a singlet bipolaron is driven mainly by symmetry-breaking shifts of atoms' equilibrium positions. This singlet bipolaron is a variant of a conventional bipolaron whose stabilization with respect to a triplet requires symmetry-breaking deformations. However, stabilization of a singlet bipolaron at moderate coupling results primarily from singlet-induced reductions of the frequencies of symmetry-breaking vibrations. This type of bipolaron is defined as a ``softening'' bipolaron. Distinctive properties of a softening bipolaron enable it to be identified. Most prominently, softening bipolarons can lack the polaronic absorption bands that characterize conventional bipolarons. In addition, the Seebeck coefficients of softening bipolarons garner a distinctive contribution from singlet-induced softening of vibrational modes. Observation of these effects for boron carbides' singlet bipolarons suggests that they are examples of softening bipolarons.