Vibronic pairing models for high-Tcsuperconductors

Vibronic polarons: Self‐trapping, local rotation, and band features

“…Another interaction constant (−) leads to vibronic polaron pairing into bipolarons or Cooper pairs 16: which renormalizes to Within the frameworks of the present model, two electrons repel each other through Coulomb interaction if in the same band, while attracting each other via dipole–dipole coupling if in the different bands. An alternative dipole–dipole repulsion constant is obtained with the opposite sign (+) to the dipolar term.…”

“…Vibronic polarons form following electron self‐trapping and subsequent relaxation to an off‐center state. The two‐band electron–phonon Hamiltonian in site representation is extended so as to incorporate pairing interactions and terms higher‐order in the electron‐mode coupling 16–18. Here, i , j , l are site labels, μ, μ′, μ″; ν, ν′, ν″ = g , u are band labels, a ( a ig ) creates (annihilates) a g ‐band electron at site i , while a ( a lu ) does so for a u ‐band electron at site I .…”

“…Excluding the lattice to adiabatic approximation involves solving for the electronic eigenvalues, depending parametrically on the nuclear coordinates, and then using the average electronic energies as potentials for the nuclear motion. This adiabatic procedure leads to a renormalized electronic Hamiltonian providing for both hopping and pairing in a quantized field of small polarons (details to be found elsewhere) 16: Renormalized equations for t llgu ˆ, ϵ l μ ˆ, and ω llgu ˆ hold good locally along the mixing‐mode coordinate Q llgu at Q ij μμ = 0. Similar equations hold good for quantities renormalized through coupling to the intersite modes Q ij μμ at Q llgu = 0 although now the Coulomb energy enters in lieu of the dipole–dipole term.…”

“…Because of the local mixing, the renormalized hopping term J ij μν ˆ splits into two components: onsite tunneling t llgu ˆ and intersite hopping J ijμμ ˆ. The pairing constant gives rise to a van der Waals binding energy 16: is the vibronic polarizability, where E gu ˆ = 2 J llgu ˆ, while is the electronic polarizability. a gu ˆ and a gu correspond to the low‐ and high‐frequency limits of polarizability, respectively 4.…”

Revisited vibronic model for Li+ ion and F A (Li) centre in alkali halides

“…Using semicontinuum arguments [23] We see that F centre polarizabilities of the order of a unit cell volume are computed by the semicontinuum method. The above static values should be corrected for the adiabatic changes of both wave functions and electronic energies, as the F centre falls either into the ground-or excited-state configurations of the lattice.…”