Superlight small bipolarons from realistic long-range Coulomb and Fröhlich interactions

We report analytical and numerical results on the two-particle states of the polaronic $t$-$J_p$ model derived recently with realistic Coulomb and electron-phonon (Fröhlich) interactions in doped polar insulators. Eigenstates and eigenvalues are calculated for two different geometries. Our results show that the ground state is a bipolaronic singlet, made up of two polarons. The bipolaron size increases with increasing ratio of the polaron hopping integral $t$ to the exchange interaction $J_p$ but remains small in the whole range $0⩽t/J_p⩽1$. Furthermore, the model exhibits a phase transition to a superconducting state with a critical temperature well in excess of 100 K since the small bipolarons are perfectly mobile. In the range $t/J_p⩽1$, there are distinct charge and spin gaps opening in the density of states, specific heat, and magnetic susceptibility well above $T_c$.

Figure 1

Probability of finding two polarons on the nearest-neighbor sites: $P_{bp}$ (squares), on more distant sites (circles) and on the same site (triangles) in the ground state of the $t$-$J_p$ Hamiltonian for chain (a) and zigzag ladder (b).

Figure 2

Two-particle ground-state energy $E_0$ as a function of the hopping. Symbols correspond to ED (squares and triangles) and variational (crosses) data on finite clusters. We also report (circles) the results at $k=0$ obtained by diagonalizing $\widehat{H}\left(k\right)$ given in Eq. (6).

Figure 3

Ratio of bipolaron to polaron mass (left panel) in the $t$-$J_p$ model for different lattices and the resulting critical temperature (right panel) estimated with this mass at $n_b=0.01/a^2$ and $J_p=1.0$ eV. For the zigzag ladder we report both the results obtained by using the linear-$t$ dispersion[11] (dashed line) and the complete one (squares) calculated numerically from (6) by diagonalizing $\widehat{H}\left(k\right)$.

Figure 4

Signatures of a pseudogap opening in ODOS for different values of the polaron hopping (left panel) and temperature (right panel) calculated for the chain with a Gaussian broadening $\delta =0.01J_p$, modeling a disorder effect in the $\delta$ function in Eq. (11).