Strongly bound yet light bipolarons for double-well electron-phonon coupling

We use the momentum average approximation to study the ground-state properties of strongly bound bipolarons in the double-well electron-phonon (el-ph) coupling model, which describes certain intercalated lattices where the linear term in the el-ph coupling vanishes due to symmetry. We show that this model predicts the existence of strongly bound yet lightweight bipolarons in some regions of the parameter space. This provides an alternative mechanism for the appearance of such bipolarons, in addition to long-range el-ph coupling and special lattice geometries.

Figure 1

Sketch of the crystal structures discussed in this work: (a) 1D chain, and (b) 2D plane, consisting of light atoms (filled circles) intercalated between heavy atoms (empty circles). In the absence of carriers, the ionic potential of a light atom is a simple harmonic well. In the presence of a carrier, the ionic potential of the light atom hosting it remains an even function of its longitudinal dis- placement, so the linear el-ph coupling vanishes. In suitable conditions the effective ionic potential becomes a double well. (Reproduced from Ref. [24].)

Figure 2

(a) Bipolaron ground-state energy, and (b) inverse effective mass for $t=1,\Omega =0.5,g_4=0.1$, computed with ED (solid black line) and MA (red dots).

Figure 3

Ground-state properties (total energy and inverse mass) of the $S0$ bipolaron and two independent polarons for $t=1,\Omega =0.5$ and $g_4=0.2,0.1$, and $0.05$ for (a), (b), and (c), respectively. For all panels, $U=0$.

Figure 4

Ground-state properties (total energy and inverse mass) of the $S0$ bipolaron and two independent polarons for $t=1,\Omega =2$ and $g_4=0.2,0.1$, and $0.05$ for (a), (b), and (c), respectively. For all panels, $U=0$.

Figure 5

Binding energy $\Delta$ and effective-mass ratio $m_{\mathrm{bp}}/2m_{\mathrm{p}}$ of the bipolarons for $\Omega =0.5$ and $\Omega =2$ at different values of $g_4$.

Figure 6

Ionic potential (above) and ionic ground-state wave function (below) in the single-well and double-well models. Solid lines correspond to the situation without an additional carrier, and dashed lines to the situation with an additional carrier.

Figure 7

Bipolaron energy (left) and effective mass (right) as a function of the Hubbard $U$, for $t=1,\Omega =0.4$ and $g_4=0.1$. Similar results are found for other parameters if $U$ is not large enough to lead to bipolaron dissociation.