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arXiv:1406.3072 · Physical Review B

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

Clemens P. J. Adolphs, Mona Berciu

Published Aug 28, 2014• 15 citations
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Abstract

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.

DOI
10.1103/physrevb.90.085149

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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.
We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion UUU and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large UUU at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and UUU. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and∕or electron-electron interaction.
Characterizing bipolaron binding, and understanding how it depends on electron-phonon interaction, is crucial to unraveling the nature of emergent many-body states in strongly interacting electron-phonon systems. So far, most studies of bipolarons have been limited to the Holstein model, in which the coupling constant is momentum-independent. The paradigmatic example of momentum-dependent electron-phonon interaction comes from the system in which phonon distortions modify electron hopping, the SSH model. Already individual polarons in the SSH model are richer than the Holstein model counterparts, and feature a phase transition into the finite momentum ground state with increasing electron-phonon interaction. In this paper, we use a variational approach to study bipolarons in the one-dimensional SSH model and discuss their ground state, dispersion, and excitation spectra. We explore the full parameter range of the system, including the adiabatic regime of slow phonons, which was inaccessible to previous theoretical studies. In agreement with earlier studies, we find that in the anti-adiabatic strongly interacting regime, bipolarons have low effective mass. By contrast, in the adiabatic case, we find that increasing electron-phonon interactions results in an exponential increase of the bipolaron mass. We establish the existence of multiple branches of bound excited states of SSH bipolaron and discuss the signatures of these bound states in dynamics. We show that in the anti-adiabatic regime, response functions obey a parity selection rule, that imposes symmetry constraints on the excitation spectra and provides a clear signature of SSH bipolarons.
We employ the diagrammatic Monte Carlo method with a lattice path-integral formulation for both electron and phonon degrees of freedom to investigate the formation and properties of bond polarons and bipolarons on a two-dimensional triangular lattice. In the deep adiabatic regime ($\ensuremath{\omega}/t<1.0$), single polarons remain light with a small effective mass, while bipolarons remain compact and lightweight, resulting in a high superfluid transition temperature Tc{T}_{c}Tc​. We systematically study the dependence of Tc{T}_{c}Tc​ on electron-phonon coupling strength and on-site interaction in the bond bipolaron model. Our results show that a moderate on-site repulsion enhances Tc{T}_{c}Tc​ by stabilizing compact yet lightweight bipolarons, leading to high-Tc{T}_{c}Tc​ superconductivity in the dilute limit. Notably, the triangular lattice sustains relatively high Tc{T}_{c}Tc​ across a wide range of phonon frequencies, outperforming square lattice geometry. This enhancement arises from the higher coordination number and the bond-centered nature of the electron-phonon coupling. These findings suggest that triangular lattice geometry offers a promising platform for realizing high-Tc{T}_{c}Tc​ bipolaronic superconductivity.
We investigate the ground-state properties of the bipolaron coupled to quantum dispersive optical phonons in the one-dimensional Holstein-Hubbard model. We concentrate on the interplay between the phonon dispersion and the Coulomb repulsion and their mutual effect on the bipolaron effective mass, the binding energy, and the phase diagram. Most surprisingly, the sign of the curvature of the optical phonon dispersion plays a decisive role in the bipolaron binding energy in the presence of the Coulomb repulsion UUU. In particular, when the sign of the phonon dispersion curvature matches the sign of the electron dispersion curvature, the bipolaron remains bound in the strong-coupling limit even when $U\ensuremath{\rightarrow}\ensuremath{\infty}$ and the binding emanates from the exchange of phonons between two electrons residing on adjacent sites. At moderate electron-phonon coupling a light bipolaron exists up to large values of UUU. Finally, an intuitive explanation of the role of the phonon dispersion on the bipolaron binding energy is derived using the strong-coupling limit where the binding emanates from the exchange of phonons between two electrons residing on adjacent sites which leads to enhanced stability of bipolarons at elevated Coulomb repulsion.
We numerically and analytically calculate the properties of the bipolaron in an extended Hubbard-Holstein model, which has a longer-range electron-phonon coupling like the Fr\"ohlich model. In the strong-coupling regime, the effective mass of the bipolaron in the extended model is much smaller than the Holstein bipolaron mass. In contrast to the Holstein bipolaron, the bipolaron in the extended model has a lower binding energy and remains bound with substantial binding energy even in the large-UUU limit. In comparison with the Holstein model where only a singlet bipolaron is bound, in the extended Holstein model a triplet bipolaron can also form a bound state. We discuss the possibility of phase separation in the case of finite electron doping.
The case of polaron and bipolaron formation due to electron-phonon coupling was studied on a lattice with soft non-linear intersite interactions. The ground state of a system that consists of one or two electrons coupled to a non-linear lattice was obtained numerically. The binding energy of the bipolaron was examined as a function of the degree of the non-linearity of the lattice. A model was investigated where the interatomic interactions in the lattice are described by a double-well potential. This type of non-linear interaction strongly influences the bipolaron formation and generally improves its stability and increases its binding energy by permitting a local structural change of the lattice.