The bipolaron ground state binding energy and the effective masses are calculated self-consistently in a scheme where the electron-phonon interaction is described by the Fröhlich interaction. We explicitly use the total linear momentum conservation and both two-and three-dimensional systems are considered. We review results for binding energies and show that the bipolaron effective mass increases with the electron-phonon coupling constant α more rapidly than two free polaron masses. As expected, the increase is greater in two than in three dimensions. We estimate the screening effects due to an electronic or hole density n in a range of values such that n R 2 b ≪ 1 (here R b is the bipolaron radius). We find that the bipolaron binding energy decreases with n and eventually becomes positive indicating the existence of a metastable bipolaron state. Finally we discuss the possible connections between our results and high T c superconductivity.
The bipolaron ground state binding energy and the effective masses are calculated self-consistently in a scheme where the electron-phonon interaction is described by the Fröhlich interaction. We explicitly use the total linear momentum conservation and both two-and three-dimensional systems are considered. We review results for binding energies and show that the bipolaron effective mass increases with the electron-phonon coupling constant α more rapidly than two free polaron masses. As expected, the increase is greater in two than in three dimensions. We estimate the screening effects due to an electronic or hole density n in a range of values such that n R 2 b ≪ 1 (here R b is the bipolaron radius). We find that the bipolaron binding energy decreases with n and eventually becomes positive indicating the existence of a metastable bipolaron state. Finally we discuss the possible connections between our results and high T c superconductivity.
The energies of bipolaron states in three- and two-dimensional systems are calculated variationally, treating the electron-phonon interaction in the Fr\"ohlich approximation, and separating the relative motion from the center-of-mass motion. The bipolaron is bound if the electron-phonon coupling constant \ensuremath{\alpha} is larger than 6 in three dimensions and 2 in two dimensions, provided the ratio \ensuremath{\eta}=${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$/${\mathrm{\ensuremath{\epsilon}}}_{0}$ is smaller than a critical value which depends on \ensuremath{\alpha}. The theory yields the free-polaron energies as given in the Lee, Low, and Pines approximation for arbitrary values of the electron-phonon coupling constant \ensuremath{\alpha}. For \ensuremath{\alpha} larger than \ensuremath{\sim}10 and \ensuremath{\sim}4 in the three- and two-dimensional cases, respectively, the lowest free-polaron self-energies are obtained in the strong-coupling approach; it is shown that a trial harmonic envelope wave function, localized both in the center-of-mass and relative coordinates, with a coherent phonon state gives a bound localized bipolaron state of lower energy. It is interesting for application to high-Tc superconductivity that the bipolaron bounds more easily in two dimensions than in three, and that the mean value of the pair radius is a few angstroms. Furthermore, bipolaron states obtained when the linear total momentum is conserved have intrinsically high mobility, which is also an important condition to make the bipolaron mechanism consistent with high-temperature superconductivity.
We present details of a continuous-time quantum Monte Carlo algorithm for the screened Hubbard-Fr\"ohlich bipolaron. We simulate the bipolaron in one dimension with arbitrary interaction range in the presence of Coulomb repulsion, computing the effective mass, binding energy, total number of phonons associated with the bipolaron, mass isotope exponent, and bipolaron radius in a comprehensive survey of the parameter space. We discuss the role of the range of the electron-phonon interaction, demonstrating the evolution from Holstein to Fr\"ohlich bipolarons and we compare the properties of bipolarons with singlet and triplet pairing. Finally, we present simulations of the bipolaron dispersion. The bandwidth of the Fr\"ohlich bipolaron is found to be broad and the decrease in bandwidth as the two polarons bind into a bipolaron is found to be far less rapid than in the case of the Holstein interaction. The properties of bipolarons formed from long-range electron-phonon interactions, such as light strongly bound bipolarons and intersite pairing when Coulomb repulsion is large, are found to be robust against screening, with qualitative differences between Holstein and screened Fr\"ohlich bipolarons found even for interactions screened within a single lattice site.
In this paper we have studied the properties of a two-fermion system interacting with the phonon field in the framework of the Holstein Hubbard model in one, two and three dimensions. We have chosen the modified Lang-Firsov variational wave function with on-site and nearest-neighbour lattice distortion for the phonon subsystem to obtain an effective electronic Hamiltonian. This effective electronic Hamiltonian is then solved exactly to obtain the binding energy and effective mass of the bipolaron. We investigated the stability of the bipolaronic phase by comparing the ground-state energy of a bipolaron and two free polarons. We observed a critical repulsive on-site Hubbard interaction U c below which the bipolaronic phases are stable for a fixed electron-phonon coupling g . In the absence of on-site repulsion, bipolaronic phases are stable over the entire range of electron-phonon coupling for one dimension, whereas there is a critical electron-phonon coupling g c for formation of a stable bipolaron in two and three dimensions.
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 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-U 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.
We have investigated bipolaron formation in the Holstein-Hubbard and the Fr\"ohlich-Hubbard model on a discrete one-dimensional lattice. Phonon enriched basis has been generated by exploiting the idea of the Lang-Firsov transformation, which results in better convergence in the strong coupling regime. The incorporation of the finite-range electron-phonon (e-ph) interaction reduces the bipolaron effective mass. We systematically increase the spatial extent of the e-ph interaction to study the effect of the long-range tail of the Fr\"ohlich model. The electron-electron (e-e) interaction also plays a crucial role in lowering the effective mass for both the Holstein and the Fr\"ohlich bipolarons. In the presence of the extended e-e interaction, the intersite S1 Holstein bipolaron becomes unstable, while the effective mass of the Fr\"ohlich bipolaron becomes significantly reduced for both the spin singlet and triplet cases.