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AIP conference proceedings

Bipolaron by inter-site electron-phonon interaction

N. S. Mondal, Subhadip Nath, S. Bose, M. Paul

Published Jan 1, 2013• 1 citation
Publisher

Abstract

An exact diagonalization calculation of the Hubbard model with inter-site electron-phonon interaction on a 2D square cluster shows that inter-site electron-phonon interaction effectively creates on-site (S0) bipolaron. There is also formation of neighboring site (S1) bipolaron. Entropy calculation shows that system goes into more ordered state with the formation of these self-trapped bipolaron.

DOI
10.1063/1.4791285

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An exact diagonalization calculation of the Hubbard model with inter-site electron-phonon interaction on a 2D square cluster shows that inter-site electron-phonon interaction effectively creates on-site (S0) bipolaron. There is also formation of neighboring site (S1) bipolaron. Entropy calculation shows that system goes into more ordered state with the formation of these self-trapped bipolaron.
An exact diagonalization study of the 2D Hubbard model extended with nearest neighbor (NN) phonon mediated interaction shows an interplay between on-site Coulomb interaction and intersite electron-phonon interaction. Initially, phonon mediated interaction between electrons is suppressed by onsite Coulomb repulsion. But after certain larger strength (depending on U) of phonon mediated interaction there is an effective attraction between electrons which forms onsite bipolaron (S0) and neighboring site bipolaron (S1).
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.
Effect of on-site hole-phonon (h-ph) interaction within Holstein t-J model has been examined numerically using exact diagonalization (ED) technique within an 8 – site tilted square cluster at a hole doping <h>=0.25. We have applied periodic boundary conditions to obtain the basis states. It appears that with the increase of on-site h-ph interaction λ1 as well as phonon energy ω0, the ground state energy of the system reduces. Also, the enhancement of the number of phonons results in a significant decrease in ground state energy. At higher temperature, entropy decreases with λ1 as a result of the formation of S0 bipolarons. Low temperature specific heat indicates non-Fermi liquid behavior of the system.
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.
The influence of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the polaron and bipolaron formation in a square Hubbard-Holstein model is investigated within a variational approach. The results for electron-phonon and electron-electron correlation functions show that a negative value of ${t}^{\ensuremath{'}}$ induces a strong anisotropy in the lattice distortions favoring the formation of nearest-neighbor intersite bipolaron. The role of ${t}^{\ensuremath{'}},$ electron-phonon and electron-electron interactions is briefly discussed in view of the formation of charged striped domains.