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AIP conference proceedings

Interplay between on-site electron-phonon interaction and inter-site Coulomb repulsion

Subhadip Nath, N. S. Mondal, K. Roy, Nanda Kumar Ghosh

Published Jan 1, 2016• 0 citations
Publisher

Abstract

We present a numerical study on the interplay between on-site electron-phonon (EP) interaction and inter-site Coulomb repulsion in the U/t =0.0 limit on a small cluster. Results show the formation of only S0 bipolarons. However, two polarons or bipolarons can be present at distances |i-j|=2. It is observed that inter-site Coulomb repulsion may favor formation of S0 bipolarons.

DOI
10.1063/1.4947996

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We present a numerical study on the interplay between on-site electron-phonon (EP) interaction and inter-site Coulomb repulsion in the U/t =0.0 limit on a small cluster. Results show the formation of only S0 bipolarons. However, two polarons or bipolarons can be present at distances |i-j|=2. It is observed that inter-site Coulomb repulsion may favor formation of S0 bipolarons.
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).
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.
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.
Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii-Kosterlitz-Thouless transition temperature T c of bipolarons on a two-dimensional square lattice. We study the bond Su-Schrieffer-Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature [C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof’ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, ]. Here, we find that long-range Coulomb repulsion suppresses the optimal T c but leaves it appreciable over a broad parameter window, including the adiabatic regime ω / t = 0.5 at a representative Coulomb strength V = U / 10 (with U the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit T c estimates in the presence of long-range repulsion.
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