Quantum Monte Carlo Simulation of Bipolaron Superconductivity in Extended Hubbard--Holstein models on Face-Centered-Cubic and Body-Centered-Cubic Lattices

TL;DR

This paper examines bipolaron formation and mobility in extended Hubbard-Holstein models on FCC and BCC lattices using a continuous-time path-integral QMC approach. By varying $U$, $\lambda$, and phonon frequency $\omega$, it maps S0 (onsite) and S1 (intersite) pairing regimes, quantifies phonon clouds and bipolaron masses, and estimates the transition temperature $T^*$ for light intersite bipolarons. The study finds that extended EPI can yield intersite and even superlight bipolarons, particularly on FCC lattices where first-order hopping processes enhance mobility, suggesting potential routes to higher $T_c$ in real materials. Retardation effects play a crucial role, and the work discusses implications for fullerides and possible extensions to include next-nearest-neighbor hopping in future analyses.

Abstract

We investigate superlight pairing of bipolarons driven by electron-phonon interactions (EPIs) in face-center-cubic (FCC) and body-center-cubic (BCC) lattices using a continuous-time path-integral quantum Monte Carlo (QMC) algorithm. The EPIs are of the Holstein and extended Holstein types, and a Hubbard interaction is also included. Effects of adiabaticity are calculated. The number of phonons associated with the bipolaron, inverse mass, and radius are calculated and used to construct a phase diagram for bipolaron pairing (identifying the regions of pairing into intersite bipolarons and onsite bipolarons). From the inverse mass we determine that for the extended interaction, there is a region of light pairing associated with intersite bipolarons formed in both BCC and FCC lattices. Intersite bipolarons in the extended model at intermediate phonon frequency and large Coulomb repulsion become superlight due to first order hopping effects. We estimate the transition temperature, determining that intersite bipolarons are associated with regions of high transition temperatures.

Figures (9)

• Figure 1: One-dimensional schematic of (a) the Holstein-Hubbard model and (b) the extended Holstein-Hubbard model with near-neighbour EPI introduced in Ref. boncaehhmbipolaron and studied here. The filled circles, empty circles and dashed oval circles represent the electron Wannier orbitals, lattice ions, and nonzero electron-phonon coupling, respectively. The nearest-neighbour electron sites have overlapping orbitals such that an electron can hop via $t$, and $b$ is the intersite spacing.
• Figure 2: Schematics of different light pair mechanisms. (A) On the triangular lattice, a pair with NN attraction $V'$ moves in the first order of NN hopping $t$. (B) In the resonant case, $V' = U'$, the pair can move in the first order of NN hopping $t$ even on the square lattice. Numbers '1' and '2' indicate hopping order.
• Figure 3: Schematic showing a three-hop loop on an FCC lattice.
• Figure 4: Phase diagram of the extended Holstein model on BCC and FCC lattices shown for three different values of $\gamma=1-\Phi_{\rm NN}/\Phi_{00}$. Calculations are in the adiabatic limit, $\hbar\omega = t$, which corresponds to $\hbar\omega = W/12$ for BCC and $W/16$ for FCC cases. The additional intersite interaction promotes S1 pairing leading to an increase in the size of the S1 region such that it can be found at lower $U$ and $\lambda$. The case $\gamma=1$ corresponds to the Holstein interaction. Lines are a guide to the eye, determined by fitting a cubic curve to the points defining the S0 boundary.
• Figure 5: Number of phonons associated with the bipolaron. Calculations are in the adiabatic limit, $\hbar\omega = t$, which corresponds to $\hbar\omega = W/12$ for BCC and $W/16$ for FCC cases. An abrupt change in the number of phonons corresponds to the boundary between S0 and S1 bipolarons. There are approximately 50% more phonons associated with the FCC lattice due to the larger kinetic energy relative to $\hbar\omega$ in that case. $N_{\rm ph}$ is constant on change of $U$ for S1 and unbound cases.