[Paper Review] Superlight bipolarons and criterion of BCS-BEC crossover in cuprates

A. S. Alexandrov|arXiv (Cornell University)|Jan 28, 2003

Physics of Superconductivity and Magnetism7 references3 citations

TL;DR

This paper proposes that high-temperature superconductivity in cuprates arises from superlight, real-space singlet and triplet bipolarons formed via long-range electron-phonon (Froehlich) interactions, stabilized by long-range Coulomb repulsion. It establishes a new criterion for the BCS-BEC crossover—$ϵ_F \lesssim \pi\Delta$—showing that real-space pairing dominates in many cuprates, contradicting collective pairing models.

ABSTRACT

Most of the proposed models of high-temperature superconductivity (HTSC) are based on the short-range electron-electron correlations or/and on a short-range electron-phonon interaction. However, in the cuprates the screening is poor due to a low carrier density, layered crystal structure, and high ionicity of the lattice. We develop further the bipolaron model of HTSC, which explicitly takes into account the long-range origin of all interactions. The long-range electron-phonon (Froehlich) interaction binds carriers into real space pairs (small bipolarons) with surprisingly low mass but sufficient binding energy, while the long-range Coulomb repulsion keeps them from forming larger clusters. The model has explained many key features of cuprates. Here it is shown that real-space pairing takes place in many cuprates at variance with some (incorrect) criteria of the BCS-BEC crossover.

Motivation & Objective

• To resolve the long-standing debate on whether pairing in cuprates is real-space (bipolaronic) or momentum-space (BCS-like) by providing a parameter-free criterion for the BCS-BEC crossover.
• To challenge the prevailing view that pairing in cuprates is collective and Fermi-surface-based, arguing instead for preformed, spatially localized bosons.
• To demonstrate that the observed pseudogap and superconducting transition temperature in cuprates are consistent with a Bose-Einstein condensation of small bipolarons.
• To reconcile experimental data—such as isotope effects, tunneling, and penetration depth—within a unified bipolaron model that accounts for both strong electron-phonon coupling and Coulomb repulsion.

Proposed method

• Derives a parameter-free expression for the renormalized Fermi energy in quasi-2D cuprates using the in-plane magnetic penetration depth: $\epsilon_F = \frac{\hbar^2 d c^2}{4ge^2\lambda_H^2}$, where $\lambda_H$ is the penetration depth.
• Uses the parabolic band approximation to relate the Fermi energy $\epsilon_F$ to the effective mass $m^\ast$ and hole density $n_i$ in each subband.
• Defines the condition for real-space pairing as $\epsilon_F \lesssim \pi\Delta$, where $\Delta$ is the bipolaron binding energy, derived from comparing pair size $\rho \sim \hbar/\sqrt{m^\ast\Delta}$ and inter-pair separation $r \sim \hbar\sqrt{\pi/(\epsilon_F m^\ast)}$.
• Applies the theorem of equal carrier numbers in normal and superconducting states to refute models with a large Fermi surface and distinguish between preformed bosons and Cooper pairs.
• Uses experimental values of the pseudogap ($\Delta/2 \gtrsim 50$ meV) to estimate $\Delta \gtrsim 100$ meV and confirms $\epsilon_F \lesssim \pi\Delta$ holds in underdoped and some optimally doped cuprates.
• Argues that the coherence length in a charged Bose gas is not related to the size of the boson, correcting a common misconception used in previous crossover criteria.

Experimental results

Research questions

• RQ1 Is real-space pairing via small bipolarons the correct mechanism for high-$T_c$ superconductivity in cuprates, rather than BCS-like Cooper pairing in momentum space?
• RQ2 What is the correct criterion for the BCS-BEC crossover in cuprates, given the limitations of using the ratio of coherence length to intercarrier distance?
• RQ3 Can the Fermi energy in cuprates be estimated without band-structure parameters, using only the magnetic penetration depth and experimental data?
• RQ4 Why is the conventional assumption of a large Fermi surface with $1+x$ holes incompatible with thermodynamic and kinetic measurements in cuprates?
• RQ5 How does the interplay between long-range electron-phonon interaction and long-range Coulomb repulsion stabilize small, light bipolarons without clustering?

Key findings

• The parameter-free estimate of the Fermi energy using the magnetic penetration depth yields $\epsilon_F \lesssim 100$ meV in many cuprates, supporting the dominance of real-space pairing.
• The condition $\epsilon_F \lesssim \pi\Delta$ is satisfied in underdoped and some optimally doped cuprates, confirming that real-space pairing occurs.
• The bipolaron binding energy $\Delta$ is approximately twice the experimentally measured pseudogap, with $\Delta/2 \gtrsim 50$ meV in many cuprates.
• The coherence length in a charged Bose gas is not a measure of the boson size, invalidating the use of $\xi / r$ as a crossover criterion.
• The model explains the pseudogap and $T_c$ without requiring a large Fermi surface, contradicting the preformed Cooper pair scenario with a large normal-state Fermi surface.
• The effective mass of the bipolarons is only about 10 times the electron mass, enabling high mobility despite strong electron-phonon coupling.