[Paper Review] Four-legged starfish-shaped Cooper pairs with ultrashort antinodal length scales in cuprate superconductors

Haoxiang Li, Xiaoqing Zhou+9 more|arXiv (Cornell University)|Sep 6, 2018

Physics of Superconductivity and Magnetism6 references4 citations

TL;DR

This study reveals that Cooper pairs in Bi₂Sr₂CaCu₂O₈₊δ exhibit a four-legged starfish shape, with an ultrashort antinodal length scale of ~4.5 Å—comparable to a lattice constant—using advanced ARPES-based reconstruction techniques. The persistence of this scale across doping levels suggests it is a fundamental property of the pairs, potentially linking to nematic order and charge/pair density fluctuations.

ABSTRACT

Cooper pairs of mutually attracting electrons form the building blocks of superconductivity. Thirty years after the discovery of high-temperature superconductivity in cuprates, many details of the pairs remain unknown, including their size and shape. Here we apply brand new ARPES-based methods that allow us to reconstruct the shape and size of the pairs in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The pairs are seen to form a characteristic starfish shape that is very long (>50Å) in the near-nodal direction but extremely short (~4.5Å) in the antinodal (Cu-O) direction. We find that this ultrashort antinodal length scale, which is of order a lattice constant, is approximately constant over a wide range of doping levels even as many other parameters including the pairing strength change. This suggests that this new length scale, along with the pair shape, is one of the most fundamental characteristics of the pairs. Further, the shape and ultrashort length scale should make the pairs create or intertwine with variations in charge and pair density, center on various types of lattice positions, and potentially explain aspects of the nematic order in these materials.

Motivation & Objective

• To determine the spatial shape and size of Cooper pairs in high-temperature cuprate superconductors, specifically Bi₂Sr₂CaCu₂O₈₊δ.
• To investigate whether the pair size and shape remain stable across varying doping levels despite changes in pairing strength.
• To explore the implications of the observed pair morphology for emergent electronic orders such as nematicity.
• To identify fundamental length scales in the pair wavefunction that may underlie unconventional superconducting behavior.

Proposed method

• Employing advanced angle-resolved photoemission spectroscopy (ARPES) combined with novel data analysis techniques to reconstruct the real-space shape of Cooper pairs.
• Using momentum-space mapping of quasiparticle excitations to infer the spatial structure of the pair wavefunction.
• Applying a theoretical framework that relates the measured spectral function to the spatial form of the Cooper pair wavefunction.
• Analyzing the anisotropy of the pair size by comparing near-nodal and antinodal directions in the Brillouin zone.
• Extracting the antinodal length scale by fitting the reconstructed pair shape to a starfish-like morphology with distinct radial extensions.
• Validating the robustness of the antinodal length scale across a range of doping levels using consistent analysis protocols.

Experimental results

Research questions

• RQ1 What is the spatial shape and size of Cooper pairs in Bi₂Sr₂CaCu₂O₈₊δ, as determined from ARPES data?
• RQ2 How does the antinodal length scale of the Cooper pairs vary with doping, and is it stable across different electronic phases?
• RQ3 Can the observed starfish-shaped pair wavefunction explain the emergence of nematic order in cuprates?
• RQ4 What is the physical significance of the ultrashort antinodal length scale (~4.5 Å) in relation to the crystal lattice and electronic correlations?
• RQ5 Is the antinodal length scale a fundamental parameter of the superconducting state, independent of pairing strength variations?

Key findings

• Cooper pairs in Bi₂Sr₂CaCu₂O₈₊δ adopt a four-legged starfish shape, extending over >50 Å in the near-nodal direction but confined to ~4.5 Å in the antinodal (Cu-O) direction.
• The antinodal length scale of ~4.5 Å is approximately constant across a wide range of doping levels, despite significant changes in pairing strength and other electronic parameters.
• This ultrashort antinodal length scale is on the order of a lattice constant, indicating a strong coupling to the underlying crystal structure.
• The persistence of this length scale suggests it is a fundamental property of the Cooper pair wavefunction, not a secondary effect.
• The starfish morphology implies that the pairs can create or couple to spatial modulations in charge and pair density, potentially explaining nematic order.
• The results indicate that the pair shape and its antinodal confinement are intrinsic to the superconducting state in cuprates, pointing to a deep connection with electronic inhomogeneity.