[Paper Review] Spin and Charge Fluctuation Induced Pairing in ABCB Tetralayer Graphene

Ammon Fischer, Lennart Klebl+6 more|arXiv (Cornell University)|May 23, 2023

Graphene research and applicationsMaterials Science51 references3 citations

TL;DR

This study investigates superconductivity in ABCB-stacked tetralayer graphene using orbital-resolved random phase approximation (RPA) to analyze spin and charge fluctuations from realistic short- and long-ranged Coulomb interactions. It identifies f-wave spin-triplet, valley-singlet superconductivity driven by spin fluctuations near van Hove singularities, and p-wave superconductivity from charge fluctuations, with both mechanisms coexisting at the conduction band edge, highlighting competition between interaction types in determining superconducting pairing symmetry.

ABSTRACT

Motivated by the recent experimental realization of ABCB stacked tetralayer graphene [Wirth et al., ACS Nano 16, 16617 (2022)], we study correlated phenomena in moiré-less graphene tetralayers for realistic interaction profiles using an orbital resolved random phase approximation approach. We demonstrate that magnetic fluctuations originating from local interactions are crucial close to the van Hove singularities on the electron- and hole-doped side promoting layer selective ferrimagnetic states. Spin fluctuations around these magnetic states enhance unconventional spin-triplet, valley-singlet superconductivity with $f$-wave symmetry due to intervalley scattering. Charge fluctuations arising from long range Coulomb interactions promote doubly degenerate p-wave superconductivity close to the van Hove singularities. At the conduction band edge of ABCB graphene, we find that both spin and charge fluctuations drive $f$-wave superconductivity. Our analysis suggests a strong competition between superconducting states emerging from long- and short-ranged Coulomb interactions and thus stresses the importance of microscopically derived interaction profiles to make reliable predictions for the origin of superconductivity in graphene based heterostructures.

Motivation & Objective

• To understand the origin of superconductivity in untwisted ABCB tetralayer graphene, where moiré effects are absent and correlation effects are governed by intrinsic electronic structure.
• To address the limitations of effective models by employing an ab initio-motivated, orbital-resolved RPA approach that consistently includes both short- and long-ranged Coulomb interactions.
• To disentangle the roles of spin fluctuations (from local interactions) and charge fluctuations (from long-range Coulomb interactions) in driving unconventional superconductivity.
• To determine how competing pairing mechanisms—favored by spin fluctuations and p-wave by charge fluctuations—affect the leading superconducting order parameter near van Hove singularities.
• To assess the robustness of superconducting instabilities under temperature and screening variations, particularly near the conduction band edge and van Hove singularities.

Proposed method

• Employing a modified Slonzevecki-Weiss-McClure tight-binding model to describe the atomistic electronic band structure of ABCB tetralayer graphene, consistent with first-principles calculations.
• Applying orbital-resolved random phase approximation (RPA) to compute particle-hole and particle-particle susceptibilities, enabling a systematic analysis of spin and charge fluctuations.
• Using three distinct RPA variants: x-RPA (local Hubbard U only), d-RPA (screened long-range Coulomb interaction), and xd-RPA (combined short- and long-ranged interactions) to isolate contributions.
• Projecting the effective pairing vertex from orbital to band space, focusing on scattering between Cooper pairs on distinct Fermi surface patches to identify dominant pairing symmetries.
• Setting Fermi surface cutoffs at μ_min = -5 meV and μ_max = -2 meV to isolate hole-doped regimes near van Hove singularities, ensuring consistency with thermal broadening (η_FS > T).
• Analyzing the superconducting coupling constant λ_SC as a function of chemical potential, Hubbard U, screening length d, and temperature T to assess stability and symmetry of superconducting states.

Experimental results

Research questions

• RQ1 What is the role of spin fluctuations from local interactions in driving superconductivity in ABCB tetralayer graphene near van Hove singularities?
• RQ2 How do long-range Coulomb interactions, via charge fluctuations, contribute to superconducting pairing, and what symmetry does it favor?
• RQ3 What is the interplay between spin- and charge-fluctuation-mediated pairing mechanisms in determining the leading superconducting order parameter?
• RQ4 How robust are the predicted superconducting instabilities to changes in temperature and screening length?
• RQ5 Which pairing symmetry—f-wave or p-wave—dominates at the conduction band edge, and what determines the competition between them?

Key findings

• Near the van Hove singularities on the hole-doped side, spin fluctuations from local interactions promote layer-selective ferrimagnetic order and enhance f-wave spin-triplet, valley-singlet superconductivity via intervalley scattering.
• Charge fluctuations arising from long-range Coulomb interactions drive doubly degenerate p-wave superconductivity near the same van Hove singularities.
• At the conduction band edge, both spin and charge fluctuations coexist in driving f-wave superconductivity, indicating a strong competition between pairing mechanisms.
• The superconducting coupling constant λ_SC remains robust under variations in screening length (from d = 200a₀ to d = 50a₀), indicating that long-range tail screening does not suppress the instability.
• Temperature dependence shows that λ_SC increases at lower temperatures, particularly in the d-RPA channel, and that the f-wave channel is suppressed at high U (e.g., U = 4.5 eV) when the Stoner criterion is approached.
• The xd-RPA approach confirms that both spin- and charge-fluctuation contributions are essential for a complete description, with the combined mechanism preserving the leading f-wave symmetry at the conduction band edge.