[Paper Review] Stabilizing fluctuating spin-triplet superconductivity in graphene via induced spin-orbit coupling

Jonathan B. Curtis, Nicholas R. Poniatowski+4 more|arXiv (Cornell University)|Sep 21, 2022

Graphene research and applications4 citations

TL;DR

This paper proposes that induced Ising spin-orbit coupling in bilayer graphene suppresses low-energy fluctuations of the spin-triplet superconducting order parameter by breaking spin-rotation symmetry, thereby stabilizing superconductivity at significantly higher critical temperatures. The mechanism explains the recent experimental observation of enhanced, zero-field spin-triplet superconductivity in WSe2-deposited bilayer graphene, with theoretical predictions matching observed Tc enhancement and suggesting a possible coexisting quasi-long-range ordered 4e charge superconducting phase.

ABSTRACT

A recent experiment showed that proximity induced Ising spin-orbit coupling enhances the spin-triplet superconductivity in Bernal bilayer graphene. Here, we show that, due to the nearly perfect spin rotation symmetry of graphene, the fluctuations of the spin orientation of the triplet order parameter suppress the superconducting transition to nearly zero temperature. Our analysis shows that both Ising spin-orbit coupling and in-plane magnetic field can eliminate these low-lying fluctuations and can greatly enhance the transition temperature, consistent with the recent experiment. Our model also suggests the possible existence of a phase at small anisotropy and magnetic field which exhibits quasi-long-range ordered spin-singlet charge 4e superconductivity, even while the triplet 2e superconducting order only exhibits short-ranged correlations. Finally, we discuss relevant experimental signatures.

Motivation & Objective

• To explain the experimental stabilization of spin-triplet superconductivity in bilayer graphene with WSe2 proximity layer, which induces Ising spin-orbit coupling.
• To address the theoretical challenge that fluctuating spin-triplet order parameters in graphene are suppressed by Goldstone modes due to near-perfect spin-rotation symmetry.
• To show that Ising spin-orbit coupling and in-plane magnetic fields suppress these fluctuations, thereby enhancing the superconducting transition temperature.
• To explore the possibility of a coexisting quasi-long-range ordered spin-singlet 4e superconducting phase in the presence of weak anisotropy and magnetic field.
• To provide experimentally testable signatures of the proposed mechanism, including spin susceptibility anomalies and critical behavior.

Proposed method

• Develops a symmetry-based effective field theory using Ginzburg-Landau formalism to describe spin-triplet superconductivity in graphene with broken spin-rotation symmetry.
• Models the induced Ising spin-orbit coupling as a Zeeman-like field in spin-valley space, which pins the d-vector of the triplet order parameter along the z-axis.
• Calculates the dimensionless pinning energy Γ⊥ using BCS theory, showing it increases by over two orders of magnitude with increasing λ.
• Analyzes the spin susceptibility χ∥, showing it diverges at zero spin-orbit coupling due to soft fluctuations, but is suppressed by finite Γ⊥.
• Uses experimental data from inverse compressibility measurements to estimate the density of states (~7 meV⁻¹Å⁻²) and Fermi energy (~0.6 meV) for quantitative parameterization.
• Considers the competition between 2e triplet and 4e singlet pairing channels, suggesting a possible phase with quasi-long-range order in the 4e channel despite short-range 2e correlations.

Experimental results

Research questions

• RQ1 How does induced Ising spin-orbit coupling stabilize fluctuating spin-triplet superconductivity in bilayer graphene?
• RQ2 Why does the superconducting transition temperature increase dramatically when WSe2 is added, even at zero magnetic field?
• RQ3 What is the role of spin-rotation symmetry breaking in suppressing Goldstone mode fluctuations of the triplet order parameter?
• RQ4 Can a quasi-long-range ordered 4e charge superconducting phase coexist with short-ranged 2e triplet pairing under weak anisotropy and magnetic field?
• RQ5 What are the experimentally observable signatures of the proposed mechanism, such as anomalies in spin susceptibility or critical behavior?

Key findings

• Induced Ising spin-orbit coupling suppresses low-energy fluctuations of the spin-triplet order parameter by pinning the d-vector along the z-axis, thereby stabilizing superconductivity.
• The dimensionless pinning energy Γ⊥ increases by over two orders of magnitude with increasing induced spin-orbit coupling strength λ, as confirmed by BCS calculations.
• The spin susceptibility χ∥ diverges at zero spin-orbit coupling due to soft fluctuations, but is suppressed by finite Γ⊥, which restores mean-field-like behavior.
• The critical temperature is significantly enhanced by both Ising spin-orbit coupling and in-plane magnetic fields, consistent with experimental observations of Tc enhancement by an order of magnitude.
• A phase with quasi-long-range order in 4e charge superconductivity may coexist with short-ranged 2e triplet pairing under small anisotropy and magnetic field, suggesting a novel competing channel.
• The model predicts an anomalous, apparent upturn in spin susceptibility at T*, which could serve as an experimental signature of fluctuating triplet order.