[Paper Review] Nematicity and Orbital Depairing in Superconducting Bernal Bilayer Graphene with Strong Spin Orbit Coupling

Ludwig Holleis, Caitlin L. Patterson+9 more|arXiv (Cornell University)|Mar 1, 2023

Graphene research and applications64 references21 citations

TL;DR

The paper reports two superconducting states (SC1 and SC2) in Bernal bilayer graphene on WSe2 with proximity-induced Ising SOC, where SC2 arises from a nematic normal state; both states are robust to in-plane fields and violate the paramagnetic limit, linking enhanced superconductivity to Ising SOC.

ABSTRACT

Superconductivity (SC) is a ubiquitous feature of graphite allotropes, having been observed in Bernal bilayers[1], rhombohedral trilayers[2], and a wide variety of angle-misaligned multilayers[3-6]. Despite significant differences in the electronic structure across these systems, supporting the graphite layer on a WSe$_2$ substrate has been consistently observed to expand the range of SC in carrier density and temperature[7-10]. Here, we report the observation of two distinct superconducting states (denoted SC$_1$ and SC$_2$) in Bernal bilayer graphene with strong proximity-induced Ising spin-orbit coupling. Quantum oscillations show that while the normal state of SC$_1$ is consistent with the single-particle band structure, SC$_2$ emerges from a nematic normal state with broken rotational symmetry. Both superconductors are robust to in-plane magnetic fields, violating the paramagnetic limit; however, neither reach fields expected for spin-valley locked Ising superconductors. We use our knowledge of the Fermi surface geometry of SC$_1$ to argue that superconductivity is limited by orbital depairing arising from the imperfect layer polarization of the electron wavefunctions. Finally, a comparative analysis of transport and thermodynamic compressibility measurements in SC$_2$ shows that the proximity to the observed isospin phase boundaries, observed in other rhombohedral graphene allotropes, is likely coincidental, constraining theories of unconventional superconducting pairing mechanisms in theses systems.

Motivation & Objective

• Investigate how proximity-induced Ising spin-orbit coupling (SOC) affects superconductivity in Bernal bilayer graphene (BBG) on WSe2.
• Identify and characterize distinct superconducting states (SC1 and SC2) and their normal-state fermiology.
• Determine the role of nematic order in the emergence of SC2 and its impact on superconductivity.
• Quantify the enhancement of superconductivity and its field dependence under Ising SOC.
• Assess how SOC influences resilience to in-plane magnetic fields and the paramagnetic limit.

Proposed method

• Use a tight-binding band structure model including Ising SOC to interpret the low-energy electronic structure.
• Measure electrical transport and quantum oscillations (Shubnikov–de Haas) to map Fermi-surface topology and validate Luttinger sum rules.
• Determine proximity-induced Ising SOC strength (λI) via Landau level coincidences.
• Analyze superconducting transitions using nonlinear transport and Berezinskii–Kosterlitz–Thouless (BKT) fits to extract Tc and TBKT.
• Test in-plane field dependence of Tc against the Ising-SOC-predicted scaling Tc/Tc0 = 1 − B_parallel^2/(B_SO B_P).
• Compare superconductivity in BBG/WSe2 to crystalline graphene without SOC by simultaneously measuring resistance and inverse compressibility κ.

Figure 1: Superconductivity in Bernal bilayer graphene (BBG) on WSe 2 . (A) Sample schematic showing dual gated BBG on WSe 2 . (B) Band structure calculated within a tight binding model including Ising SOC. Bands correspond to the different isospin flavors as indicated. Here $a_{0}$ = 2.46 Åis the g

Experimental results

Research questions

• RQ1 Does BBG on WSe2 host multiple superconducting states under Ising SOC?
• RQ2 What is the nature of the normal state from which SC1 and SC2 condensate, and does nematic order participate?
• RQ3 How does Ising SOC influence the robustness of superconductivity to in-plane magnetic fields and the paramagnetic limit?
• RQ4 Can fermiology changes and nematicity be linked to enhanced superconductivity in these systems?
• RQ5 Is the scaling of Tc with in-plane field consistent with Ising superconductivity across different densities and displacement fields?

Key findings

• Two distinct superconducting states, SC1 and SC2, appear in hole-doped BBG/WSe2 at large displacement fields; Tc for SC1 is ~40 mK, while SC2 reaches a higher Tc with a Berezinskii–Kosterlitz–Thouless temperature TBKT ≈ 255 mK.
• SC2 arises from a nematic normal state (N2,4) with broken rotational symmetry, as evidenced by the evolution of quantum oscillation frequencies and Luttinger-sum-rule analysis.
• Both SC1 and SC2 are robust to in-plane magnetic fields and violate the paramagnetic limit, consistent with Ising spin-orbit–coupled superconductivity; Tc scales with in-plane field following a law involving B_SO and B_P.
• The measured Ising SOC strength is λI ≈ 1.6 meV, and the Fermi-surface topology in the presence of SOC explains the observed Landau level coincidences and multiple oscillation frequencies (fν) that satisfy generalized Luttinger sum rules.
• SC2’s field dependence collapses onto a universal scaling η = Tc/(1 − B_parallel^2/(B_SO B_P)), indicating pairing occurs between spin-defined Fermi surfaces and supporting spin-valley locking as a mechanism for Ising superconductivity.
• A comparison to graphene systems without proximity SOC shows superconductivity in BBG/WSe2 is enhanced and not solely tied to isospin transitions, implicating SOC-induced stabilization of nematic orders as a route to higher Tc.

Figure 2: Fermiology of the superconducting states in the presence of Ising SOC. (A) R xx at $D$ = 0.95 V/nm, including the domain of SC 1 . (B) Fourier transform of $R_{xx}(1/B_{\perp})$ over the same density range. The Fourier transforms are performed over a field range of 130 - 400 mT and 130 - 2