[Paper Review] Twist-Programmable Superconductivity in Spin-Orbit Coupled Bilayer Graphene

Yiran Zhang, Gal Shavit+9 more|arXiv (Cornell University)|Aug 19, 2024

Graphene research and applications4 citations

TL;DR

This study demonstrates twist-programmable superconductivity in spin-orbit coupled bilayer graphene by tuning the relative twist angle between graphene and tungsten diselenide (WSe₂), which controls the strength of induced Ising spin-orbit coupling (SOC). As SOC increases, superconductivity emerges at higher displacement fields and reaches a critical temperature of up to 0.5 K, with enhanced resilience to in-plane magnetic fields and evidence of nematic hole redistribution among trigonally warped Fermi pockets.

ABSTRACT

The relative twist angle between layers of near-lattice-matched van der Waals materials is critical for the emergent correlated phenomena associated with moire flat bands. However, the concept of angle rotation control is not exclusive to moiré superlattices in which electrons directly experience a twist-angle-dependent periodic potential. Instead, it can also be employed to induce programmable symmetry-breaking perturbations with the goal of stabilizing desired correlated states. Here, we experimentally demonstrate `moireless' twist-tuning of superconductivity together with other correlated orders in Bernal bilayer graphene proximitized by tungsten diselenide. The alignment between the two materials systematically controls the strength of the induced Ising spin-orbit coupling (SOC), profoundly altering the phase diagram. As Ising SOC is increased, superconductivity onsets at a higher displacement field and features a higher critical temperature, reaching up to 0.5K. Within the main superconducting dome and in the strong Ising SOC limit, we find an unusual phase transition characterized by a nematic redistribution of holes among trigonally warped Fermi pockets and enhanced resilience to in-plane magnetic fields. The behavior of the superconducting phase is well captured by our theoretical model, which emphasizes the role of interband interactions between Fermi pockets arising due to interaction-enhanced symmetry breaking. Moreover, we identify two additional superconducting regions, one of which descends from an inter-valley coherent normal state and exhibits a Pauli-limit violation ratio exceeding 40, among the highest for all known superconductors. Our results provide new insights into ultra-clean graphene-based superconductors and underscore the potential of utilizing moireless-twist engineering across a range of van der Waals heterostructures.

Motivation & Objective

• To explore the role of spin-orbit coupling (SOC) in tuning superconductivity and correlated states in bilayer graphene (BLG) without relying on moiré superlattices.
• To experimentally demonstrate that the relative twist angle between BLG and WSe₂ can be used as a precise tuning knob for controlling Ising SOC strength.
• To investigate how induced SOC modifies the superconducting phase diagram, including critical temperature, magnetic field resilience, and Fermi surface reconstruction.
• To identify and characterize multiple superconducting phases, including one with extreme Pauli-limit violation.
• To establish a moiréless twist-engineering platform for ultra-clean, highly tunable superconductors in van der Waals heterostructures.

Proposed method

• Fabricated BLG-WSe₂ heterostructures by mechanically exfoliating and sequentially twisting BLG flakes relative to a fixed WSe₂ substrate with ~6° increments.
• Used high-resolution Shubnikov–de Haas oscillations to measure Fermi surface anisotropy and quantify the degree of hole-pockets imbalance due to Ising SOC.
• Applied a strong displacement field (D ≈ 0.2 V/nm) to maximize Ising SOC by polarizing hole wavefunctions toward the WSe₂-adjacent layer.
• Employed a theoretical model based on the BCS-Bardeen-Cooper-Schrieffer (BCS) framework with spin-orbit and Zeeman coupling to describe the suppression of Tc by in-plane magnetic fields.
• Calculated the coefficient α in the Tc(B) = Tc,0 − αB² dependence to analyze magnetic field resilience, incorporating interband interactions and symmetry-breaking effects.
• Used self-consistent Hartree-Fock calculations to explore nematic Fermi surface reconstruction under magnetic fields, testing the validity of the 'flocking' model.

Figure 1: Programmable Ising SOC by interfacial twisting between BLG and WSe 2 . a , Schematic showing the twisting of the BLG-WSe 2 interface; tuning the interfacial twist angle $\theta$ between the two largely lattice-mismatched materials modifies the Ising SOC strength $|\lambda_{I}|$ and the cor

Experimental results

Research questions

• RQ1 How does the relative twist angle between BLG and WSe₂ control the strength of induced Ising spin-orbit coupling in the absence of a moiré potential?
• RQ2 What is the impact of increasing Ising SOC on the onset field and critical temperature of superconductivity in BLG?
• RQ3 Does enhanced Ising SOC lead to a nematic phase transition involving hole redistribution among trigonally warped Fermi pockets?
• RQ4 Can the superconducting state survive strong in-plane magnetic fields, and what mechanisms underlie its enhanced resilience?
• RQ5 What is the origin of the Pauli-limit violation exceeding 40 in one of the superconducting phases, and how does it relate to inter-valley coherence?

Key findings

• The critical temperature of superconductivity increases to a maximum of 0.5 K as Ising spin-orbit coupling is enhanced via twist-angle tuning.
• Superconductivity emerges at higher displacement fields with increasing Ising SOC, indicating a strong stabilization effect from spin-orbit coupling.
• A nematic phase transition is observed within the main superconducting dome, characterized by a redistribution of holes among three trigonally warped Fermi pockets.
• The superconducting state exhibits exceptional resilience to in-plane magnetic fields, with a Tc suppression consistent with Tc(B) = Tc,0 − αB² and α ≈ 0.1 K/T².
• An additional superconducting region is identified that descends from an inter-valley coherent normal state, showing a Pauli-limit violation ratio exceeding 40 — among the highest reported for any superconductor.
• Theoretical modeling confirms that interband interactions due to interaction-enhanced symmetry breaking are essential for explaining the observed phase diagram and magnetic field resilience.

Figure 2: Twist-programmable superconducting phase diagram. a – d , $R_{xx}$ versus doping density $n$ and displacement field $D$ for devices with Ising strength $|\lambda_{I}|\approx 0.4$ meV ( a ), $0.9$ meV ( b ), $1.4$ meV ( c ), and $1.5$ meV ( d ), respectively. e , Optimal superconducting cri