[Paper Review] Superconductivity and spin canting in spin-orbit proximitized rhombohedral trilayer graphene

Caitlin L. Patterson, Owen Sheekey+16 more|arXiv (Cornell University)|Aug 19, 2024

Graphene research and applicationsMaterials Science3 citations

TL;DR

This study demonstrates that spin-orbit coupling induced via substrate proximity in rhombohedral trilayer graphene (RTG) enhances superconductivity, with critical temperatures reaching ~300 mK—three times higher than in BN-encapsulated RTG. The enhancement arises not from symmetry changes but from a spin-canting transition driven by competition between spin-orbit coupling and Hund’s interaction, as confirmed by Hartree-Fock calculations and magnetometry, linking superconductivity to fluctuations in canted spin order.

ABSTRACT

Graphene and transition metal dichalcogenide flat-band systems show similar phase diagrams, replete with magnetic and superconducting phases. An abiding question has been whether magnetic ordering competes with superconductivity or facilitates pairing. The advent of crystalline graphene superconductors enables a new generation of controlled experiments to probe the microscopic origin of superconductivity. For example, recent studies of Bernal bilayer graphene show a dramatic increase in the observed domain and critical temperature $T_c$ of superconducting states in the presence of enhanced spin-orbit coupling; the mechanism for this enhancement, however, remains unclear. Here, we show that introducing spin-orbit coupling in rhombohedral trilayer graphene (RTG) via substrate proximity effect generates new superconducting pockets for both electron and hole doping, with maximal $T_c\approx$ 300mK three times larger than in RTG encapsulated by hexagonal boron nitride alone. Using local magnetometry and thermodynamic compressibility measurements, we show that superconductivity straddles an apparently continuous transition between a spin-canted state with a finite in-plane magnetic moment and a state with complete spin-valley locking. This transition is reproduced in our Hartree-Fock calculations, where it is driven by the competition between spin-orbit coupling and the carrier-density-tuned Hund's interaction. Our experiment suggests that the enhancement of superconductivity by spin-orbit coupling is driven not by a change in the ground state symmetry or degeneracy but rather by a quantitative change in the canting angle. These results align with a recently proposed mechanism for the enhancement of superconductivity in spin-orbit coupled rhombohedral multilayers, in which fluctuations in the spin-canting order contribute to the pairing interaction.

Motivation & Objective

• To understand how spin-orbit coupling enhances superconductivity in rhombohedral trilayer graphene (RTG).
• To determine whether magnetic order competes with or facilitates superconducting pairing in RTG.
• To investigate the role of spin-canting and spin-valley locking in mediating superconducting pairing.
• To establish a microscopic mechanism linking spin-orbit coupling and enhanced $T_c$ in flat-band RTG systems.

Proposed method

• Used local magnetometry and thermodynamic compressibility measurements to probe spin and superconducting order parameters.
• Performed Hartree-Fock calculations to model the competition between spin-orbit coupling ($\lambda$) and Hund’s exchange ($J_H$).
• Applied a Ginzburg-Landau free energy formalism to describe spin-canting and spin-valley locking transitions.
• Defined the canting angle $\varphi = \arccos(\lambda / (2J_H n_p))$ as a function of polarization density $n_p$.
• Extracted the canting angle from Hartree-Fock expectation values $\varphi = \arctan|\langle \tau^0 s^x \rangle / \langle \tau^z s^z \rangle|$.
• Mapped the phase diagram in $\Delta_1$-$n_e$ space to identify transitions between spin-valley-locked and canted states.

Figure 1: Superconductivity in WSe 2 -supported rhombohedral trilayer graphene. (a) Schematic of a RTG device encapsulated between hBN and WSe 2 flakes. (b) $n_{e}$ - and $D$ -dependent inverse compressibility ( $\kappa=\partial\mu/\partial n$ ) at $B=0$ T and $T=20$ mK for Device A1. Both the overa

Experimental results

Research questions

• RQ1 How does spin-orbit coupling from substrate proximity affect superconductivity in rhombohedral trilayer graphene?
• RQ2 Does the enhancement of $T_c$ arise from symmetry changes or from a quantitative modification of spin order?
• RQ3 What is the role of spin canting in mediating superconducting pairing in spin-orbit-coupled RTG?
• RQ4 How does the competition between spin-orbit coupling and Hund’s interaction govern the transition between spin-valley-locked and canted magnetic states?
• RQ5 Is the observed superconductivity correlated with fluctuations in the spin-canting order parameter?

Key findings

• Superconductivity in spin-orbit-proximitized RTG reaches a maximal critical temperature of $T_c \approx 300$ mK, three times higher than in BN-encapsulated RTG.
• The superconducting phase coexists with a continuous transition between a spin-canted state (with in-plane magnetic moment) and a spin-valley-locked state.
• The spin-canting transition is driven by the competition between spin-orbit coupling ($\lambda$) and Hund’s exchange ($J_H$), with the canting angle $\varphi = \arccos(\lambda / (2J_H n_p))$ determining the magnetic order.
• Hartree-Fock simulations reproduce the experimentally observed phase diagram, confirming that spin canting emerges when $n_p \sim \lambda / J_H$.
• The enhancement of superconductivity is not due to a change in ground state symmetry or degeneracy, but rather to a quantitative shift in the canting angle.
• The results support a recently proposed mechanism where spin-canting fluctuations contribute to the pairing interaction in spin-orbit-coupled multilayers.

Figure 2: Magnetic imaging of symmetry broken states in rhombohedral trilayer graphene. (a) Magnetic signal $\delta B_{V}$ in response to a modulation of the bottom gate voltage (see Methods), plotted as a function of $n_{\textrm{e}}$ and $D$ at a single point above Device B1. (b) Same measurement a