Pervasive spin-triplet superconductivity in rhombohedral graphene

TL;DR

The study demonstrates spin-triplet, field-induced superconductivity in rhombohedral graphene under strong in-plane magnetic fields, with critical fields far beyond the Pauli limit. A Ginzburg-Landau analysis of ferromagnetic half metals incorporating Kane-Mele SOC and Hund's coupling explains the gate-tunable competition between valley-balanced and valley-imbalanced ground states, predicting spin-canting and valley-imbalance regimes that couple to superconductivity. Transport reveals a nonmonotonic Tc(B_||) and a superconducting diode near IQAH regions, signaling intertwined spin, valley, and layer degrees of freedom. These findings reveal a robust, gate-tunable platform for spin-triplet superconductivity in thick rhombohedral graphene and point toward possible topological superconducting states adjacent to Chern insulators.

Abstract

Magnetic fields typically suppress superconductivity once the Zeeman energy exceeds the pairing gap, unless mechanisms such as unconventional pairing, strong spin-orbit coupling, or intrinsic magnetism intervene. Several graphene platforms realize such mitigating routes, exhibiting superconductivity resilient to magnetic fields. Here we report superconductivity in rhombohedral heptalayer graphene that is both induced and stabilized by in-plane magnetic field ($B_{\parallel}$), with critical fields far beyond the Pauli paramagnetic limit. The superconductivity spans a wide gate range and emerges from a sharp zero-field resistive ridge that tracks approximately constant conduction band filling. The presence of zero-field superconductivity and the evolution of the critical temperature with $B_{\parallel}$ are highly gate sensitive. We also observe a weak superconducting diode effect in several distinct regimes within the superconducting phase, including nearby to an integer quantum anomalous Hall state generated by a boron nitride moiré superlattice, indicating a potential coexistence of valley imbalance and superconductivity. These results establish several intriguing new properties of spin-triplet, field-induced superconductivity in a thick rhombohedral graphene stack.

Figures (28)

• Figure 1: Spin-triplet superconductivity in moiré R7G induced by $B_{\parallel}$.a, Schematic of the rhombohedral heptalayer graphene device with a $13.5$ nm moiré superlattice from alignment with the bottom hBN. b, Measurements of $\rho_{xx}$ versus $V_t$ at fixed $V_b=1.4$ V with $B_{\parallel}=0$ and $1$ T. c, Same with $V_b=2.1$ V d, Map of $\rho_{xx}$ versus $V_b$ and $V_t$ at zero field. Arrows denote the sharp resistive feature discussed in the text. Diagonal lines denote selected integer band filling factors, $\nu$. e, Same map at $B_{\parallel}=1$ T. f, Landau fan of $\rho_{xx}$ taken versus $V_t$ and $B_{\perp}$ with $B_{\parallel}=0$ and fixed $V_b=2.1$ V. g, Same measurement taken versus $B_{\parallel}$ at $B_{\perp}=0$. The black dashed lines in f and g are identical guides for the eye.
• Figure 1: Device image and $n-D$ maps.a, Optical micrograph of the R7G sample with source, drain and voltage probe contacts annotated. The scale bar is 10 $\mu$m. b, Map of $\rho_{xx}$ plotted as a function of $n-D$ axis (see Methods for conversion), taken at $B_{\parallel}=0$ T. c, same as (b) but taken at $B_{\parallel}=1$ T.
• Figure 1: Spin canting vs valley imbalance at $B_\parallel = 0$. Relative valley imbalance $\delta/S_0$ (left) and sum of the canting angles $\theta_\pm$ in the two valleys (right) as a function of the ratio $\gamma/\beta$ that captures tendency towards valley polarization. The spin-canted half metal is characterized by the condition $\theta_+ + \theta_- = \pi$. Results are obtained by numerically minimizing Eq. \ref{['eq:free_energy']}; numerical values of parameters used are mention in the text. The two gray vertical lines denote the onset of valley-imbalance in the cases with (at $\gamma/\beta = 1$) and without (at $\gamma/\beta = 1.4$) Kane-Mele SOC. Note that when $\lambda=0$ the canting angle (right panel) is ill-defined due to the SU(2) spin symmetry of the theory---we therefore did not include it.
• Figure 2: Nonlinearities associated with states along the sharp resistive bump.a, $\rho_{xx}$ versus $V_t$ and $T$ at $B_\parallel=1$ T and $V_b=-3$ V. b, $\rho_{xx}$ versus $V_t$ and $B_{\parallel}$ at $V_b=-3$ V. c, Selected traces from (b). d, d$V$/d$I$ versus $I_{dc}$ and $T$ at $B_\parallel=1$ T, $V_b=-3$ V and $V_t=-3$ V (black dashed line in (a)). e, d$V$/d$I$ versus $I_{dc}$ and $B_{\parallel}$ taken along the trajectory of the tilted black dashed line in b. f, Selected traces from (e). g, d$V$/d$I$ versus $V_t$ and $I_{dc}$ taken at $V_b=0$ V and $B_{\parallel}=0$ T. h, Same as (h) with $B_{\parallel}=1$ T.
• Figure 2: Extent of superconductivity at different $B_{\parallel}$. Maps of $\rho_{xx}$ versus $V_b$ and $V_t$ taken at a, $B_\parallel=0.5$ T, b, $1$ T, c, $1.5$ T, d, $2.5$ T, e, $4$ T, and f, $6$ T.