Magnetic-field-induced superconductivity in hexalayer rhombohedral graphene

Abstract

In conventional superconductors, superconductivity is generally suppressed by external magnetic fields due to spin-singlet pairing. Here, we report signatures of in-plane-magnetic-field-induced superconductivity in hexalayer rhombohedral graphene and reveal electric-field control of its depairing behavior. With the application of a small in-plane magnetic field $B_{\parallel}$, a superconducting state emerges within a narrow band along a phase boundary. Its properties evolve continuously with increasing $B_{\parallel}$: the superconducting region progressively shifts toward higher electric field as the $B_{\parallel}$ increases and the transition temperature rises with increasing $B_{\parallel}$. Remarkably, the superconducting state remains robust under $B_{\parallel}$ up to 14 T, far exceeding the conventional Pauli limit. Quantum oscillation measurements further reveal that the superconductivity emerges from nematic Fermi surface reconstruction. These results suggest a spin-polarized superconducting states with unconventional origins.

Figures (7)

• Figure 1: In-plane-field-induced superconductivity in rhombohedral hexalayer graphene. (a),(b) Color-coded $R_{xx}$ as a function of carrier density $n$ and electric field $E$ at zero field and at an in-plane magnetic field $B_{\parallel}=0.5~\mathrm{T}$. The dashed curves indicate the phase boundary from which superconductivity arises. SC1 and SC2 correspond to previously reported superconducting states in this system Deng2025SuperconductivityFerroelectricOrbital. SC3 denotes the superconducting phase observed in this work. The inset in panel (a) illustrates rhomhehdral hexalayer graphene under electric field and inplane magnetic field. (c) $B_{\parallel}$-dependent $R_{xx}$--$n$ line cuts at $E=0$. At this specific electric field, superconductivity arises with $B_{\parallel} \approx 0.07~\mathrm{T}$ and disappears above $B_{\parallel} \approx 1.2~\mathrm{T}$ (d) Temperature dependence of $R_{xx}$ vs $n$ at $B_{\parallel}=0.4~\mathrm{T}$. (e) Differential resistance $dV/dI$ at $E=0$ and $B_{\parallel}=0.4~\mathrm{T}$. (f) $dV/dI$ at $E=0$, $B_{\parallel}=0.4~\mathrm{T}$, and $n=-3.46 \times 10^{12}~\mathrm{cm}^{-2}$, measured below and above the transition temperature at $10~\mathrm{mK}$ and $150~\mathrm{mK}$, respectively.
• Figure 2: Tunable superconductivity controlled by in-plane magnetic field and electric field. (a) Schematic of the superconducting phase space under various in-plane magnetic field, constructed from a series of $n$--$E$--$R_{\mathrm{xx}}$ maps (see Supplemental Material). The inset shows schematic wave-function weight distributions in rhombohedral hexalayer graphene at zero and large $E$, where red and blue indicate localization near the top and bottom surfaces, respectively. (b,c) $n$--$E$--$R_{\mathrm{xx}}$ maps measured at $(T,~B_\parallel)$ = (20 mK, 10 T) and (300 mK, 10 T), respectively. (d) $R_{xx}$ vs $E$ and $B_{\parallel}$ measured at a fixed carrier density of $n = -6.57 \times 10^{12}~\mathrm{cm}^{-2}$. The position of this linecut in $n$-$E$ space is indicated by a vertical dashed line in (a). (e,f) Temperature-dependent differential resistance $dV/dI$ measured at $B_{\parallel} = 0$ and $B_{\parallel} = 10~\mathrm{T}$, respectively. 0 T data is measured at $E = 0$, $n=-3.46 \times 10^{12}~\mathrm{cm}^{-2}$, and $10~\mathrm{T}$ data is measured at $E = 124.4~\mathrm{mV/nm}$ and $n=-6.57 \times 10^{12}~\mathrm{cm}^{-2}$.
• Figure 3: Fermiology around the superconductivity. (a) $R_{xx}$–$n$–$E$ map at $B_{\parallel}=0.5~\mathrm{T}$. The black and orange dashed lines indicate the SdH measurement paths corresponding to panels (b) and Fig. 4, respectively. The red and green dots mark the locations of the SdH measurements shown in panels (f) and (g). (b) $R_{xx}$ as a function of carrier density $n$ and out-of-plane magnetic field $B_{\perp}$. (c) $R_{xx}$ versus carrier density $n$ at $B_{\perp}=0$ and in-plane magnetic field $B_{\parallel}=0.5~\mathrm{T}$, showing density range of superconductivity. (d), (e) FFT analysis of the quantum oscillations and the extracted peak frequencies at $E=0$. Distinct peaks $f_{\nu}$ are indicated by colored markers in panel (e). The corresponding sum-rule results are shown as gray markers and are divided by 2 for clarity. (f), (g) Top panels show schematic Fermi-surface contours for representative phases corresponding to the red and green markers in panel (a). The labels I and II correspond to the same labels in panel (e) and Fig. 4(b). In each schematic, four pockets represent an approximate fourfold degeneracy arising from spin ($\uparrow,\downarrow$) and valley ($K,K'$) degrees of freedom. Bottom panels show the FFT analysis of the quantum oscillations and the corresponding sum-rule calculations for the $(n,E)$ positions indicated by the red and green dots in panel (a).
• Figure 4: Dual-surface to single-surface nematic Fermi surface transition. (a) Linecut of carrier-density-normalized FFT from $R_{xx}$ as a function of $1/B_{\perp}$ along the orange dashed line in Fig. 3(a). (b) Sketch of the frequency peaks in (a). Inset shows schematic diagram of dual-surface and single-surface nematicity behavior in regions I and II, respectively
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