Extreme Anisotropy in the Metallic and Superconducting Phases of Rhombohedral Hexalayer Graphene

TL;DR

The study shows that rhombohedral hexalayer graphene hosts an electronically driven smectic (stripe) order that yields extreme transport anisotropy, with $R_{\max}/R_{\min}$ exceeding typical values and a superconducting phase emerging only along the easy axis. Using angle-resolved transport in sunflower devices across multiple samples, the authors extract a consistent resistivity tensor and identify a low-temperature regime where superconductivity coexists with strong anisotropy, accompanied by pronounced hysteresis and tunability tied to the underlying smectic order. The onset of smectic order occurs around $T \sim 1.5$ K, while a Curie-Weiss-like enhancement of anisotropy emerges at higher temperatures, pointing to a rich interplay between orbital magnetism, valley polarization, and electronic liquid-crystal orders. Together, these results provide new insights into how rotational symmetry breaking shapes unconventional superconductivity in rhombohedral graphene and demonstrate a powerful, tensor-based, angle-resolved transport framework for diagnosing anisotropic electronic phases.

Abstract

In strongly correlated electronic systems, Coulomb interactions frequently manifest through emergent electronic orders that spontaneously break rotational symmetry. Understanding how such symmetry breaking intertwines with other collective phenomena -- such as unconventional superconductivity -- and how it shapes experimental observables, particularly transport responses, remains a central challenge in modern condensed matter physics. Here, we report a metallic phase with extreme transport anisotropy in rhombohedral hexalayer graphene, with an anisotropy ratio rivaling that of quantum Hall stripe phases. At low temperature, a superconducting state emerges from this metallic phase. Strikingly, the superconductor not only inherits strong anisotropy but also exhibits a wide range of hysteretic transitions arising from the tunability of the underlying anisotropic order. Together, these findings reveal a previously unrecognized coexistence between superconductivity and extreme transport anisotropy, shedding new light on the role of rotational symmetry breaking in shaping unconventional superconductivity in rhombohedral graphene.

Figures (28)

• Figure 1: Extreme transport anisotropy in the low-temperature phase space of rhombohedral hexalayer graphene. (a) Schematic diagram of the R6G heterostructure. (b) Schematic diagram of the sunflower sample geometry with a disk-shaped channel and eight evenly spaced leads. (c) Color-scale map of the longitudinal resistance $R_{\parallel}$, measured at $T = 1.5\,\mathrm{K}$ and $B = 0$, along $\phi = 135^{\circ}$ (left) and $\phi = 45^{\circ}$ (right), shown as a function of carrier density $n$ and displacement field $D$. Inset: measurement configuration. (d) $R_{\parallel}$ measured along $\phi = 135^{\circ}$ (red trace) and $\phi = 45^{\circ}$ (blue trace) as a function of $D$ at $n = 0.45 \times 10^{12}\,\mathrm{cm}^{-2}$. Inset: logarithmic scale. (e) Ratio between the red and blue traces in panel (d). (f) $R$—$T$ curves measured along $\phi = 135^{\circ}$ (red trace) and $\phi = 45^{\circ}$ (blue trace) at $n = 0.34 \times 10^{12}\,\mathrm{cm}^{-2}$ and $D = 810\,\mathrm{mV/nm}$ (location marked by the open circle in panel (c)). Inset: logarithmic scale. (g) Ratio between the red and blue traces in panel (f).
• Figure 2: An extensive angle-resolved transport measurement. Angle-resolved transport measured from an extensive set of measurement configurations. The inset in each panel shows a schematic of the corresponding configuration. The black circles represent the measured response for each configuration at given values of $\phi$ (see Methods for a detailed discussion of the measurement procedures), while the black solid line denotes the expected angular dependence of each configuration, computed from a single conductivity matrix according to the theoretical framework of Ref. Vafek2023anisotropy. All measurements are performed at $T = 1.5\,\mathrm{K}$, $D = 850\,\mathrm{mV/nm}$, and $n = 0.31 \times 10^{12}\,\mathrm{cm}^{-2}$.
• Figure 3: Anisotropic superconducting transport and temperature-driven hysteresis. (a) Color-scale map of $R_{\parallel}$, measured at $T = 30\,\mathrm{mK}$ along $\phi = 135^{\circ}$ (left) and $\phi = 45^{\circ}$ (right), shown as a function of carrier density $n$ and displacement field $D$. Inset: measurement configuration. (b) Temperature dependence of $R_{\parallel}$ measured with current flowing along different directions. Inset: measurement configurations. (c--d) $R$--$T$ traces measured in alternative configurations distinct from $R_{\parallel}$. The observation of superconducting or insulating responses is solely determined by the alignment of voltage probes relative to the orientation of the easy axis. All measurements in panels (b--d) are performed at $n = 0.74 \times 10^{12}\,\mathrm{cm}^{-2}$ and $D = 954\,\mathrm{mV/nm}$, within the SC i region. (e--f) Temperature sweeps of (e) $R_{\parallel}$ and (f) $R_{\perp}$ measured continuously on warming (red) and cooling (blue), with current flowing along $\phi = 135^{\circ}$, which is perpendicular to the easy axis. (g) $R_{\parallel}$ as a function of temperature measured continuously on warming (red) and cooling (blue), with current flowing along the easy axis at $\phi = 45^{\circ}$. All measurements in panels (b--g) are performed at $n = 0.74 \times 10^{12}\,\mathrm{cm}^{-2}$ and $D = 954\,\mathrm{mV/nm}$, within the SC i region.
• Figure 4: Tunable hysteresis and nonlinear transport emerging at low temperature. (a) $R$--$T$ curves measured in the superconducting phase of the Hall-bar sample (HB1). The shaded red and blue traces correspond to continuous warming and cooling sweeps, respectively, whereas the black open circles are measured at the same $(n, D)$ point but with $n$ swept outside the anisotropy regime between consecutive temperature points. (b) $R$--$T$ curves measured in the superconducting phase of a sunflower sample (SF1). The shaded red and blue traces correspond to continuous warming and cooling sweeps, respectively, whereas the black open circles are measured at the same $(n, D)$ point but with the current applied along different directions between consecutive temperature points. (c) Differential resistance $dV/dI$ measured from SF1 as a function of d.c. current bias $I_{\mathrm{DC}}$ applied parallel (blue) and perpendicular (red) to the easy axis. (d) $R$--$T$ curves measured from HB1 under different d.c. current biases. Inset: logarithmic scale. Both panels (c) and (d) are measured in the anisotropic regime but outside the superconducting pocket. (e--f) $R_{\parallel}$ (top) and $R_{\perp}$ (bottom), measured from SF1 below the superconducting transition, as the out-of-plane magnetic field $B$ is swept back and forth, with current flowing parallel to the easy axis. The $(n, D)$ values associated with each measurement are indicated in the panels.
• Figure M1: Definition of $\phi$. Schematic of the angle-resolved transport measurement setup used to extract $R_{\parallel}$ in a sample shaped into the so-called "sunflower" geometry.