Evidence of Momentum Space Condensation in Rhombohedral Hexalayer Graphene

TL;DR

This work reports the experimental observation of momentum-space condensation in rhombohedral hexalayer graphene, manifested by simultaneous breaking of rotational, time-reversal, and inversion symmetries. Angle-resolved transport in a sunflower device reveals two-fold anisotropy and an orbital ferromagnetic contribution through a nonzero $R_H$, with hysteresis linking symmetry-breaking orders. The data connect transport anisotropy, anomalous Hall effects, and a nonlinear Hall response to momentum-space polarization, consistent with theoretical predictions for flat-band graphene. Fermiology analysis shows Fermi-surface reconstruction and multiple pockets that accompany the multiferroic state, establishing a framework for understanding intertwined orders in two-dimensional materials and offering electrical tunability of such phases.

Abstract

Spontaneous symmetry breaking provides a powerful window into the nature of underlying electronic orders. In strongly correlated systems, multiple symmetry-breaking orders can arise simultaneously. and their interplay generates an intricate landscape of quantum phases that has remained a central focus of condensed-matter research. In this work, we report a previously unidentified electronic phase in rhombohedral hexalayer graphene, distinguished by the simultaneous breaking of rotational, time-reversal, and inversion symmetries. Broken rotational symmetry is evidenced through anisotropic transport in angle-resolved measurements, while the onset of both the anomalous Hall effect and the nonlinear Hall effect signals the breaking of time-reversal and inversion symmetries. These combined signatures reveal an emergent order consistent with momentum-space condensation, a theoretically anticipated phenomenon realized here experimentally for the first time. This mechanism establishes a natural framework for understanding a broader class of correlated phases known to emerge from the flat bands of two-dimensional materials.

Figures (13)

• Figure 1: Rhombohedral-stacking hexalayer graphene and angle-resolved transport measurement. (a) Longitudinal resistance $R_{\parallel}$ as a function of carrier density $n$ and displacement field $D$ in a dual-encapsulated, dual-gated rhombohedral hexalayer graphene device. The inset shows a schematic diagram of the heterostructure. (b) Schematic of the angle-resolved transport measurement setup used to extract $R_{\parallel}$ (left) and $R_{\perp}$ (right) in a disk-shaped sample. (c) Angular dependence of $R_{\parallel}$ and $R_{\perp}$ inside the triangular multiferroic region, measured at $T = 40$ mK and $B = 0$ T. (d) $R_0$ and (e) $R_H$, extracted from the angular dependence using Eq. 1-2, measured as $B$ is swept back and forth.
• Figure 2: Multiferroicity and electric-field-driven switching of transport anisotropy. Parameters describing the angular dependence are extracted from the multiferroic regime. (a) $R_0$ and (b-c) $R_H$ extracted from angle-resolved transport measurements as a function of $n$ and $D$ around the multiferroic regime. $R_H$ exhibits a sign reversal as $D$ is swept (b) from positive to negative, and (c) from negative to positive. As $D$ is swept back and forth at $n = -0.82 \times 10^{12}$ cm$^{-2}$, the multiferroic order manifests in the electric-field-driven switching in (d) the anomalous Hall effect $R_H$, which is accompanied by the hysteretic behaviors in (e) $R_0$, (f) $\Delta R / R_0$, and (g) $\alpha$. (h-i) Angular dependence measured at $n = -0.82 \times 10^{12}$ cm$^{-2}$ and $D = 25$ mV/nm as $D$ is swept (h) backwards and (i) forward.
• Figure 3: Nematic phase transitions. (a-b) Temperature dependence of (a) the magnitude of the anomalous Hall coefficient $|R_H|$ and (b) the strength of transport anisotropy $\Delta R / R_0$. Upper right inset shows a zoomed in plot of $\Delta R / R_0$ around $T_{nem}$, where the dashed curve denote the best fit using the Curie-Weiss law. (c-e) Angular dependence of $R_{\parallel}$ and $R_{\perp}$ measured (c) in temperature regime i at $T = 10$ K, (d) in temperature regime ii at $T = 2.8$ K, and (e) in temperature regime iii at $T = 0.4$ K. (f-h) Anomalous Hall coeffecient $R_H$ measured with sweeping $D$ back and forth (f)) in temperature regime i at $T = 5$ K, (g) in temperature regime ii at $T = 3.5$ K, and (h) in temperature regime iii at $T = 40$ mK.
• Figure 4: Nonlinear Hall effect. Angular dependence of the second-harmonic nonlinear transport response (a) parallel ($V_{\parallel}^{2\omega}$) and (b) perpendicular ($V_{\perp}^{2\omega}$) to current flow, taken in the multiferroic regime. $\Delta V_{\perp}^{2\omega}$ denotes the angular oscillation in $V_{\perp}^{2\omega}$. (c) Angular dependence of linear transport response measured at the same $n$ and $D$ as panels (a) and (b). (d) $\Delta V_{\perp}^{2\omega}$ (top panel) and $|R_H|$ (bottom panel) measured as a function of $T$ at $D = 10$ mV/nm and $n=-0.58 \times 10^{12}$ cm$^{-2}$. (e) $\Delta V_{\perp}^{2\omega}$ (top panel) and $|R_H|$ (bottom panel) measured as a function of $D$ at $T = 3.5$ K and $n=-0.58 \times 10^{12}$ cm$^{-2}$. (f-g) The angular dependence of $V_{\perp}^{2\omega}$ measured at $n=-0.75\times 10^{12}$ cm$^{-2}$ and $D = -27$ mV/nm, with different sweeping directions in $D$.
• 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.