Evidence of Momentum Space Condensation in Rhombohedral Hexalayer Graphene

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.

💡 Research Summary

This groundbreaking study provides the first experimental evidence for “momentum-space condensation,” a long-theorized quantum phenomenon, in rhombohedral hexalayer graphene (R6G). The research demonstrates the emergence of a novel electronic phase characterized by the simultaneous breaking of three fundamental symmetries: rotational (C3), time-reversal, and inversion symmetry.

The experiments were conducted on a dual-gated, hexagonal boron nitride (hBN)-encapsulated R6G device. Electronic transport measurements revealed a distinctive triangular region of high resistance near charge neutrality on the hole-doped side. To probe the nature of this state, the team employed advanced angle-resolved transport measurements using a specially designed disk-shaped “sunflower” device with eight contacts. By varying the direction of current flow and measuring longitudinal (R∥) and transverse (R⊥) resistances, they reconstructed the full conductivity tensor.

Key findings include: 1) Anisotropic Transport: A strong two-fold oscillation in resistance with current direction signifies electronic nematicity, i.e., spontaneous rotational symmetry breaking. 2) Anomalous Hall Effect (AHE): A non-zero average transverse resistance (R_H) at zero magnetic field signals time-reversal symmetry breaking due to orbital ferromagnetism. 3) Multiferroic Switching: Sweeping the perpendicular displacement field (D) triggers a hysteretic, “butterfly-shaped” reversal in both the sign of the AHE and the strength/direction of the anisotropy. This demonstrates coupled and electrically tunable magnetic and nematic orders—a hallmark of multiferroicity. 4) Two-Stage Phase Transition: Temperature-dependent measurements identified two transitions: a nematic transition at T_nem ≈ 2.1 K, where anisotropy diverges in a Curie-Weiss manner, and the onset of multiferroic hysteresis at T_multi ≈ 1.5 K. The AHE emerges near T_nem, indicating a common origin for both broken symmetries. 5) Nonlinear Hall Effect (NLHE): Measurements of the second-harmonic voltage response revealed a pronounced nonlinear Hall effect, whose angular dependence is consistent with broken inversion symmetry. Crucially, the NLHE emerges at the same temperature and follows the same displacement-field dependence as the AHE and anisotropy.

The co-emergence and intertwinement of these three symmetry-breaking orders—nematicity (from anisotropy), magnetism (from AHE), and inversion-symmetry breaking (from NLHE)—provide a definitive fingerprint for momentum-space condensation. This phenomenon arises from a Coulomb-driven “flocking instability” in systems with flat bands and trigonal warping, where electrons spontaneously condense into a single momentum-state pocket, generating a finite net momentum for the ground state.

This work not only confirms a major theoretical prediction but also establishes a unified framework for understanding the complex landscape of correlated phases—such as nematicity, ferromagnetism, and superconductivity—observed in various flat-band systems, including twisted bilayer graphene and other graphene multilayers. It highlights R6G as a pristine platform for exploring fundamental correlated electron physics and introduces powerful angle-resolved nonlinear transport techniques for future studies.