The discovery of magic-angle graphene moiré systems has unlocked a wide variety of intriguing emergent phenomena. Inside the nearly dispersionless band structures, the combination of isospin symmetry breaking and strong correlation gives rise to an intricate landscape of emergent quantum phases, such as superconductivity and orbital ferromagnetism. The subtle interplay between the flat moiré band and strong Coulomb interaction provides an ideal venue for exploring novel electronic orders. For instance, a recent experiment reported a prominent zero-field superconducting diode effect in twisted trilayer graphene, revealing a new type of symmetry breaking order [1]. The nonreciprocal superconducting transport behavior, evidenced by the direction-dependence in the critical current points towards spontaneous breaking of both parity and time-reversal symmetry in the superconducting state, which motivates our search for a parity-breaking electronic order in metallic states of graphene-based moiré systems.

Such an electronic order can be identified based on highly nonreciprocal, diode-like current-voltage characteristics throughout the moiré flatband, which exhibits a one-fold or three-fold symmetric angular dependence as a function of the azimuth direction of current flow (Figure 1). We show that this parity-breaking order can be described as a valley-polarized loop current state, which is highly tunable with magnetic field, current flow, and field-effect doping. Our findings point towards the universal presence of valley-polarized isospin order and rotational symmetry breaking across the moiré flatband, with important implications for understanding intertwined and competing orders, such as ferromagnetism, nematicity, and superconductivity, in graphene-based moiré systems.

[1] Lin, J-X. et al. Zero-field superconducting diode effect in small-twist-angle trilayer graphene. Nature Physics, in press (2022).

We performed atomic-scale scanning tunneling microscopy (STM) of a cleaved highly oriented pyrolytic graphite [1]. Together with a (√3×√3)R30° phase (Fig. 1(c)), a unique rectangular-like lattice (Fig. 1(d)) was resolved on a graphene nanosheet at a sample bias (V_s) of -0.05 V. To clarify the origin of this rectangular lattice, we conducted first-principles calculations [2] based on density functional theory and obtained simulated STM images of armchair-edged graphene nanoribbons (AGNRs) with different widths. In terms of the ribbon width (Fig. 2(a)), W is defined as the number of dimer lines across the ribbon width [3]. To avoid inaccuracies in the Fermi level, we used the sum of the electron density of orbitals in [ε_HOMO+eV_s, ε_HOMO] for a negative sample bias, where ε_HOMO indicates the energy level of the highest occupied molecular orbitals (HOMO). The band structure was magnified in Fig. 2(c). V₁ and V₂ denote different energy levels at k=0. Fig. 2(d) shows simulated STM images at both sample bias of V₁ and V₂. At the lower sample bias (V₁), we find a rectangular superstructure similar to our experimental results [1]. The other image at V₂ indicates the ring-like shapes within the AGNR, which is in good agreement with the hexagonal lattice of graphene.