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Bilayer graphene (BLG) has multiple internal degrees of freedom and a constant density of states down to the charge neutrality point when trigonal warping is ignored. Consequently, it is susceptible to various competing ground states. However, a coherent experimental determination of the ground state has been challenging due to the interaction-disorder interplay. Here we present an extensive transport study in a series of dually gated freestanding BLG devices and identify the layer-antiferromagnet as the ground state with a continuous strength across all devices. This strength correlates with the width of the state in the electric field. We systematically identify electric-field disorder─spatial variations in the interlayer potential difference─as the main source responsible for the observations. Our results pinpoint for the first time the importance of electric-field disorder on spontaneous symmetry breaking in BLG and solve a long-standing debate on its ground state. The electric-field disorder should be universal to all 2D materials.

An established way of realising topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene intriguingly, even in the absence of a magnetic field, topologically protected electronic states can emerge at naturally occurring stacking domain walls. While individually both types of topologically protected states have been investigated, their intriguing interplay remains poorly understood. Here, we focus on the interplay between topological domain wall states and quantum Hall edge transport within the eight-fold degenerate zeroth Landau level of high-quality suspended bilayer graphene. We find that the two-terminal conductance remains approximately constant for low magnetic fields throughout the distinct quantum Hall states since the conduction channels are traded between domain wall and device edges. For high magnetic fields, however, we observe evidence of transport suppression at the domain wall, which can be attributed to the emergence of spectral minigaps. This indicates that stacking domain walls potentially do not correspond to a topological domain wall in the order parameter.

Bernal-stacked multilayer graphene is a versatile platform to explore quantum transport phenomena and interaction physics due to its exceptional tunability via electrostatic gating. For instance, upon applying a perpendicular electric field, its band structure exhibits several off-center Dirac points (so-called Dirac gullies) in each valley. Here, the formation of Dirac gullies and the interaction-induced breakdown of gully coherence is explored via magnetotransport measurements in high-quality Bernal-stacked (ABA) trilayer graphene. In the absence of a magnetic field, multiple Lifshitz transitions as function of electric field and charge carrier density indicating the formation of Dirac gullies are identified. In the quantum Hall regime and high electric fields, the emergence of Dirac gullies is evident as an increase in Landau level degeneracy. When tuning both electric and magnetic fields, electron-electron interactions can be controllably enhanced until the gully degeneracy is eventually lifted. The arising correlated ground state is consistent with a previously predicted nematic phase that spontaneously breaks the rotational gully symmetry.

Miniaturization of electronic circuits increases their overall performance. So far, electronics based on organic semiconductors has not played an important role in the miniaturization race. Here, we show the fabrication of liquid electrolyte gated vertical organic field effect transistors with channel lengths down to 2.4 nm. These ultrashort channel lengths are enabled by using insulating hexagonal boron nitride with atomically precise thickness and flatness as a spacer separating the vertically aligned source and drain electrodes. The transistors reveal promising electrical characteristics with output current densities of up to 2.95 MA cm-2 at -0.4 V bias, on-off ratios of up to 106, a steep subthreshold swing of down to 65 mV dec-1 and a transconductance of up to 714 S m-1. Realizing channel lengths in the sub-5 nm regime and operation voltages down to 100 μV proves the potential of organic semiconductors for future highly integrated or low power electronics.

The quantum anomalous Hall (QAH) effect-a macroscopic manifestation of chiral band topology at zero magnetic field-has been experimentally realized only by the magnetic doping of topological insulators

The quantum anomalous Hall (QAH) effect—a macroscopic manifestation of chiral band topology at zero magnetic field—has been experimentally realized only by the magnetic doping of topological insulators1–3 and the delicate design of moire heterostructures4–8. However, the seemingly simple bilayer graphene without magnetic doping or moire engineering has long been predicted to host competing ordered states with QAH effects9–11. Here we explore states in bilayer graphene with a conductance of 2 e2 h−1 (where e is the electronic charge and h is Planck’s constant) that not only survive down to anomalously small magnetic fields and up to temperatures of five kelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin–valley Hall behaviour9. Bilayer graphene states are observed at anomalously small magnetic fields and show magnetic hysteresis, providing evidence for a quantum anomalous Hall effect driven by orbital magnetism.