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Summary
Symmetries play a critical role in physical systems. The famous Noether's theorem states that a continuous symmetry of a system has a corresponding conserved physical quantity. For example, a physical system that is invariant in position and time must obey conservation of linear momentum and energy, respectively. The breaking of symmetries has equally important consequences—some examples being the Higgs boson, superconductivity, and ferromagnetism. Electrons in graphene, a monolayer sheet of hexagonally bonded carbon atoms, exhibit an approximate fourfold symmetry due to the two equivalent atoms per unit cell and spin degeneracy. The unusual electronic transport properties that result when a magnetic field is applied reflect these symmetries (1–3). The two layers of carbon atoms in bilayer graphene provide an extra degree of freedom, making it an even richer system for complex electronic states to emerge. Using different measurement techniques, a trio of studies in this issue—by Kou et al. (4) on page 55, Lee et al. (5) on page 58, and Maher et al. (6) on page 61—have elucidated the nature of these exotic broken-symmetry states.
