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Knowing degeneracy and exact nature of brokensymmetry states of a system is a central problem in physics. It also plays a vital role in understanding electronic properties of materials. Owing to the 2D nature of graphene's structure and electrons, it is convenient to measure the degeneracy and exotic broken-symmetry states of graphene through a magneto-transport measurement of quantum Hall effect (QHE) [1][2][3][4][5][6][7]. As schematically shown in figures 1(a) and (b), it is expected to observe quantum Hall conductance plateaus at values 4(n + 1/2)e 2 /h in pristine graphene without electron-electron interaction (n is integer, e is electron, and h is Planck's constant). Here four directly reflects the four-fold, including double-spin and double-valley, degeneracy of graphene. If the degeneracy of graphene is lifted and broken-symmetry states emerge, there should be new QHE plateau not at the values 4(n + 1/2)e 2 /h (figure 1(b) shows one of the simplest case: the valley degeneracy is lifted in the zeroth Landau level) [4][5][6][7]. Therefore, the QHE provides a quite powerful method in detecting the degeneracy and broken-symmetry states of a system. However, the magneto-transport measurement lacks spatial resolution that limits its application at nanoscale. Atomic defects, such as single carbon vacancy [8] and adatoms [9], are almost unavoidable in graphene. An individual atomic defect could locally break the equivalence of two sublattices, which is expected to lift the degeneracies of graphene at nanoscale [10][11][12][13][14][15]. However, measuring the degeneracy and broken-symmetry electronic states around the atomic defects requires nanometerscale spatial resolution, which is a key challenge to probe these interesting properties, leaving them unexplored in experiment up to now. Here, we realize the measurement of the broken-symmetry states of graphene at the nanoscale. Large valley-dependent spin splitting are directly detected around the atomic defects of graphene at the single-electron level.In our experiment, the measurement is realized by using a recently developed edge-free graphene quant um dots (QDs) [16,17], which can be generated by a combination of electrostatic and magnetic fields, as schematically shown in figures 1(c) and (d). The magnetic fields quantize the continuous electronic spectrum of graphene into discrete Landau levels (LLs). The probing scanning tunneling microscopy (STM) tip, acting as a moveable top gate in the measurement [18][19][20][21][22], shifts quasiparticles in the region beneath the tip into the gaps between the LLs of the

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The interplay between interlayer van der Waals interaction and intralayerlattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle θ c . Experimentally, the θ c is demonstrated to be very close to the magic angle (θ ≈ 1.05°). In this work, we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunnelling microscopy (STM). Our experiment demonstrates that both the two structures are stable in the TBG around the magic angle. By applying a STM tip pulse, we show that the two structures can be switched to each other and the bandwidth of the flat bands, which plays a vital role in the emergent strongly correlated states in the magic-angle TBG, can be tuned. The observed tunable lattice reconstruction and bandwidth of the flat bands provide an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle.

A remarkable property of twisted bilayer graphene (TBG) with small twist angle is the presence of a well-defined and conserved low-energy valley degrees of freedom 1 , which can potentially bring about new types of valley-associated spontaneous-symmetry breaking phases. Electron-electron (e-e) interactions in the TBG near the magic angle ~ 1.1º can lift the valley degeneracy, allowing for the realization of orbital magnetism and topological phases 2-11 . However, direct measurement of the orbital-based magnetism in the TBG is still lacking up to now. Here we report evidence for orbital magnetic moment generated by the moiréscale current loops in a TBG with a twist angle θ ~ 1.68º . The valley degeneracy of the 1.68º TBG is removed by e-e interactions when its low-energy van Hove singularity (VHS) is nearly half filled. A large and linear response of the valley splitting to magnetic fields is observed, attributing to coupling to the large orbital magnetic moment induced by chiral current loops circulating in the moiré pattern.According to our experiment, the orbital magnetic moment is about 10.7 B per moiré supercell. Our result paves the way to explore magnetism that is purely orbital in slightly twisted graphene system.