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Register a new userCollective resonances near zero energy induced by a point defect in bilayer graphene
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Intrinsic defects give rise to scattering processes governing the transport properties of mesoscopic systems. We investigate analytically and numerically the local density of states in Bernal stacking bilayer graphene with a point defect. With Bernal stacking structure, there are two types of lattice sites. One corresponds to connected sites, where carbon atoms from each layer stack on top of each other, and the other corresponds to disconnected sites. From our theoretical study, a picture emerges in which the pronounced zero-energy peak in the local density of states does not attribute to zero-energy impurity states associated to two different types of defects but to a collective phenomenon of the low-energy resonant states induced by the defect. To corroborate this description, we numerically show that at small system size $N$, where $N$ is the number of unit cells, the zero-energy peak near the defect scales as $1/ln N$ for the quasi-localized zero-energy state and as $1/N$ for the delocalized zero-energy state. As the system size approaches to the thermodynamic limit, the former zero-energy peak becomes a power-law singularity $1/|E|$ in low energies, while the latter is broadened into a Lorentzian shape. A striking point is that both types of zero-energy peaks decay as $1/r^2$ away from the defect, manifesting the quasi-localized character. Based on our results, we propose a general formula for the local density of states in low-energy and in real space. Our study sheds light on this fundamental problem of defects.
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It is generally believed that a point defect in graphene gives rise to an impurity state at zero energy and causes a sharp peak in the local density of states near the defect site. We revisit the defect problem in graphene and find the general consensus incorrect. By both analytic and numeric methods, we show that the contribution to the local density of states from the impurity state vanishes in the thermodynamic limit. Instead, the pronounced peak of the zero-bias anomaly is a power-law singularity $1/|E|$ from infinite resonant peaks in the low-energy regime induced by the defect. Our finding shows that the peak shall be viewed as a collective phenomenon rather than a single impurity state in previous studies.
Using scanning tunneling microscopy (STM) and Fourier Transform STM (FT-STM), we have studied a point defect in an epitaxial graphene sample grown on silicon carbide substrate. This analysis allows us to extract the quasiparticle energy dispersion, and to give a first experimental proof of the validity of Fermi liquid theory in graphene for a wide range of energies from -800 meV to +800 meV. We also find evidence of a strong threefold anisotropy in the standing waves generated by the defect. We discuss possible relations between this anisotropy, the chirality of the electrons, and the asymmetry between graphenes two sublattices. All experimental measurements are compared and related to theoretical T-matrix calculations.
The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high field regime, the eight-fold degeneracy in the zero energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding filling factors $ u=$0, 1, 2, & 3. Measurements of the activation energy gap in tilted magnetic fields suggest that the Landau level splitting at the newly formed $ u=$1, 2, & 3 filling factors are independent of spin, consistent with the formation of a quantum Hall ferromagnet. In addition, measurements taken at the $ u$ = 0 charge neutral point show that, similar to single layer graphene, the bilayer becomes insulating at high fields.
In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed11-16. Heterostrain, which is almost unavoidable in the TBG, can modify its single-particle band structure and lead to novel properties of the TBG that have never been considered so far. Here, we show that heterostrain in a TBG near the magic angle generates a new zero-energy flat band between the two VHSs. Doping the TBG to partially fill the zero-energy flat band, we observe a correlation-induced gap of about 10 meV that splits the flat band. By applying perpendicular magnetic fields, a large and linear response of the gap to magnetic fields is observed, attributing to the emergence of large orbital magnetic moments in the TBG when valley degeneracy of the flat band is lifted by electron-electron interactions. The orbital magnetic moment per moire supercell is measured as about 15 uB in the TBG.
Intrinsic Hall conductivity, emerging when chiral symmetry is broken, is at the heart of future low energy consumption devices because it can generate non-dissipative charge neutral current. A symmetry breaking state is also induced by electronic correlation even for the centro-symmetric crystalline materials. However, generation of non-dissipative charge neutral current by intrinsic Hall conductivity induced by such spontaneous symmetry breaking is experimentally elusive. Here we report intrinsic Hall conductivity and generation of a non-dissipative charge neutral current in a spontaneous antiferromagnetic state of zero Landau level of bilayer graphene, where spin and valley contrasting Hall conductivity has been theoretically predicted. We performed nonlocal transport experiment and found cubic scaling relationship between the local and nonlocal resistance, as a striking evidence of the intrinsic Hall effect. Observation of such spontaneous Hall transport is a milestone toward understanding the electronic correlation effect on the non-dissipative transport. Our result also paves a way toward electrical generation of a spin current in non-magnetic graphene via coupling of spin and valley in this symmetry breaking state combined with the valley Hall effect.
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