We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate.The degree of flatness can be tuned by varying the number of graphene layers N.For N = 7 the bands become nearly flat, with a small bandwidth ∼ 3.6 meV. 2019 Nov 8;123(19):196403. doi: 10.1103/PhysRevLett.123.196403. Many-body interactions and disorder 1968 3. In the present paper we have directly computed the Berry curvature terms relevant for graphene in the presence of an inhomogeneous lattice distortion. Abstract. At the end, our recipe was to first obtain a Dirac cone, add a mass term to it and finally to make this mass change sign. Following this recipe we were able to obtain chiral edge states without applying an external magnetic field. layer graphene and creates nite Berry curvature in the Moir e at bands [6, 33{35]. I. Inspired by this finding, we also study, by first-principles method, a concrete example of graphene with Fe atoms adsorbed on top, obtaining the same result. The surface represents the low energy bands of the bilayer graphene around the K valley and the colour of the surface indicates the magnitude of Berry curvature, which acts as a new information carrier. 74 the Berry curvature of graphene. Since the absolute magnitude of Berry curvature is approximately proportional to the square of inverse of bandgap, the large Berry curvature can be seen around K and K' points, where the massive Dirac point appears if we include spin-orbit interaction. 1 IF [1973-2019] - Institut Fourier [1973-2019] Berry curvature B(n) = −Im X n′6= n hn|∇ RH|n′i ×hn′|∇ RH|ni (E n −E n′)2 This form manifestly show that the Berry curvature is gaugeinvariant! A pre-requisite for the emergence of Berry curvature is either a broken inversion symmetry or a broken time-reversal symmetry. Institut für Physik, Ernst‐Moritz‐Arndt‐Universität Greifswald, 17487 Greifswald, Germany. 1 Instituut-Lorentz and !/ !t = −!e / ""E! Well defined for a closed path Stokes theorem Berry Curvature. Remarks i) The sum of the Berry curvatures of all eigenstates of a Hamiltonian is zero ii) if the eigenstates are degenerate, then the dynamics must be projected onto the degenerate subspace. Berry Curvature in Graphene: A New Approach. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. Example: The two-level system 1964 D. Berry phase in Bloch bands 1965 II. Berry curvature Magnetic field Berry connection Vector potential Geometric phase Aharonov-Bohm phase Chern number Dirac monopole Analogies. 1. E-mail: vozmediano@icmm.csic.es Abstract. Due to the nonzero Berry curvature, the strong electronic correlations in TBG can result in a quantum anomalous Hall state with net orbital magnetization [6, 25, 28{31, 33{35] and current-induced magnetization switching [28, 29, 36]. Our procedure is based on a reformulation of the Wigner formalism where the multiband particle-hole dynamics is described in terms of the Berry curvature. We have employed t @ idˆ p ⇥ @ j dˆ p. net Berry curvature ⌦ n(k)=⌦ n(k) ⌦ n(k)=⌦ n(k) Time reversal symmetry: Inversion symmetry: all on A site all on B site Symmetry constraints | pi Example: two-band model and “gapped” graphene. 4 and find nonvanishing elements χ xxy = χ xyx = χ yxx = − χ yyy ≡ χ, consistent with the point group symmetry. Onto the self-consistently converged ground state, we applied a constant and uniform static E field along the x direction (E = E 0 x ^ = 1.45 × 1 0 − 3 x ^ V/Å) and performed the time propagation. 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