Extended Data Fig. 9: DFT calculations of the lattice structure, Fermi surfaces, and band structure for 12-bilayer bismuth. | Nature Materials

Extended Data Fig. 9: DFT calculations of the lattice structure, Fermi surfaces, and band structure for 12-bilayer bismuth.

From: Exceptional electronic transport and quantum oscillations in thin bismuth crystals grown inside van der Waals materials

Extended Data Fig. 9

a, Lattice structure of the bulk bismuth (111) for orientation aligned with the c-axis. The lattice constants are a = 4.57 Å, c = 11.75 Å and the Bi bond length is 3.10 Å. The intra-bilayer height is 1.63 Å and inter-bilayer spacing is 2.29 Å. b, Lattice structure of 12 bilayer bismuth with two (111) surfaces. After relaxation, the average of the intra bilayer height is 1.50 Å and inter bilayer spacing is 2.13 Å. c, The 2D first Brillouin zone of bismuth (111). d, Fermi surface at kz = 0, calculated using WannierTools47 with a dense 201 × 201 × 1 k mesh, based on the tight-binding Hamiltonian obtained by employing maximally localized Wannier functions (MLWFs) method using WANNIER9048 with initial projections to Bi-p orbitals. e, Band structure with Fermi surfaces at 0 eV. This plot is used as the basis of the Fermi surface schematic in Fig. 4f.

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