Fig. 2: 3D Landau levels in an inhomogeneous anisotropic diamond lattice.
From: Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal
a Cubic cell of the anisotropic diamond lattice. The cubic cell has side length a. Red and blue bonds denote nearest-neighbor couplings t and \(t{\prime}=1\), respectively, and nearest-neighbor sites are separated by the vectors δi(i = 1, 2, 3, 4). The Cartesian coordinate axes are xi(i = 1, 2, 3), such that x3 is parallel to −δ1, and x2 is parallel to −δ3 + δ4. b Schematic of the first Brillouin zone. The reciprocal lattice vectors ki(i = 1, 2, 3) are oriented along LK, LW, and ΓL, respectively. c Shapes of the nodal ring for various t. d Projections of the nodal ring onto the k1−k2 plane, for the values of t used in (c). e and f Local density of states in the k2 direction for B = 0 (e) and B = 0.0073a−2 (f), calculated using a 600-site chain. Solid white lines in f represent the analytically predicted Landau levels. g Wavefunction amplitude of the zeroth Landau level at \(\left({k}_{1},{k}_{2}\right)=\left(0,0.70\pi /a\right)\).
