Strain-induced Landau Levels in arbitrary dimensions with an exact spectrum

Abstract

Certain non-uniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudo-magnetic field for electrons near the Dirac points. However, this Landau level structure is in general approximate and restricted to low energies. Here we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d=3 our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d.

arXiv comment5 + 9 pages; v4: final version including references to hyperdiamond lattices

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• Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal
• Magnon Landau levels and emergent supersymmetry in strained antiferromagnets
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Impurity bound states as detectors of topological band structures revisited
• Synthetic Landau levels and spinor vortex matter on Haldane spherical surface with magnetic monopole
• Unification of valley and anomalous Hall effects in a strained lattice
• Landau levels in curved space realized in strained graphene
• Ideal flat and resolved SU(3) Landau levels in three dimensions
• Three-dimensional valley-contrasting sound
• Strain tuning of highly frustrated magnets: Order and disorder in the distorted kagome Heisenberg antiferromagnet
• Programmable Kondo Effect Formed by Landau Levels
• Pseudo-magnetic fields in square lattices
• Nodal semimetals in $d\ge 3$ to sharp pseudo-Landau levels by dimensional reduction
• Relativistic Mechanism of Chiral Magnetic Current in Weyl Semimetals with Tilted Dispersion
• Flux-induced midgap states between strain-engineered flat bands